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Solution
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Q.1 Correct
Q.1 In-correct
Q.1 Unattempt

The least count of a screw guage is 0.01 mm . If the pitch is increased by $75 \%$ and number of divisions on the circular scale is reduced by $50 \%$, the new least count will be ________ $\times 10^{-3} \mathrm{~mm}$



JEE Main 2025 (Online) 24th January Morning Shift

The least count of a screw guage is 0.01 mm . If the pitch is increased by $75 \%$ and number of divisions on the circular scale is reduced by $50 \%$, the new least count will be ________ $\times 10^{-3} \mathrm{~mm}$



JEE Main 2025 (Online) 24th January Morning Shift
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt

A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm , respectively. Using a specially designed screw gauge which has pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be $\frac{x}{100}$ where $x$ is _______ .



JEE Main 2025 (Online) 28th January Morning Shift

A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm , respectively. Using a specially designed screw gauge which has pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be $\frac{x}{100}$ where $x$ is _______ .



JEE Main 2025 (Online) 28th January Morning Shift
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt

Q is related to four observables a,b,c,d as follows : 

Q=ab4cd

where, a=(60±3)Pa;b=(20±0.1)m;c=(40±0.2)Nsm−2 and d=(50±0.1)m, then the percentage error in Q is x1000, where x= _________ .



JEE Main 2025 (Online) 29th January Evening Shift

Q is related to four observables a,b,c,d as follows : 

Q=ab4cd

where, a=(60±3)Pa;b=(20±0.1)m;c=(40±0.2)Nsm−2 and d=(50±0.1)m, then the percentage error in Q is x1000, where x= _________ .



JEE Main 2025 (Online) 29th January Evening Shift
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt

A physical quantity C is related to four other quantities $\mathrm{p}, \mathrm{q}, \mathrm{r}$ and s as follows

$$ C=\frac{p q^2}{r^3 \sqrt{s}} $$

The percentage errors in the measurement of $\mathrm{p}, \mathrm{q}, \mathrm{r}$ and s are $1 \%, 2 \%, 3 \%$ and $2 \%$, respectively. The percentage error in the measurement of $C$ will be__________%



JEE Main 2025 (Online) 3rd April Evening Shift

A physical quantity C is related to four other quantities $\mathrm{p}, \mathrm{q}, \mathrm{r}$ and s as follows

$$ C=\frac{p q^2}{r^3 \sqrt{s}} $$

The percentage errors in the measurement of $\mathrm{p}, \mathrm{q}, \mathrm{r}$ and s are $1 \%, 2 \%, 3 \%$ and $2 \%$, respectively. The percentage error in the measurement of $C$ will be__________%



JEE Main 2025 (Online) 3rd April Evening Shift
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt

Given below are two statements :

Statement I: In a vernier callipers, one vernier scale division is always smaller than one main scale division.

Statement II : The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions.

In the light of the above statements, choose the correct answer from the options given below.



JEE Main 2025 (Online) 22nd January Morning Shift

Given below are two statements :

Statement I: In a vernier callipers, one vernier scale division is always smaller than one main scale division.

Statement II : The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions.

In the light of the above statements, choose the correct answer from the options given below.



JEE Main 2025 (Online) 22nd January Morning Shift
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt

If $B$ is magnetic field and $\mu_0$ is permeability of free space, then the dimensions of $\left(B / \mu_0\right)$ is



JEE Main 2025 (Online) 22nd January Morning Shift

If $B$ is magnetic field and $\mu_0$ is permeability of free space, then the dimensions of $\left(B / \mu_0\right)$ is



JEE Main 2025 (Online) 22nd January Morning Shift
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt

The maximum percentage error in the measurment of density of a wire is

[Given, mass of wire $=(0.60 \pm 0.003) \mathrm{g}$

radius of wire $=(0.50 \pm 0.01) \mathrm{cm}$

length of wire $=(10.00 \pm 0.05) \mathrm{cm}]$



JEE Main 2025 (Online) 22nd January Evening Shift

The maximum percentage error in the measurment of density of a wire is

[Given, mass of wire $=(0.60 \pm 0.003) \mathrm{g}$

radius of wire $=(0.50 \pm 0.01) \mathrm{cm}$

length of wire $=(10.00 \pm 0.05) \mathrm{cm}]$



JEE Main 2025 (Online) 22nd January Evening Shift
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt

The position of a particle moving on $x$-axis is given by $x(t)=A \sin t+B \cos ^2 t+C t^2+D$, where $t$ is time. The dimension of $\frac{A B C}{D}$ is



JEE Main 2025 (Online) 23rd January Morning Shift

The position of a particle moving on $x$-axis is given by $x(t)=A \sin t+B \cos ^2 t+C t^2+D$, where $t$ is time. The dimension of $\frac{A B C}{D}$ is



JEE Main 2025 (Online) 23rd January Morning Shift
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt

Match List - I with List - II

List - I List - II
(A) Permeability of free space (I) $\left[\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-2}\right]$
(B) Magnetic field (II) $\left[\mathrm{M} \mathrm{T}^{-2} \mathrm{~A}^{-1}\right]$
(C) Magnetic moment (III) $\left[\mathrm{M} \mathrm{L} \mathrm{T}^{-2} \mathrm{~A}^{-2}\right]$
(D) Torsional constant (IV) $\left[\mathrm{L}^2 \mathrm{~A}\right]$

Choose the correct answer from the options given below :



JEE Main 2025 (Online) 23rd January Evening Shift

Match List - I with List - II

List - I List - II
(A) Permeability of free space (I) $\left[\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-2}\right]$
(B) Magnetic field (II) $\left[\mathrm{M} \mathrm{T}^{-2} \mathrm{~A}^{-1}\right]$
(C) Magnetic moment (III) $\left[\mathrm{M} \mathrm{L} \mathrm{T}^{-2} \mathrm{~A}^{-2}\right]$
(D) Torsional constant (IV) $\left[\mathrm{L}^2 \mathrm{~A}\right]$

Choose the correct answer from the options given below :



JEE Main 2025 (Online) 23rd January Evening Shift
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt
The energy of a system is given as $\mathrm{E}(\mathrm{t})=\alpha^3 \mathrm{e}^{-\beta t}$, where t is the time and $\beta=0.3 \mathrm{~s}^{-1}$. The errors in the measurement of $\alpha$ and $t$ are $1.2 \%$ and $1.6 \%$, respectively. At $t=5 \mathrm{~s}$, maximum percentage error in the energy is :

JEE Main 2025 (Online) 23rd January Evening Shift
The energy of a system is given as $\mathrm{E}(\mathrm{t})=\alpha^3 \mathrm{e}^{-\beta t}$, where t is the time and $\beta=0.3 \mathrm{~s}^{-1}$. The errors in the measurement of $\alpha$ and $t$ are $1.2 \%$ and $1.6 \%$, respectively. At $t=5 \mathrm{~s}$, maximum percentage error in the energy is :

JEE Main 2025 (Online) 23rd January Evening Shift
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt

For an experimental expression $y=\frac{32.3 \times 1125}{27.4}$, where all the digits are significant. Then to report the value of $y$ we should write



JEE Main 2025 (Online) 24th January Morning Shift

For an experimental expression $y=\frac{32.3 \times 1125}{27.4}$, where all the digits are significant. Then to report the value of $y$ we should write



JEE Main 2025 (Online) 24th January Morning Shift
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt

Match List - I with List - II.

List - I List - II
(A) Angular Impulse (I) M0 L2 T-2
(B) Latent Heat (II) M L2 T-3 A-1
(C) Electrical resistivity (III) M L2 T-1
(D) Electromotive force (IV) M L3 T-3 A-2

Choose the correct answer from the options given below:



JEE Main 2025 (Online) 28th January Evening Shift

Match List - I with List - II.

List - I List - II
(A) Angular Impulse (I) M0 L2 T-2
(B) Latent Heat (II) M L2 T-3 A-1
(C) Electrical resistivity (III) M L2 T-1
(D) Electromotive force (IV) M L3 T-3 A-2

Choose the correct answer from the options given below:



JEE Main 2025 (Online) 28th January Evening Shift
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt

The expression given below shows the variation of velocity (v) with time (t),

$v=\mathrm{At}^2+\frac{\mathrm{Bt}}{\mathrm{C}+\mathrm{t}}$.

The dimension of ABC is :



JEE Main 2025 (Online) 29th January Morning Shift

The expression given below shows the variation of velocity (v) with time (t),

$v=\mathrm{At}^2+\frac{\mathrm{Bt}}{\mathrm{C}+\mathrm{t}}$.

The dimension of ABC is :



JEE Main 2025 (Online) 29th January Morning Shift
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt

The pair of physical quantities not having the same dimensions is :



JEE Main 2025 (Online) 29th January Morning Shift

The pair of physical quantities not having the same dimensions is :



JEE Main 2025 (Online) 29th January Morning Shift
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt

Match List - I with List - II.

List - I List - II
(A) Young’s Modulus (I) M L-1 T-1
(B) Torque (II) M L-1 T-2
(C) Coefficient of Viscosity (III) M-1 L3 T-2
(D) Gravitational Constant (IV) M L2 T-2

Choose the correct answer from the options given below :



JEE Main 2025 (Online) 29th January Evening Shift

Match List - I with List - II.

List - I List - II
(A) Young’s Modulus (I) M L-1 T-1
(B) Torque (II) M L-1 T-2
(C) Coefficient of Viscosity (III) M-1 L3 T-2
(D) Gravitational Constant (IV) M L2 T-2

Choose the correct answer from the options given below :



JEE Main 2025 (Online) 29th January Evening Shift
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt

Match List I with List II.

List - I List - II
(A) Coefficient of viscosity (I) $\left[\mathrm{ML}^0 \mathrm{~T}^{-3}\right]$
(B) Intensity of wave (II) $\left[\mathrm{ML}^{-2} \mathrm{~T}^{-2}\right]$
(C) Pressure gradient (III) $\left[\mathrm{M}^{-1} \mathrm{LT}^2\right]$
(D) Compressibility (IV) $\left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right]$

Choose the correct answer from the options given below:



JEE Main 2025 (Online) 2nd April Morning Shift

Match List I with List II.

List - I List - II
(A) Coefficient of viscosity (I) $\left[\mathrm{ML}^0 \mathrm{~T}^{-3}\right]$
(B) Intensity of wave (II) $\left[\mathrm{ML}^{-2} \mathrm{~T}^{-2}\right]$
(C) Pressure gradient (III) $\left[\mathrm{M}^{-1} \mathrm{LT}^2\right]$
(D) Compressibility (IV) $\left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right]$

Choose the correct answer from the options given below:



JEE Main 2025 (Online) 2nd April Morning Shift
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt
Given a charge q , current I and permeability of vacuum $\mu_{\mathrm{o}^*}$. Which of the following quantity has the dimension of momentum ?

JEE Main 2025 (Online) 2nd April Evening Shift
Given a charge q , current I and permeability of vacuum $\mu_{\mathrm{o}^*}$. Which of the following quantity has the dimension of momentum ?

JEE Main 2025 (Online) 2nd April Evening Shift
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt
If $\mu_0$ and $\epsilon_0$ are the permeability and permittivity of free space, respectively, then the dimension of $\left(\frac{1}{\mu_0 \epsilon_0}\right)$ is :

JEE Main 2025 (Online) 2nd April Evening Shift
If $\mu_0$ and $\epsilon_0$ are the permeability and permittivity of free space, respectively, then the dimension of $\left(\frac{1}{\mu_0 \epsilon_0}\right)$ is :

JEE Main 2025 (Online) 2nd April Evening Shift
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt

A person measures mass of 3 different particles as $435.42 \mathrm{~g}, 226.3 \mathrm{~g}$ and 0.125 g . According to the rules for arithmetic operations with significant figures, the addition of the masses of 3 particles will be.



JEE Main 2025 (Online) 3rd April Morning Shift

A person measures mass of 3 different particles as $435.42 \mathrm{~g}, 226.3 \mathrm{~g}$ and 0.125 g . According to the rules for arithmetic operations with significant figures, the addition of the masses of 3 particles will be.



JEE Main 2025 (Online) 3rd April Morning Shift
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt

 Match the LIST-I with LIST-II  Match the LIST-I with LIST-II 

LIST-I LIST-II
A.  Boltzmann constant  Boltzmann constant  I  ML2 T−1
B  Coefficient of viscosity  Coefficient of viscosity  II  MLT−3 K−1
C  Planck's constant  Planck's constant  III   ML2 T−2 K−1
D  Thermal conductivity  Thermal conductivity  IV  ML−1 T−1

Choose the correct answer from the options given below:

JEE Main 2025 (Online) 3rd April Evening Shift

 Match the LIST-I with LIST-II  Match the LIST-I with LIST-II 

LIST-I LIST-II
A.  Boltzmann constant  Boltzmann constant  I  ML2 T−1
B  Coefficient of viscosity  Coefficient of viscosity  II  MLT−3 K−1
C  Planck's constant  Planck's constant  III   ML2 T−2 K−1
D  Thermal conductivity  Thermal conductivity  IV  ML−1 T−1

Choose the correct answer from the options given below:

JEE Main 2025 (Online) 3rd April Evening Shift
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt

In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of $M^P L^Q T^R A^S$, where value of ' $Q$ ' and ' $R$ ' are



JEE Main 2025 (Online) 4th April Morning Shift

In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of $M^P L^Q T^R A^S$, where value of ' $Q$ ' and ' $R$ ' are



JEE Main 2025 (Online) 4th April Morning Shift
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt

For the determination of refractive index of glass slab, a travelling microscope is used whose main scale contains 300 equal divisions equals to 15 cm . The vernier scale attached to the microscope has 25 divisions equals to 24 divisions of main scale. The least count (LC) of the travelling microscope is (in cm ) :



JEE Main 2025 (Online) 4th April Evening Shift

For the determination of refractive index of glass slab, a travelling microscope is used whose main scale contains 300 equal divisions equals to 15 cm . The vernier scale attached to the microscope has 25 divisions equals to 24 divisions of main scale. The least count (LC) of the travelling microscope is (in cm ) :



JEE Main 2025 (Online) 4th April Evening Shift
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt

In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of $\left[\mathrm{M}^{\mathrm{P}} \mathrm{L}^{\mathrm{Q}} \mathrm{T}^R A^{\mathrm{S}}\right]$. The value of P and Q are :



JEE Main 2025 (Online) 4th April Evening Shift

In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of $\left[\mathrm{M}^{\mathrm{P}} \mathrm{L}^{\mathrm{Q}} \mathrm{T}^R A^{\mathrm{S}}\right]$. The value of P and Q are :



JEE Main 2025 (Online) 4th April Evening Shift
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt

Match List - I with List - II.

List - I List - II
(A) Mass density (I) [ML2T−3]
(B) Impulse (II) [MLT−1]
(C) Power (III) [ML2T0]
(D) Moment of inertia (IV) [ML−3T0]

Choose the correct answer from the options given below :



JEE Main 2025 (Online) 7th April Evening Shift

Match List - I with List - II.

List - I List - II
(A) Mass density (I) [ML2T−3]
(B) Impulse (II) [MLT−1]
(C) Power (III) [ML2T0]
(D) Moment of inertia (IV) [ML−3T0]

Choose the correct answer from the options given below :



JEE Main 2025 (Online) 7th April Evening Shift
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt

The dimension of $ \sqrt{\frac{\mu_0}{\epsilon_0}} $ is equal to that of:

($ \mu_0 $ = Vacuum permeability and $ \epsilon_0 $ = Vacuum permittivity)



JEE Main 2025 (Online) 7th April Evening Shift

The dimension of $ \sqrt{\frac{\mu_0}{\epsilon_0}} $ is equal to that of:

($ \mu_0 $ = Vacuum permeability and $ \epsilon_0 $ = Vacuum permittivity)



JEE Main 2025 (Online) 7th April Evening Shift
Q.26 Correct
Q.26 In-correct
Q.26 Unattempt

A quantity Q is formulated as $X^{-2}Y^{+\frac{3}{2}}Z^{-\frac{2}{5}}$. X, Y, and Z are independent parameters which have fractional errors of 0.1, 0.2, and 0.5, respectively in measurement. The maximum fractional error of Q is



JEE Main 2025 (Online) 8th April Evening Shift

A quantity Q is formulated as $X^{-2}Y^{+\frac{3}{2}}Z^{-\frac{2}{5}}$. X, Y, and Z are independent parameters which have fractional errors of 0.1, 0.2, and 0.5, respectively in measurement. The maximum fractional error of Q is



JEE Main 2025 (Online) 8th April Evening Shift
Q.27 Correct
Q.27 In-correct
Q.27 Unattempt

Identify the physical quantity that cannot be measured using spherometer :

[27-Jan-2024 Shift 1]

Identify the physical quantity that cannot be measured using spherometer :

[27-Jan-2024 Shift 1]
Q.28 Correct
Q.28 In-correct
Q.28 Unattempt

Given below are two statements: one is labelled as Assertion(A) and the other is labelled as Reason (R).

Assertion (A) : In Vernier calliper if positive zero error exists, then while taking measurements, the reading taken will be more than the actual reading.
Reason (R) : The zero error in Vernier Calliper might have happened due to manufacturing defect or due to rough handling.

In the light of the above statements, choose the correct answer from the options given below :

[27-Jan-2024 Shift 2]

Given below are two statements: one is labelled as Assertion(A) and the other is labelled as Reason (R).

Assertion (A) : In Vernier calliper if positive zero error exists, then while taking measurements, the reading taken will be more than the actual reading.
Reason (R) : The zero error in Vernier Calliper might have happened due to manufacturing defect or due to rough handling.

In the light of the above statements, choose the correct answer from the options given below :

[27-Jan-2024 Shift 2]
Q.29 Correct
Q.29 In-correct
Q.29 Unattempt

If 50 Vernier divisions are equal to 49 main scale divisions of a travelling microscope and one smallest reading of main scale is 0.5 mm, the Vernier constant of travelling microscope is:

[30-Jan-2024 Shift 2]

If 50 Vernier divisions are equal to 49 main scale divisions of a travelling microscope and one smallest reading of main scale is 0.5 mm, the Vernier constant of travelling microscope is:

[30-Jan-2024 Shift 2]
Q.30 Correct
Q.30 In-correct
Q.30 Unattempt

The measured value of the length of a simple pendulum is 20cm with 2mm accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is N%. The value of N is:

[31-Jan-2024 Shift 2]

The measured value of the length of a simple pendulum is 20cm with 2mm accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is N%. The value of N is:

[31-Jan-2024 Shift 2]
Q.31 Correct
Q.31 In-correct
Q.31 Unattempt

The resistance R = V/1 where V = (200 ± 5)V and I = (20 ± 0.2)A, the percentage error in the measurement of R is :

[29-Jan-2024 Shift 1]

The resistance R = V/1 where V = (200 ± 5)V and I = (20 ± 0.2)A, the percentage error in the measurement of R is :

[29-Jan-2024 Shift 1]
Q.32 Correct
Q.32 In-correct
Q.32 Unattempt

A physical quantity Q is found to depend on quantities a, b, c by the relation Q = a4b3/c2. The percentage error in a, b and c are 3%,4% and 5% respectively. Then, the percentage error in Q is :

[29-Jan-2024 Shift 2]

A physical quantity Q is found to depend on quantities a, b, c by the relation Q = a4b3/c2. The percentage error in a, b and c are 3%,4% and 5% respectively. Then, the percentage error in Q is :

[29-Jan-2024 Shift 2]
Q.33 Correct
Q.33 In-correct
Q.33 Unattempt

A vector has magnitude same as that of   The x and y components of this vector in first quadrant are x and 3 respectively where x =____

[30-Jan-2024 Shift 2]

A vector has magnitude same as that of   The x and y components of this vector in first quadrant are x and 3 respectively where x =____

[30-Jan-2024 Shift 2]
Q.34 Correct
Q.34 In-correct
Q.34 Unattempt

If the percentage errors in measuring the length and the diameter of a wire are 0.1% each. The percentage error in measuring its resistance will be:

[31-Jan-2024 Shift 1]

If the percentage errors in measuring the length and the diameter of a wire are 0.1% each. The percentage error in measuring its resistance will be:

[31-Jan-2024 Shift 1]
Q.35 Correct
Q.35 In-correct
Q.35 Unattempt

If two vectors  having equal magnitude R are inclined at an angle θ, then

[31-Jan-2024 Shift 2]

If two vectors  having equal magnitude R are inclined at an angle θ, then

[31-Jan-2024 Shift 2]
Q.36 Correct
Q.36 In-correct
Q.36 Unattempt

Given below are two statements :

Statement (I) : Planck's constant and angular momentum have same dimensions.
Statement (II) : Linear momentum and moment of force have same dimensions.

In the light of the above statements, choose the correct answer from the options given below :

[27-Jan-2024 Shift 1]

Given below are two statements :

Statement (I) : Planck's constant and angular momentum have same dimensions.
Statement (II) : Linear momentum and moment of force have same dimensions.

In the light of the above statements, choose the correct answer from the options given below :

[27-Jan-2024 Shift 1]
Q.37 Correct
Q.37 In-correct
Q.37 Unattempt

The equation of state of a real gas is given by  (V − b) = RT, where P,V and T are pressure. volume and temperature respectively and R is the universal gas constant. The dimensions of a/b2 is similar to that of :

[27-Jan-2024 Shift 2]

The equation of state of a real gas is given by  (V − b) = RT, where P,V and T are pressure. volume and temperature respectively and R is the universal gas constant. The dimensions of a/b2 is similar to that of :

[27-Jan-2024 Shift 2]
Q.38 Correct
Q.38 In-correct
Q.38 Unattempt

Match List-I with List-II.

[30-Jan-2024 Shift 1]

Match List-I with List-II.

[30-Jan-2024 Shift 1]
Q.39 Correct
Q.39 In-correct
Q.39 Unattempt

If mass is written as m = kcPG−1∕2h1∕2 then the value of P will be : (Constants have their usual meaning with k a dimensionless constant)

[30-Jan-2024 Shift 2]

If mass is written as m = kcPG−1∕2h1∕2 then the value of P will be : (Constants have their usual meaning with k a dimensionless constant)

[30-Jan-2024 Shift 2]
Q.40 Correct
Q.40 In-correct
Q.40 Unattempt

A force is represented by F = ax2 + bt1∕2

Where x = distance and t = time. The dimensions of b2∕a are :

[31-Jan-2024 Shift 1]

A force is represented by F = ax2 + bt1∕2

Where x = distance and t = time. The dimensions of b2∕a are :

[31-Jan-2024 Shift 1]
Q.41 Correct
Q.41 In-correct
Q.41 Unattempt

Consider two physical quantities A and B related to each other as E =  where E, x and t have dimensions of energy,

[31-Jan-2024 Shift 2]

Consider two physical quantities A and B related to each other as E =  where E, x and t have dimensions of energy,

[31-Jan-2024 Shift 2]
Q.42 Correct
Q.42 In-correct
Q.42 Unattempt

The dimensional formula of angular impulse is :

[1-Feb-2024 Shift 1]

The dimensional formula of angular impulse is :

[1-Feb-2024 Shift 1]
Q.43 Correct
Q.43 In-correct
Q.43 Unattempt

10 divisions on the main scale of a Vernier calliper coincide with 11 divisions on the Vernier scale. If each division on the main scale is of 5 units, the least count of the instrument is :

[1-Feb-2024 Shift 1]

10 divisions on the main scale of a Vernier calliper coincide with 11 divisions on the Vernier scale. If each division on the main scale is of 5 units, the least count of the instrument is :

[1-Feb-2024 Shift 1]
Q.44 Correct
Q.44 In-correct
Q.44 Unattempt

The radius (r), length (l) and resistance (R) of a metal wire was measured in the laboratory as

The percentage error in resistivity of the material of the wire is :

[1-Feb-2024 Shift 1]

The radius (r), length (l) and resistance (R) of a metal wire was measured in the laboratory as

The percentage error in resistivity of the material of the wire is :

[1-Feb-2024 Shift 1]
Q.45 Correct
Q.45 In-correct
Q.45 Unattempt

Choose the correct answer from the options given below :

Match List - I with List - II.

List - I
(Number)		 List - II
(Significant figure)
(A) 1001 (I) 3
(B) 010.1 (II) 4
(C) 100.100 (III) 5
(D) 0.0010010 (IV) 6

 

[1-Feb-2024 Shift 2]

Choose the correct answer from the options given below :

Match List - I with List - II.

List - I
(Number)		 List - II
(Significant figure)
(A) 1001 (I) 3
(B) 010.1 (II) 4
(C) 100.100 (III) 5
(D) 0.0010010 (IV) 6

 

[1-Feb-2024 Shift 2]
Q.46 Correct
Q.46 In-correct
Q.46 Unattempt
Match List I with List II

[24-Jan-2023 Shift 1]
Match List I with List II

[24-Jan-2023 Shift 1]
Q.47 Correct
Q.47 In-correct
Q.47 Unattempt
The frequency (v) of an oscillating liquid drop may depend upon radius (r) of the drop, density (ρ) of liquid and the surface tension (s) of the liquid as : v=raρb sc. The values of a,b and c respectively are
[24-Jan-2023 Shift 2]
The frequency (v) of an oscillating liquid drop may depend upon radius (r) of the drop, density (ρ) of liquid and the surface tension (s) of the liquid as : v=raρb sc. The values of a,b and c respectively are
[24-Jan-2023 Shift 2]
Q.48 Correct
Q.48 In-correct
Q.48 Unattempt
Match List I with List II

Choose the correct answer from the options given below :
[25-Jan-2023 Shift 1]
Match List I with List II

Choose the correct answer from the options given below :
[25-Jan-2023 Shift 1]
Q.49 Correct
Q.49 In-correct
Q.49 Unattempt
Match List I with List II

Choose the correct answer from the options given below:
[25-Jan-2023 Shift 2]
Match List I with List II

Choose the correct answer from the options given below:
[25-Jan-2023 Shift 2]
Q.50 Correct
Q.50 In-correct
Q.50 Unattempt
Match List I with List II :

Choose the correct answer from the options given below:
[29-Jan-2023 Shift 1]
Match List I with List II :

Choose the correct answer from the options given below:
[29-Jan-2023 Shift 1]
Q.51 Correct
Q.51 In-correct
Q.51 Unattempt
The equation of a circle is given by x2+y2=a2, where a is the radius. If the equation is modified to change the origin other than (0,0), then find out the correct dimensions of A and B in a new equation: (x−At)2+(y−‌
t
B
)2=a2.
The dimensions of t is given as [T−1].
[29-Jan-2023 Shift 2]
The equation of a circle is given by x2+y2=a2, where a is the radius. If the equation is modified to change the origin other than (0,0), then find out the correct dimensions of A and B in a new equation: (x−At)2+(y−‌
t
B
)2=a2.
The dimensions of t is given as [T−1].
[29-Jan-2023 Shift 2]
Q.52 Correct
Q.52 In-correct
Q.52 Unattempt
Electric field in a certain region is given by
→
E
=(‌
A
x2
⋀
i
+‌
B
y3
⋀
j
). The SI unit of A and B are :
[30-Jan-2023 Shift 1]
Electric field in a certain region is given by
→
E
=(‌
A
x2
⋀
i
+‌
B
y3
⋀
j
). The SI unit of A and B are :
[30-Jan-2023 Shift 1]
Q.53 Correct
Q.53 In-correct
Q.53 Unattempt
Match List I with List II.

Choose the correct answer from the options given below :
[30-Jan-2023 Shift 2]
Match List I with List II.

Choose the correct answer from the options given below :
[30-Jan-2023 Shift 2]
Q.54 Correct
Q.54 In-correct
Q.54 Unattempt
If R,XL and XC represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless:
[31-Jan-2023 Shift 1]
If R,XL and XC represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless:
[31-Jan-2023 Shift 1]
Q.55 Correct
Q.55 In-correct
Q.55 Unattempt
Match List-I with List-II.

Choose the correct answer from the options given below:
[31-Jan-2023 Shift 2]
Match List-I with List-II.

Choose the correct answer from the options given below:
[31-Jan-2023 Shift 2]
Q.56 Correct
Q.56 In-correct
Q.56 Unattempt
Vectors a
∧
i
+b
∧
j
+
∧
k
 and 2
∧
i
−3
∧
j
+4
∧
k
 are perpendicular to each other when 3a+2b=7, the ratio of a to b is ‌
x
2
. The value of x is____
[24-Jan-2023 Shift 1]
Vectors a
∧
i
+b
∧
j
+
∧
k
 and 2
∧
i
−3
∧
j
+4
∧
k
 are perpendicular to each other when 3a+2b=7, the ratio of a to b is ‌
x
2
. The value of x is____
[24-Jan-2023 Shift 1]
Q.57 Correct
Q.57 In-correct
Q.57 Unattempt
If two vectors
→
P
=
^
i
+2m
^
j
+mk and
→
Q
=4
^
i
−2
^
j
+mk are perpendicular to each other.
Then, the value of m will be :
[24-Jan-2023 Shift 2]
If two vectors
→
P
=
^
i
+2m
^
j
+mk and
→
Q
=4
^
i
−2
^
j
+mk are perpendicular to each other.
Then, the value of m will be :
[24-Jan-2023 Shift 2]
Q.58 Correct
Q.58 In-correct
Q.58 Unattempt
If
→
P
=3
^
i
+√3
^
j
+2
^
k
 and
→
Q
=4
^
i
+√3
^
j
+2.5
^
k
 then, The unit vector in the direction of
→
P
×
→
Q
 is ‌
1
x
(√3
^
i
+
^
j
−2√3
^
k
). The value of x is
[25-Jan-2023 Shift 1]
If
→
P
=3
^
i
+√3
^
j
+2
^
k
 and
→
Q
=4
^
i
+√3
^
j
+2.5
^
k
 then, The unit vector in the direction of
→
P
×
→
Q
 is ‌
1
x
(√3
^
i
+
^
j
−2√3
^
k
). The value of x is
[25-Jan-2023 Shift 1]
Q.59 Correct
Q.59 In-correct
Q.59 Unattempt
In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as 5.25‌mm and apparent thickness of the glass slab at 5.00‌mm. Travelling microscope has 20 divisions in one cm on main scale and 50 divisions on Vernier scale is equal to 49 divisions on main scale. The estimated uncertainty in the measurement of refractive index of the slab is ‌
x
10
×10−3, where x is ________
[29-Jan-2023 Shift 2]
In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as 5.25‌mm and apparent thickness of the glass slab at 5.00‌mm. Travelling microscope has 20 divisions in one cm on main scale and 50 divisions on Vernier scale is equal to 49 divisions on main scale. The estimated uncertainty in the measurement of refractive index of the slab is ‌
x
10
×10−3, where x is ________
[29-Jan-2023 Shift 2]
Q.60 Correct
Q.60 In-correct
Q.60 Unattempt
In a metre bridge experiment the balance point in obtained if the gaps are closed by 2Ω and 3Ω. A shunt of XΩ is added to 3Ω resistor to shift the balancing point by 22.5‌cm. The value of X is _______
[29-Jan-2023 Shift 1]
In a metre bridge experiment the balance point in obtained if the gaps are closed by 2Ω and 3Ω. A shunt of XΩ is added to 3Ω resistor to shift the balancing point by 22.5‌cm. The value of X is _______
[29-Jan-2023 Shift 1]
Q.61 Correct
Q.61 In-correct
Q.61 Unattempt
A null point is found at 200‌cm in potentiometer when cell in secondary circuit is shunted by 5Ω. When a resistance of 15Ω is used for shunting null point moves to 300‌cm. The internal resistance of the cell is ______ Ω.
[29-Jan-2023 Shift 2]
A null point is found at 200‌cm in potentiometer when cell in secondary circuit is shunted by 5Ω. When a resistance of 15Ω is used for shunting null point moves to 300‌cm. The internal resistance of the cell is ______ Ω.
[29-Jan-2023 Shift 2]
Q.62 Correct
Q.62 In-correct
Q.62 Unattempt
In a screw gauge, there are 100 divisions on the circular scale and the main scale moves by 0.5‌mm on a complete rotation of the circular scale. The zero of circular scale lies 6 divisions below the line of graduation when two studs are brought in contact with each other. When a wire is placed between the studs, 4 linear scale divisions are clearly visible while 46‌th ‌ division the circular scale coincide with the reference line. The diameter of the wire is _______ ×10−2‌mm.
[30-Jan-2023 Shift 1]
In a screw gauge, there are 100 divisions on the circular scale and the main scale moves by 0.5‌mm on a complete rotation of the circular scale. The zero of circular scale lies 6 divisions below the line of graduation when two studs are brought in contact with each other. When a wire is placed between the studs, 4 linear scale divisions are clearly visible while 46‌th ‌ division the circular scale coincide with the reference line. The diameter of the wire is _______ ×10−2‌mm.
[30-Jan-2023 Shift 1]
Q.63 Correct
Q.63 In-correct
Q.63 Unattempt
(P+‌
a
V2
)(V−b)=RT represents the equation of state of some gases. Where P is the pressure, V is the volume, T is the temperature and a,b,R are the constants. The physical quantity, which has dimensional formula as that of ‌
b2
a
, will be :
[1-Feb-2023 Shift 1]
(P+‌
a
V2
)(V−b)=RT represents the equation of state of some gases. Where P is the pressure, V is the volume, T is the temperature and a,b,R are the constants. The physical quantity, which has dimensional formula as that of ‌
b2
a
, will be :
[1-Feb-2023 Shift 1]
Q.64 Correct
Q.64 In-correct
Q.64 Unattempt
If the velocity of light c, universal gravitational constant G and planck's constant h are chosen as fundamental quantities. The dimensions of mass in the new system is:
[1-Feb-2023 Shift 2]
If the velocity of light c, universal gravitational constant G and planck's constant h are chosen as fundamental quantities. The dimensions of mass in the new system is:
[1-Feb-2023 Shift 2]
Q.65 Correct
Q.65 In-correct
Q.65 Unattempt
In an experiment to find emf of a cell using potentiometer, the length of null point for a cell of emf 1.5V is found to be 60‌cm. If this cell is replaced by another cell of emf E. the length-of null point increases by 40‌cm. The value of E is ‌
x
10
V. The value of x is ________.
[1-Feb-2023 Shift 1]
In an experiment to find emf of a cell using potentiometer, the length of null point for a cell of emf 1.5V is found to be 60‌cm. If this cell is replaced by another cell of emf E. the length-of null point increases by 40‌cm. The value of E is ‌
x
10
V. The value of x is ________.
[1-Feb-2023 Shift 1]
Q.66 Correct
Q.66 In-correct
Q.66 Unattempt
Dimension of ‌
1
µ0∈0
 should be equal to
[8-Apr-2023 shift 1]
Dimension of ‌
1
µ0∈0
 should be equal to
[8-Apr-2023 shift 1]
Q.67 Correct
Q.67 In-correct
Q.67 Unattempt
Match List I with List II

Choose the correct answer from the options given below:
[8-Apr-2023 shift 2]
Match List I with List II

Choose the correct answer from the options given below:
[8-Apr-2023 shift 2]
Q.68 Correct
Q.68 In-correct
Q.68 Unattempt
Given below are two statements :
Statements I : Astronomical unit (Au), Parsec (Pc) and Light year (ly) are units for measuring astronomical distances.
Statements II : Au< Parsec (Pc)< ly
In the light of the above statements, choose the most appropriate answer from the options given below :
[11-Apr-2023 shift 1]
Given below are two statements :
Statements I : Astronomical unit (Au), Parsec (Pc) and Light year (ly) are units for measuring astronomical distances.
Statements II : Au< Parsec (Pc)< ly
In the light of the above statements, choose the most appropriate answer from the options given below :
[11-Apr-2023 shift 1]
Q.69 Correct
Q.69 In-correct
Q.69 Unattempt
If force (F), velocity (V) and time (T) are considered as fundamental physical quantity, then dimensional formula of density will be:
[11-Apr-2023 shift 2]
If force (F), velocity (V) and time (T) are considered as fundamental physical quantity, then dimensional formula of density will be:
[11-Apr-2023 shift 2]
Q.70 Correct
Q.70 In-correct
Q.70 Unattempt

Choose the correct answer from the options given below :
[12-Apr-2023 shift 1]

Choose the correct answer from the options given below :
[12-Apr-2023 shift 1]
Q.71 Correct
Q.71 In-correct
Q.71 Unattempt
In the equation [x+‌
a
y2
][Y−b]=RT,X is pressure, Y is volume, R is universal gas constant ant T is temperature. The physical quantity equivalent to the ratio ‌
a
b
 is :
[13-Apr-2023 shift 2]
In the equation [x+‌
a
y2
][Y−b]=RT,X is pressure, Y is volume, R is universal gas constant ant T is temperature. The physical quantity equivalent to the ratio ‌
a
b
 is :
[13-Apr-2023 shift 2]
Q.72 Correct
Q.72 In-correct
Q.72 Unattempt
The speed of a wave produced in water is given by v=λagbρc. Where λ,g and ρ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of a,b and c respectively, are :
[15-Apr-2023 shift 1]
The speed of a wave produced in water is given by v=λagbρc. Where λ,g and ρ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of a,b and c respectively, are :
[15-Apr-2023 shift 1]
Q.73 Correct
Q.73 In-correct
Q.73 Unattempt
Two resistances are given as R1=(10±0.5)Ω and R2=(15±0.5)Ω. The percentage error in the measurement of equivalent resistance when they are connected in parallel is -
[6-Apr-2023 shift 1]
Two resistances are given as R1=(10±0.5)Ω and R2=(15±0.5)Ω. The percentage error in the measurement of equivalent resistance when they are connected in parallel is -
[6-Apr-2023 shift 1]
Q.74 Correct
Q.74 In-correct
Q.74 Unattempt
The length of a metallic wire is increased by 20% and its area of cross section is reduced by 4%. The percentage change in resistance of the metallic wire is ________
[6-Apr-2023 shift 1]
The length of a metallic wire is increased by 20% and its area of cross section is reduced by 4%. The percentage change in resistance of the metallic wire is ________
[6-Apr-2023 shift 1]
Q.75 Correct
Q.75 In-correct
Q.75 Unattempt
Two forces having magnitude A and ‌
A
2
 are perpendicular to each other. The magnitude of their resultant is:
[8-Apr-2023 shift 1]
Two forces having magnitude A and ‌
A
2
 are perpendicular to each other. The magnitude of their resultant is:
[8-Apr-2023 shift 1]
Q.76 Correct
Q.76 In-correct
Q.76 Unattempt
A physical quantity P is given as
P=‌
a2b3
c√d

The percentage error in the measurement of a,b,c and d are 1%,2%,3% and 4% respectively. The percentage error in the measurement of quantity P will be
[10-Apr-2023 shift 1]
A physical quantity P is given as
P=‌
a2b3
c√d

The percentage error in the measurement of a,b,c and d are 1%,2%,3% and 4% respectively. The percentage error in the measurement of quantity P will be
[10-Apr-2023 shift 1]
Q.77 Correct
Q.77 In-correct
Q.77 Unattempt
Three forces F1=10N,F2=8N,F3=6N are acting on a particle of mass 5‌kg. The forces F2 and F3 are applied perpendicularly so that particle remains at rest. If the force F1 is removed, then the acceleration of the particle is :
[12-Apr-2023 shift 1]
Three forces F1=10N,F2=8N,F3=6N are acting on a particle of mass 5‌kg. The forces F2 and F3 are applied perpendicularly so that particle remains at rest. If the force F1 is removed, then the acceleration of the particle is :
[12-Apr-2023 shift 1]
Q.78 Correct
Q.78 In-correct
Q.78 Unattempt
A vector in x−y plane makes an angle of 30∘ with y-axis. The magnitude of y-component of vector is 2√3. The magnitude of x-component of the vector will be :
[15-Apr-2023 shift 1]
A vector in x−y plane makes an angle of 30∘ with y-axis. The magnitude of y-component of vector is 2√3. The magnitude of x-component of the vector will be :
[15-Apr-2023 shift 1]
Q.79 Correct
Q.79 In-correct
Q.79 Unattempt
In an experiment with vernier calipers of least count 0.1‌mm, when two jaws are joined together the zero of vernier scale lies right to the zero of the main scale and 6‌th ‌ division of vernier scale coincides with the main scale division. While measuring the diameter of a spherical bob, the zero of vernier scale lies in between 3.2‌cm and 3.3‌cm marks, and 4‌th ‌ division of vernier scale coincides with the main scale division. The diameter of bob is measured as
[10-Apr-2023 shift 2]
In an experiment with vernier calipers of least count 0.1‌mm, when two jaws are joined together the zero of vernier scale lies right to the zero of the main scale and 6‌th ‌ division of vernier scale coincides with the main scale division. While measuring the diameter of a spherical bob, the zero of vernier scale lies in between 3.2‌cm and 3.3‌cm marks, and 4‌th ‌ division of vernier scale coincides with the main scale division. The diameter of bob is measured as
[10-Apr-2023 shift 2]
Q.80 Correct
Q.80 In-correct
Q.80 Unattempt
Identify the pair of physical quantities which have different dimensions:
[24-Jun-2022-Shift-1]
Identify the pair of physical quantities which have different dimensions:
[24-Jun-2022-Shift-1]
Q.81 Correct
Q.81 In-correct
Q.81 Unattempt
Identify the pair of physical quantities that have same dimensions:
[24-Jun-2022-Shift-2]
Identify the pair of physical quantities that have same dimensions:
[24-Jun-2022-Shift-2]
Q.82 Correct
Q.82 In-correct
Q.82 Unattempt
An expression for a dimensionless quantity P is given by P=‌
α
β
loge(‌
kt
βx
); where α and β are constants, x is distance; k is Boltzmann constant and t is the temperature. Then the dimensions of α will be :
[26-Jun-2022-Shift-1]
An expression for a dimensionless quantity P is given by P=‌
α
β
loge(‌
kt
βx
); where α and β are constants, x is distance; k is Boltzmann constant and t is the temperature. Then the dimensions of α will be :
[26-Jun-2022-Shift-1]
Q.83 Correct
Q.83 In-correct
Q.83 Unattempt
The dimension of mutual inductance is :
[26-Jun-2022-Shift-2]
The dimension of mutual inductance is :
[26-Jun-2022-Shift-2]
Q.84 Correct
Q.84 In-correct
Q.84 Unattempt
The SI unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be :
[27-Jun-2022-Shift-2]
The SI unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be :
[27-Jun-2022-Shift-2]
Q.85 Correct
Q.85 In-correct
Q.85 Unattempt
If L,C and R are the self inductance, capacitance and resistance respectively, which of the following does not have the dimension of time?
[27-Jun-2022-Shift-2]
If L,C and R are the self inductance, capacitance and resistance respectively, which of the following does not have the dimension of time?
[27-Jun-2022-Shift-2]
Q.86 Correct
Q.86 In-correct
Q.86 Unattempt
In van der Waal equation [P+‌
a
V2
][V−b]=RT;P is pressure, V is volume, R is universal gas constant and T is temperature. The ratio of constants ‌
a
b
 is dimensionally equal to:
[29-Jun-2022-Shift-1]
In van der Waal equation [P+‌
a
V2
][V−b]=RT;P is pressure, V is volume, R is universal gas constant and T is temperature. The ratio of constants ‌
a
b
 is dimensionally equal to:
[29-Jun-2022-Shift-1]
Q.87 Correct
Q.87 In-correct
Q.87 Unattempt
If Z=‌
A2B3
C4
, then the relative error in Z will be :
[25-Jun-2022-Shift-1]
If Z=‌
A2B3
C4
, then the relative error in Z will be :
[25-Jun-2022-Shift-1]
Q.88 Correct
Q.88 In-correct
Q.88 Unattempt
→
A
 is a vector quantity such that |
→
A
|= non-zero constant. Which of the following expression is true for
→
A
 ?
[25-Jun-2022-Shift-1]
→
A
 is a vector quantity such that |
→
A
|= non-zero constant. Which of the following expression is true for
→
A
 ?
[25-Jun-2022-Shift-1]
Q.89 Correct
Q.89 In-correct
Q.89 Unattempt
Which of the following relations is true for two unit vector
∧
A
 and
∧
B
 making an angle θ to each other?
[25-Jun-2022-Shift-1]
Which of the following relations is true for two unit vector
∧
A
 and
∧
B
 making an angle θ to each other?
[25-Jun-2022-Shift-1]
Q.90 Correct
Q.90 In-correct
Q.90 Unattempt
For z=a2x3y‌
1
2
, where 'a' is a constant. If percentage error in measurement of ' x ' and ' y ' are 4% and 12% respectively, then the percentage error for 'z' will be ______ %
[25-Jun-2022-Shift-2]
For z=a2x3y‌
1
2
, where 'a' is a constant. If percentage error in measurement of ' x ' and ' y ' are 4% and 12% respectively, then the percentage error for 'z' will be ______ %
[25-Jun-2022-Shift-2]
Q.91 Correct
Q.91 In-correct
Q.91 Unattempt
A silver wire has a mass (0.6±0.006)g, radius (0.5±0.005)‌mm and length (4±0.04)‌cm. The maximum percentage error in the measurement of its density will be :
[27-Jun-2022-Shift-1]
A silver wire has a mass (0.6±0.006)g, radius (0.5±0.005)‌mm and length (4±0.04)‌cm. The maximum percentage error in the measurement of its density will be :
[27-Jun-2022-Shift-1]
Q.92 Correct
Q.92 In-correct
Q.92 Unattempt
The distance of the Sun from earth is 1.5×1011m and its angular diameter is (2000) s when observed from the earth. The diameter of the Sun will be :
[27-Jun-2022-Shift-2]
The distance of the Sun from earth is 1.5×1011m and its angular diameter is (2000) s when observed from the earth. The diameter of the Sun will be :
[27-Jun-2022-Shift-2]
Q.93 Correct
Q.93 In-correct
Q.93 Unattempt
Two vectors
→
A
 and
→
B
 have equal magnitudes. If magnitude of
→
A
+
→
B
 is equal to two times the magnitude of
→
A
−
→
B
, then the angle between
→
A
 and
→
B
 will be :
[29-Jun-2022-Shift-1]
Two vectors
→
A
 and
→
B
 have equal magnitudes. If magnitude of
→
A
+
→
B
 is equal to two times the magnitude of
→
A
−
→
B
, then the angle between
→
A
 and
→
B
 will be :
[29-Jun-2022-Shift-1]
Q.94 Correct
Q.94 In-correct
Q.94 Unattempt
In a vernier callipers, each cm on the main scale is divided into 20 equal parts. If tenth vernier scale division coincides with nineth main scale division. Then the value of vernier constant will be _____×10−2‌mm
[26-Jun-2022-Shift-1]
In a vernier callipers, each cm on the main scale is divided into 20 equal parts. If tenth vernier scale division coincides with nineth main scale division. Then the value of vernier constant will be _____×10−2‌mm
[26-Jun-2022-Shift-1]
Q.95 Correct
Q.95 In-correct
Q.95 Unattempt
A travelling microscope is used to determine the refractive index of a glass slab. If 40 divisions are there in 1‌cm on main scale and 50 Vernier scale divisions are equal to 49 main scale divisions, then least count of the travelling microscope is ____× 10−6m.
[26-Jun-2022-Shift-2]
A travelling microscope is used to determine the refractive index of a glass slab. If 40 divisions are there in 1‌cm on main scale and 50 Vernier scale divisions are equal to 49 main scale divisions, then least count of the travelling microscope is ____× 10−6m.
[26-Jun-2022-Shift-2]
Q.96 Correct
Q.96 In-correct
Q.96 Unattempt
A student in the laboratory measures thickness of a wire using screw gauge. The readings are 1.22‌mm,1.23‌mm,1.19‌mm and 1.20‌mm. The percentage error is ‌
x
121
%. The value of x is
[28-Jun-2022-Shift-2]
A student in the laboratory measures thickness of a wire using screw gauge. The readings are 1.22‌mm,1.23‌mm,1.19‌mm and 1.20‌mm. The percentage error is ‌
x
121
%. The value of x is
[28-Jun-2022-Shift-2]
Q.97 Correct
Q.97 In-correct
Q.97 Unattempt
The Vernier constant of Vernier callipers is 0.1‌mm and it has zero error of (−0.05)‌cm. While measuring diameter of a sphere, the main scale reading is 1.7‌cm and coinciding vernier division is 5 . The corrected diameter will be ____×10−2‌cm
[29-Jun-2022-Shift-2]
The Vernier constant of Vernier callipers is 0.1‌mm and it has zero error of (−0.05)‌cm. While measuring diameter of a sphere, the main scale reading is 1.7‌cm and coinciding vernier division is 5 . The corrected diameter will be ____×10−2‌cm
[29-Jun-2022-Shift-2]
Q.98 Correct
Q.98 In-correct
Q.98 Unattempt
If momentum [P], area [A] and time [T] are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is:
[25-Jul-2022-Shift-1]
If momentum [P], area [A] and time [T] are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is:
[25-Jul-2022-Shift-1]
Q.99 Correct
Q.99 In-correct
Q.99 Unattempt
A torque meter is calibrated to reference standards of mass, length and time each with 5% accuracy. After calibration, the measured torque with this torque meter will have net accuracy of :
[27-Jul-2022-Shift-1]
A torque meter is calibrated to reference standards of mass, length and time each with 5% accuracy. After calibration, the measured torque with this torque meter will have net accuracy of :
[27-Jul-2022-Shift-1]
Q.100 Correct
Q.100 In-correct
Q.100 Unattempt
An expression of energy density is given by u=‌
α
β
‌sin(‌
αx
kt
), where α,β are constants, x is displacement, k is Boltzmann constant and t is the temperature. The dimensions of β will be :
[27-Jul-2022-Shift-2]
An expression of energy density is given by u=‌
α
β
‌sin(‌
αx
kt
), where α,β are constants, x is displacement, k is Boltzmann constant and t is the temperature. The dimensions of β will be :
[27-Jul-2022-Shift-2]
Q.101 Correct
Q.101 In-correct
Q.101 Unattempt
The dimensions of (‌
B2
µ0
) will be :
(if µ0 : permeability of free space and B : magnetic field)
[28-Jul-2022-Shift-1]
The dimensions of (‌
B2
µ0
) will be :
(if µ0 : permeability of free space and B : magnetic field)
[28-Jul-2022-Shift-1]
Q.102 Correct
Q.102 In-correct
Q.102 Unattempt
Consider the efficiency of carnot's engine is given by η=‌
αβ
sinθ
‌log‌e‌
βx
kT
, where α and β are constants. If T is temperature, k is Boltzmann constant, θ is angular displacement and x has the dimensions of length. Then, choose the incorrect option:
[28-Jul-2022-Shift-2]
Consider the efficiency of carnot's engine is given by η=‌
αβ
sinθ
‌log‌e‌
βx
kT
, where α and β are constants. If T is temperature, k is Boltzmann constant, θ is angular displacement and x has the dimensions of length. Then, choose the incorrect option:
[28-Jul-2022-Shift-2]
Q.103 Correct
Q.103 In-correct
Q.103 Unattempt
Match List I with List II.

Choose the correct answer from the options given below :
[29-Jul-2022-Shift-2]
Match List I with List II.

Choose the correct answer from the options given below :
[29-Jul-2022-Shift-2]
Q.104 Correct
Q.104 In-correct
Q.104 Unattempt
The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are 1%,2% and 3% respectively. The maximum percentage error in the detection of the dissipated heat will be :
[25-Jul-2022-Shift-2]
The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are 1%,2% and 3% respectively. The maximum percentage error in the detection of the dissipated heat will be :
[25-Jul-2022-Shift-2]
Q.105 Correct
Q.105 In-correct
Q.105 Unattempt
If
→
A
=(2
∧
i
+3
∧
j
−
∧
k
)m and
→
B
=(
∧
i
+2
∧
j
+2
∧
k
)m. The magnitude of component of vector
→
A
 along vector
→
B
 will be m.
[26-Jul-2022-Shift-2]
If
→
A
=(2
∧
i
+3
∧
j
−
∧
k
)m and
→
B
=(
∧
i
+2
∧
j
+2
∧
k
)m. The magnitude of component of vector
→
A
 along vector
→
B
 will be m.
[26-Jul-2022-Shift-2]
Q.106 Correct
Q.106 In-correct
Q.106 Unattempt
The one division of main scale of Vernier callipers reads 1‌mm and 10 divisions of Vernier scale is equal to the 9 divisions on main scale. When the two jaws of the instrument touch each other, the zero of the Vernier lies to the right of zero of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws, the zero of the Vernier scale lies in between 4.1‌cm and 4.2‌cm and 6‌th ‌ Vernier division coincides scale division. The diameter of the bob will be ________ ×10−2‌cm.
[27-Jul-2022-Shift-1]
The one division of main scale of Vernier callipers reads 1‌mm and 10 divisions of Vernier scale is equal to the 9 divisions on main scale. When the two jaws of the instrument touch each other, the zero of the Vernier lies to the right of zero of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws, the zero of the Vernier scale lies in between 4.1‌cm and 4.2‌cm and 6‌th ‌ Vernier division coincides scale division. The diameter of the bob will be ________ ×10−2‌cm.
[27-Jul-2022-Shift-1]
Q.107 Correct
Q.107 In-correct
Q.107 Unattempt
If the projection of 2
∧
i
+4
∧
j
−2
∧
k
 on
∧
i
+2
∧
j
+α
∧
k
 is zero. Then, the value of α will be _______.
[28-Jul-2022-Shift-1]
If the projection of 2
∧
i
+4
∧
j
−2
∧
k
 on
∧
i
+2
∧
j
+α
∧
k
 is zero. Then, the value of α will be _______.
[28-Jul-2022-Shift-1]
Q.108 Correct
Q.108 In-correct
Q.108 Unattempt
In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of 0.5 s is measured from time of 100 oscillation with a watch of 1 s resolution. If measured value of length is 10‌cm known to 1‌mm accuracy, The accuracy in the determination of g is found to be x%. The value of x is________.
[28-Jul-2022-Shift-2]
In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of 0.5 s is measured from time of 100 oscillation with a watch of 1 s resolution. If measured value of length is 10‌cm known to 1‌mm accuracy, The accuracy in the determination of g is found to be x%. The value of x is________.
[28-Jul-2022-Shift-2]
Q.109 Correct
Q.109 In-correct
Q.109 Unattempt
A screw gauge of pitch 0.5‌mm is used to measure the diameter of uniform wire of length 6.8‌cm, the main scale reading is 1.5‌mm and circular scale reading is 7 . The calculated curved surface area of wire to appropriate significant figures is :
[Screw gauge has 50 divisions on its circular scale]
[26-Jul-2022-Shift-1]
A screw gauge of pitch 0.5‌mm is used to measure the diameter of uniform wire of length 6.8‌cm, the main scale reading is 1.5‌mm and circular scale reading is 7 . The calculated curved surface area of wire to appropriate significant figures is :
[Screw gauge has 50 divisions on its circular scale]
[26-Jul-2022-Shift-1]
Q.110 Correct
Q.110 In-correct
Q.110 Unattempt
In a Vernier Calipers, 10 divisions of Vernier scale is equal to the 9 divisions of main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and 4‌th ‌ Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to 1‌mm. While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between 30 and 31 divisions of main scale reading and 6‌th ‌ Vernier scale division exactly coincides with the main scale reading. The diameter of the spherical body will be :
[26-Jul-2022-Shift-2]
In a Vernier Calipers, 10 divisions of Vernier scale is equal to the 9 divisions of main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and 4‌th ‌ Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to 1‌mm. While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between 30 and 31 divisions of main scale reading and 6‌th ‌ Vernier scale division exactly coincides with the main scale reading. The diameter of the spherical body will be :
[26-Jul-2022-Shift-2]
Q.111 Correct
Q.111 In-correct
Q.111 Unattempt
In a meter bridge experiment, for measuring unknown resistance ' S ', the null point is obtained at a distance 30‌cm from the left side as shown at point D. If R is 5.6kΩ, then the value of unknown resistance 'S' will be _______ Ω.

 [27-Jul-2022-Shift-1]
In a meter bridge experiment, for measuring unknown resistance ' S ', the null point is obtained at a distance 30‌cm from the left side as shown at point D. If R is 5.6kΩ, then the value of unknown resistance 'S' will be _______ Ω.

[27-Jul-2022-Shift-1]
Q.112 Correct
Q.112 In-correct
Q.112 Unattempt
In an experiment with a convex lens, The plot of the image distance (v′) against the object distance (µ′) measured from the focus gives a curve v′µ′=225. If all the distances are measured in cm. The magnitude of the focal length of the lens is ____cm
[28-Jul-2022-Shift-2]
In an experiment with a convex lens, The plot of the image distance (v′) against the object distance (µ′) measured from the focus gives a curve v′µ′=225. If all the distances are measured in cm. The magnitude of the focal length of the lens is ____cm
[28-Jul-2022-Shift-2]
Q.113 Correct
Q.113 In-correct
Q.113 Unattempt
A travelling microscope has 20 divisions per cm on the main scale while its vernier scale has total 50 divisions and 25 vernier scale divisions are equal to 24 main scale divisions, what is the least count of the travelling microscope?
[29-Jul-2022-Shift-1]
A travelling microscope has 20 divisions per cm on the main scale while its vernier scale has total 50 divisions and 25 vernier scale divisions are equal to 24 main scale divisions, what is the least count of the travelling microscope?
[29-Jul-2022-Shift-1]
Q.114 Correct
Q.114 In-correct
Q.114 Unattempt
In an experiment to find out the diameter of wire using screw gauge, the following observations were noted :
(A) Screw moves 0.5‌mm on main scale in one complete rotation
(B) Total divisions on circular scale =50
(C) Main scale reading is 2.5‌mm
(D) 45‌th ‌ division of circular scale is in the pitch line
(E) Instrument has 0.03‌mm negative error
Then the diameter of wire is :
[29-Jul-2022-Shift-1]
In an experiment to find out the diameter of wire using screw gauge, the following observations were noted :

(A) Screw moves 0.5‌mm on main scale in one complete rotation
(B) Total divisions on circular scale =50
(C) Main scale reading is 2.5‌mm
(D) 45‌th ‌ division of circular scale is in the pitch line
(E) Instrument has 0.03‌mm negative error
Then the diameter of wire is :
[29-Jul-2022-Shift-1]
Q.115 Correct
Q.115 In-correct
Q.115 Unattempt
The pitch of the screw gauge is 1mm and there are 100 divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lies 8 divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while 72 nd division on circular scale coincides with the reference line. The radius of the wire is
[25 Feb 2021 Shift 1]
The pitch of the screw gauge is 1mm and there are 100 divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lies 8 divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while 72 nd division on circular scale coincides with the reference line. The radius of the wire is
[25 Feb 2021 Shift 1]
Q.116 Correct
Q.116 In-correct
Q.116 Unattempt
A large number of water drops, each of radius r, combine to have a drop of radius R. If the surface tension is T and mechanical equivalent of heat is J, the rise in heat energy per unit volume will be
[26 Feb 2021 Shift 1]
A large number of water drops, each of radius r, combine to have a drop of radius R. If the surface tension is T and mechanical equivalent of heat is J, the rise in heat energy per unit volume will be
[26 Feb 2021 Shift 1]
Q.117 Correct
Q.117 In-correct
Q.117 Unattempt
The period of oscillation of a simple pendulum is T=2π√‌
L
g
. Measured value of L is 1.0m from metre scale having a minimum division of 1mm and time of one complete oscillation is 1.95s measured from stopwatch of 0.01s resolution. The percentage error in the determination of g will be
[24 Feb 2021 Shift 2]
The period of oscillation of a simple pendulum is T=2π√‌
L
g
. Measured value of L is 1.0m from metre scale having a minimum division of 1mm and time of one complete oscillation is 1.95s measured from stopwatch of 0.01s resolution. The percentage error in the determination of g will be
[24 Feb 2021 Shift 2]
Q.118 Correct
Q.118 In-correct
Q.118 Unattempt
If C and V represent capacity and voltage respectively, then what are the dimensions of λ, where ‌
C
V
=λ?
[26 Feb 2021 Shift 2]
If C and V represent capacity and voltage respectively, then what are the dimensions of λ, where ‌
C
V
=λ?
[26 Feb 2021 Shift 2]
Q.119 Correct
Q.119 In-correct
Q.119 Unattempt
In a typical combustion engine, the work done by a gas molecule is given W=α2βe‌
−βx2
kT
, where x is the displacement, k is the Boltzmann constant and T is the temperature. If α and β are constants, dimensions of α will be
[26 Feb 2021 Shift 1]
In a typical combustion engine, the work done by a gas molecule is given W=α2βe‌
−βx2
kT
, where x is the displacement, k is the Boltzmann constant and T is the temperature. If α and β are constants, dimensions of α will be
[26 Feb 2021 Shift 1]
Q.120 Correct
Q.120 In-correct
Q.120 Unattempt
Match List-I with List-II

Choose the correct answer from the options given below.
[25 Feb 2021 Shift 1]
Match List-I with List-II

Choose the correct answer from the options given below.
[25 Feb 2021 Shift 1]
Q.121 Correct
Q.121 In-correct
Q.121 Unattempt
The work done by a gas molecule in an isolated system is given by, W=αβ2e−‌
x2
αkT
, where x is the displacement k is the Boltzmann constant and T is the temperature, α and β are constants. Then the dimension of β will be :
24Feb2021
The work done by a gas molecule in an isolated system is given by, W=αβ2e−‌
x2
αkT
, where x is the displacement k is the Boltzmann constant and T is the temperature, α and β are constants. Then the dimension of β will be :
24Feb2021
Q.122 Correct
Q.122 In-correct
Q.122 Unattempt
Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes 0.01cm3 of oleic acid per cm3 of the solution. Then, you make a thin film of this solution (monomolecular thickness) of area 4cm2 by considering 100 spherical drops of radius (‌
3
40π
)‌
1
3
×10−3 cm2. Then, the thickness of oleic acid layer will be x×10−14m, where x is
[17 Mar 2021 Shift 2]
Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes 0.01cm3 of oleic acid per cm3 of the solution. Then, you make a thin film of this solution (monomolecular thickness) of area 4cm2 by considering 100 spherical drops of radius (‌
3
40π
)‌
1
3
×10−3 cm2. Then, the thickness of oleic acid layer will be x×10−14m, where x is
[17 Mar 2021 Shift 2]
Q.123 Correct
Q.123 In-correct
Q.123 Unattempt
In order to determine the Young's modulus of a wire of radius 0.2cm (measured using a scale of least count =0.001cm ) and length 1m (measured using a scale of least count =1mm ), a weight of mass 1kg (measured using a scale of least count =1g ) was hanged to get the elongation of 0.5cm (measured using a scale of least count 0.001cm ). What will be the fractional error in the value of Young's modulus determined by this experiment?
[16 Mar 2021 Shift 2]
In order to determine the Young's modulus of a wire of radius 0.2cm (measured using a scale of least count =0.001cm ) and length 1m (measured using a scale of least count =1mm ), a weight of mass 1kg (measured using a scale of least count =1g ) was hanged to get the elongation of 0.5cm (measured using a scale of least count 0.001cm ). What will be the fractional error in the value of Young's modulus determined by this experiment?
[16 Mar 2021 Shift 2]
Q.124 Correct
Q.124 In-correct
Q.124 Unattempt
One main scale division of a vernier callipers is acm and nth division of the vernier scale coincide with ( n−1) th division of the main scal
[16 Mar 2021 Shift 1]
One main scale division of a vernier callipers is acm and nth division of the vernier scale coincide with ( n−1) th division of the main scal
[16 Mar 2021 Shift 1]
Q.125 Correct
Q.125 In-correct
Q.125 Unattempt
The resistance R=‌
V
I
, where V=(50±2)V and I=(20±0.2) A. The percentage error in R is x%. The value of x to the nearest integer is..........
[16 Mar 2021 Shift 1]
The resistance R=‌
V
I
, where V=(50±2)V and I=(20±0.2) A. The percentage error in R is x%. The value of x to the nearest integer is..........
[16 Mar 2021 Shift 1]
Q.126 Correct
Q.126 In-correct
Q.126 Unattempt
A person is swimming with a speed of 10m/s at an angle of 120∘ with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is xm/s. The value of x to the nearest integer is .........
[18 Mar 2021 Shift 1]
A person is swimming with a speed of 10m/s at an angle of 120∘ with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is xm/s. The value of x to the nearest integer is .........
[18 Mar 2021 Shift 1]
Q.127 Correct
Q.127 In-correct
Q.127 Unattempt
The vernier scale used for measurement has a positive zero error of 0.2mm. If while taking a measurement, it was noted that ' 0 ' on the vernier scale lies between 8.5cm and 8.6cm, vernier coincidence is 6 , then the correct value of measurement is ......... cm.
[17 Mar 2021 Shift 1]
The vernier scale used for measurement has a positive zero error of 0.2mm. If while taking a measurement, it was noted that ' 0 ' on the vernier scale lies between 8.5cm and 8.6cm, vernier coincidence is 6 , then the correct value of measurement is ......... cm.
[17 Mar 2021 Shift 1]
Q.128 Correct
Q.128 In-correct
Q.128 Unattempt
Assertion A : If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is 5 mm and there are 50 total divisions on circular scale, then least count is 0.001 cm.
Reason R :
Least Count =
Pitch
Total divisionson circular scale

In the light of the above statements, choose the most appropriate answer from the options given below :
[27 Jul 2021 Shift 1]
Assertion A : If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is 5 mm and there are 50 total divisions on circular scale, then least count is 0.001 cm.
Reason R :
Least Count =
Pitch
Total divisionson circular scale

In the light of the above statements, choose the most appropriate answer from the options given below :
[27 Jul 2021 Shift 1]
Q.129 Correct
Q.129 In-correct
Q.129 Unattempt
The force is given in terms of time t and displacement x by the equation
F=A‌cos‌Bx+C‌sin‌Dt
The dimensional formula of
AD
B
 is :
[25 Jul 2021 Shift 2]
The force is given in terms of time t and displacement x by the equation
F=A‌cos‌Bx+C‌sin‌Dt
The dimensional formula of
AD
B
 is :
[25 Jul 2021 Shift 2]
Q.130 Correct
Q.130 In-correct
Q.130 Unattempt
If time (t), velocity (v), and angular momentum (l) are taken as the fundamental units. Then thedimension of mass (m) in terms of t,v and l is :
[20 Jul 2021 Shift 2]
If time (t), velocity (v), and angular momentum (l) are taken as the fundamental units. Then thedimension of mass (m) in terms of t,v and l is :
[20 Jul 2021 Shift 2]
Q.131 Correct
Q.131 In-correct
Q.131 Unattempt
The entropy of any system is given by
S=α2β‌ln[
µkR
Jβ2
+3]
where α and beta are the constants. mu,J,k and R are no. of moles, mechanical equivalent of heat, Boltzmann constant and gas constant respectively.
[Take S=
dQ
T
]
Choose the incorrect option from the following :
[20 Jul 2021 Shift 1]
The entropy of any system is given by
S=α2β‌ln[
µkR
Jβ2
+3]
where α and beta are the constants. mu,J,k and R are no. of moles, mechanical equivalent of heat, Boltzmann constant and gas constant respectively.
[Take S=
dQ
T
]
Choose the incorrect option from the following :
[20 Jul 2021 Shift 1]
Q.132 Correct
Q.132 In-correct
Q.132 Unattempt
Student A and Student B used two screw gauges of equal pitch and 100 equal circular divisions to measure the radius of a given wire. The actual value of the radius of the wire is 0.322 cm. The absolute value of the difference between the final circular scale readings observed by the students A and B is ________.
[Figure shows position of reference 'O' when jaws of screw gauge are closed]
Given pitch = 0.1 cm.

[25 Jul 2021 Shift 1]
Student A and Student B used two screw gauges of equal pitch and 100 equal circular divisions to measure the radius of a given wire. The actual value of the radius of the wire is 0.322 cm. The absolute value of the difference between the final circular scale readings observed by the students A and B is ________.
[Figure shows position of reference 'O' when jaws of screw gauge are closed]
Given pitch = 0.1 cm.

[25 Jul 2021 Shift 1]
Q.133 Correct
Q.133 In-correct
Q.133 Unattempt
Three students S1,S2 and S3 perform an experiment for determining the acceleration due to gravity (g) using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observation same as shown in the table.

(Least count of length = 0.1 m
least count for time = 0.1 s)
If E1,E2 and E3 are the percentage errors in 'g' for students 1, 2 and 3 respectively, then the minimum percentage error is obtained by student no._____.
[22 Jul 2021 Shift 2]
Three students S1,S2 and S3 perform an experiment for determining the acceleration due to gravity (g) using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observation same as shown in the table.

(Least count of length = 0.1 m
least count for time = 0.1 s)
If E1,E2 and E3 are the percentage errors in 'g' for students 1, 2 and 3 respectively, then the minimum percentage error is obtained by student no._____.
[22 Jul 2021 Shift 2]
Q.134 Correct
Q.134 In-correct
Q.134 Unattempt
The diameter of a spherical bob is measured using a Vernier callipers. 9 divisions of the main scale, in the vernier calipers, are equal to 10 divisions of vernier scale. One main scale division is 1‌mm. The main scale reading is 10‌mm and 8thdivision of vernier scale was found to coincide exactly with one of the main scale division. If the given vernier callipers has positive zero error of 0.04 cm, then the radius of the bob is .......... ×10−2‌cm.
[31 Aug 2021 Shift 2]
The diameter of a spherical bob is measured using a Vernier callipers. 9 divisions of the main scale, in the vernier calipers, are equal to 10 divisions of vernier scale. One main scale division is 1‌mm. The main scale reading is 10‌mm and 8thdivision of vernier scale was found to coincide exactly with one of the main scale division. If the given vernier callipers has positive zero error of 0.04 cm, then the radius of the bob is .......... ×10−2‌cm.
[31 Aug 2021 Shift 2]
Q.135 Correct
Q.135 In-correct
Q.135 Unattempt
If the length of the pendulum in pendulum clock increases by 0.1%, then the error in time per day is
[26 Aug 2021 Shift 2]
If the length of the pendulum in pendulum clock increases by 0.1%, then the error in time per day is
[26 Aug 2021 Shift 2]
Q.136 Correct
Q.136 In-correct
Q.136 Unattempt
In a screw gauge, 5th division of the circular scale coincides with the reference line when the ratchet is closed. There are 50 divisions on the circular scale, and the main scale moves by 0.5‌mm on a complete rotation. For a particular observation the reading on the main scale is 5‌mm and the 20th division of the circular scale coincides with reference line. Calculate the true reading.
[26 Aug 2021 Shift 1]
In a screw gauge, 5th division of the circular scale coincides with the reference line when the ratchet is closed. There are 50 divisions on the circular scale, and the main scale moves by 0.5‌mm on a complete rotation. For a particular observation the reading on the main scale is 5‌mm and the 20th division of the circular scale coincides with reference line. Calculate the true reading.
[26 Aug 2021 Shift 1]
Q.137 Correct
Q.137 In-correct
Q.137 Unattempt
Which of the following equations is dimensionally incorrect? Where, t = time, h = height, s = surface tension, θ = angle, ρ = density, a, r = radius, g = acceleration due to gravity, V = volume, p = pressure, W = work done, τ = torque,ε = permittivity, E = electric field, J = current density, L = length.
[31 Aug 2021 Shift 1]
Which of the following equations is dimensionally incorrect? Where, t = time, h = height, s = surface tension, θ = angle, ρ = density, a, r = radius, g = acceleration due to gravity, V = volume, p = pressure, W = work done, τ = torque,ε = permittivity, E = electric field, J = current density, L = length.
[31 Aug 2021 Shift 1]
Q.138 Correct
Q.138 In-correct
Q.138 Unattempt
If velocity [v], time [T] and force [F] are choosen as the base quantities, the dimensions of the mass will be
[31 Aug 2021 Shift 2]
If velocity [v], time [T] and force [F] are choosen as the base quantities, the dimensions of the mass will be
[31 Aug 2021 Shift 2]
Q.139 Correct
Q.139 In-correct
Q.139 Unattempt
If force (F), length (L) and time (T) are taken as the fundamental quantities. Then what will be the dimension of density:
[27 Aug 2021 Shift 2]
If force (F), length (L) and time (T) are taken as the fundamental quantities. Then what will be the dimension of density:
[27 Aug 2021 Shift 2]
Q.140 Correct
Q.140 In-correct
Q.140 Unattempt
Which of the following is not a dimensionless quantity?
[27 Aug 2021 Shift 1]
Which of the following is not a dimensionless quantity?
[27 Aug 2021 Shift 1]
Q.141 Correct
Q.141 In-correct
Q.141 Unattempt
Match List-I with List-II.

Choose the most appropriate answer from the options given below.
[26 Aug 2021 Shift 2]
Match List-I with List-II.

Choose the most appropriate answer from the options given below.
[26 Aug 2021 Shift 2]
Q.142 Correct
Q.142 In-correct
Q.142 Unattempt
If E,L,M and G denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimension of P in the formula P=EL2M−5G−2 is
[26 Aug 2021 Shift 1]
If E,L,M and G denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimension of P in the formula P=EL2M−5G−2 is
[26 Aug 2021 Shift 1]
Q.143 Correct
Q.143 In-correct
Q.143 Unattempt
If E and H represent the intensity of electric field and magnetising field respectively, then the unit of E / H will be
[27 Aug 2021 Shift 1]
If E and H represent the intensity of electric field and magnetising field respectively, then the unit of E / H will be
[27 Aug 2021 Shift 1]
Q.144 Correct
Q.144 In-correct
Q.144 Unattempt
Match List-I with List-II.

Choose the most appropriate answer from the options given below.
[27 Aug 2021 Shift 2]
Match List-I with List-II.

Choose the most appropriate answer from the options given below.
[27 Aug 2021 Shift 2]
Q.145 Correct
Q.145 In-correct
Q.145 Unattempt
Two resistors R1=(4±0.8)Ω and R2=(4±0.4)Ω are connected in parallel. The equivalent resistance of their parallel combination will be
[1 Sep 2021 Shift 2]
Two resistors R1=(4±0.8)Ω and R2=(4±0.4)Ω are connected in parallel. The equivalent resistance of their parallel combination will be
[1 Sep 2021 Shift 2]
Q.146 Correct
Q.146 In-correct
Q.146 Unattempt
A student determined Young's modulus of elasticity using the formula Y=
MgL3
4bd3δ
.
The value of g is taken to be 9.8m∕s2, without any significant error, his observations are as following.

Then, the fractional error in the measurement of Y is
[1 Sep 2021 Shift 2]
A student determined Young's modulus of elasticity using the formula Y=
MgL3
4bd3δ
.
The value of g is taken to be 9.8m∕s2, without any significant error, his observations are as following.

Then, the fractional error in the measurement of Y is
[1 Sep 2021 Shift 2]
Q.147 Correct
Q.147 In-correct
Q.147 Unattempt
If the screw on a screw-gauge is given six rotations, it moves by 3 mm on the main scale. If there are 50 divisions on the circular scale the least count of the screw gauge is:
[9 Jan. 2020 I]
If the screw on a screw-gauge is given six rotations, it moves by 3 mm on the main scale. If there are 50 divisions on the circular scale the least count of the screw gauge is:
[9 Jan. 2020 I]
Q.148 Correct
Q.148 In-correct
Q.148 Unattempt
For the four sets of three measured physical quantities as given below. Which of the following options is correct?
(A) A1=24.36,B1=0.0724,C1=256.2
(B) A2=24.44,B2=16.082,C2=240.2
(C) A3=25.2,B3=19.2812,C3=236.183
(D) AA=25,BA=236.191,CA=19.5
[9 Jan. 2020 II]
For the four sets of three measured physical quantities as given below. Which of the following options is correct?
(A) A1=24.36,B1=0.0724,C1=256.2
(B) A2=24.44,B2=16.082,C2=240.2
(C) A3=25.2,B3=19.2812,C3=236.183
(D) AA=25,BA=236.191,CA=19.5
[9 Jan. 2020 II]
Q.149 Correct
Q.149 In-correct
Q.149 Unattempt
A simple pendulum is being used to determine the value of gravitational acceleration g at a certain place. The length of the pendulum is 25.0 cm and a stop watch with 1 s resolution measures the time taken for 40 oscillations to be 50 s. The accuracy in g is:
[8 Jan. 2020 II]
A simple pendulum is being used to determine the value of gravitational acceleration g at a certain place. The length of the pendulum is 25.0 cm and a stop watch with 1 s resolution measures the time taken for 40 oscillations to be 50 s. The accuracy in g is:
[8 Jan. 2020 II]
Q.150 Correct
Q.150 In-correct
Q.150 Unattempt
Quantities The quantities x=1√µ0ε0,y=
E
B
 and z=
1
CR
 are defined where C -capacitance, R -Resistance, l -length, E -Electric field, B -magnetic field and ε0,µ0,− free space permittivity and permeability respectively. Then :
[Sep. 05,2020 (II)]
Quantities The quantities x=1√µ0ε0,y=
E
B
 and z=
1
CR
 are defined where C -capacitance, R -Resistance, l -length, E -Electric field, B -magnetic field and ε0,µ0,− free space permittivity and permeability respectively. Then :
[Sep. 05,2020 (II)]
Q.151 Correct
Q.151 In-correct
Q.151 Unattempt
Dimensional formula for thermal conductivity is (here K denotes the temperature :
[Sep. 04, 2020 (I)]
Dimensional formula for thermal conductivity is (here K denotes the temperature :
[Sep. 04, 2020 (I)]
Q.152 Correct
Q.152 In-correct
Q.152 Unattempt
A quantity x is given by (
IFv2
WL4
) in terms of moment of inertia I, force F, velocity v, work W and Length L. The dimensional formula for x is same as that of :
[Sep. 04, 2020 (II)]
A quantity x is given by (
IFv2
WL4
) in terms of moment of inertia I, force F, velocity v, work W and Length L. The dimensional formula for x is same as that of :
[Sep. 04, 2020 (II)]
Q.153 Correct
Q.153 In-correct
Q.153 Unattempt
Amount of solar energy received on the earth's surface per unit area per unit time is defined a solar constant. Dimension of solar constant is :
[Sep. 03, 2020 (II)]
Amount of solar energy received on the earth's surface per unit area per unit time is defined a solar constant. Dimension of solar constant is :
[Sep. 03, 2020 (II)]
Q.154 Correct
Q.154 In-correct
Q.154 Unattempt
If speed V, area A and force F are chosen as fundamental units, then the dimension of Young's modulus will be :
[Sep. 02, 2020 (I)]
If speed V, area A and force F are chosen as fundamental units, then the dimension of Young's modulus will be :
[Sep. 02, 2020 (I)]
Q.155 Correct
Q.155 In-correct
Q.155 Unattempt
If momentum (P), area (A) and time (T) are taken to be the fundamental quantities then the dimensional formula for energy is :
[Sep. 02, 2020 (II)]
If momentum (P), area (A) and time (T) are taken to be the fundamental quantities then the dimensional formula for energy is :
[Sep. 02, 2020 (II)]
Q.156 Correct
Q.156 In-correct
Q.156 Unattempt
A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displacement of 0.5 mm is noticed on the pitch scale. The nature of zero error involved, and the least count of the screw gauge, are respectively :
[Sep. 06, 2020 (I)]
A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displacement of 0.5 mm is noticed on the pitch scale. The nature of zero error involved, and the least count of the screw gauge, are respectively :
[Sep. 06, 2020 (I)]
Q.157 Correct
Q.157 In-correct
Q.157 Unattempt
The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is (
x
100
)% . If the relative errors in measuring the mass and the diameter are 6.0% and 1.5% respectively, the value of x is ______.
[NA Sep. 06, 2020 (I)]
The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is (
x
100
)% . If the relative errors in measuring the mass and the diameter are 6.0% and 1.5% respectively, the value of x is ______.
[NA Sep. 06, 2020 (I)]
Q.158 Correct
Q.158 In-correct
Q.158 Unattempt
A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the following four readings 5.50 mm, 5.55 mm, 5.45 mm, 5.65 mm, The average of these four reading is 5.5375 mm and the standard deviation of the data is 0.07395 mm. The average diameter of the pencil should therefore be recorded as :
[Sep. 06, 2020 (II)]
A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the following four readings 5.50 mm, 5.55 mm, 5.45 mm, 5.65 mm, The average of these four reading is 5.5375 mm and the standard deviation of the data is 0.07395 mm. The average diameter of the pencil should therefore be recorded as :
[Sep. 06, 2020 (II)]
Q.159 Correct
Q.159 In-correct
Q.159 Unattempt
A physical quantity z depends on four observables a,b,c and d, as z=
a2b
2
3
√cd3
. The percentages of error in the measurement of a,b,c and d are 2%,1.5%,4% and 2.5% respectively. The percentage of error in z is :
[Sep. 05, 2020 (I)]
A physical quantity z depends on four observables a,b,c and d, as z=
a2b
2
3
√cd3
. The percentages of error in the measurement of a,b,c and d are 2%,1.5%,4% and 2.5% respectively. The percentage of error in z is :
[Sep. 05, 2020 (I)]
Q.160 Correct
Q.160 In-correct
Q.160 Unattempt
Using screw gauge of pitch 0.1 cm and 50 divisions on its circular scale, the thickness of an object is measured. It should correctly be recorded as :
[Sep. 03, 2020 (I)]
Using screw gauge of pitch 0.1 cm and 50 divisions on its circular scale, the thickness of an object is measured. It should correctly be recorded as :
[Sep. 03, 2020 (I)]
Q.161 Correct
Q.161 In-correct
Q.161 Unattempt
The least count of the main scale of a vernier callipers is 1 mm. Its vernier scale is divided into 10 divisions and coincide with 9 divisions of the main scale. When jaws are touching each other, the 7th division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of a cylinder the zero of the vernier scale between 3.1 cm and 3.2 cm and 4th VSD coincides with a main scale division. The length of the cylinder is : (VSD is vernier scale division)
[Sep. 02, 2020 (I)]
The least count of the main scale of a vernier callipers is 1 mm. Its vernier scale is divided into 10 divisions and coincide with 9 divisions of the main scale. When jaws are touching each other, the 7th division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of a cylinder the zero of the vernier scale between 3.1 cm and 3.2 cm and 4th VSD coincides with a main scale division. The length of the cylinder is : (VSD is vernier scale division)
[Sep. 02, 2020 (I)]
Q.162 Correct
Q.162 In-correct
Q.162 Unattempt
The density of a material in SI unit is 128‌kg‌m−3. In certain units in which the unit of length is 25‌cm and the unit of mass is 50g, the numerical value of density of the material is:
[10 Jan. 2019 I]
The density of a material in SI unit is 128‌kg‌m−3. In certain units in which the unit of length is 25‌cm and the unit of mass is 50g, the numerical value of density of the material is:
[10 Jan. 2019 I]
Q.163 Correct
Q.163 In-correct
Q.163 Unattempt
Let l,r,c and v represent inductance, resistance, capacitance and voltage, respectively. The dimension of
l
rcv
 in SI units will be:
[12 Jan. 2019 II]
Let l,r,c and v represent inductance, resistance, capacitance and voltage, respectively. The dimension of
l
rcv
 in SI units will be:
[12 Jan. 2019 II]
Q.164 Correct
Q.164 In-correct
Q.164 Unattempt
The force of interaction between two atoms is given by F=αβ‌exp(−
x2
αkT
); where x is the distance, k is the Boltzmann constant and T is temperature and alpha and β are two constants. The dimensions of beta is:
[11 Jan. 2019 I ]
The force of interaction between two atoms is given by F=αβ‌exp(−
x2
αkT
); where x is the distance, k is the Boltzmann constant and T is temperature and alpha and β are two constants. The dimensions of beta is:
[11 Jan. 2019 I ]
Q.165 Correct
Q.165 In-correct
Q.165 Unattempt
If speed (V), acceleration (A) and force (F) are considered as fundamental units, the dimension of Young's modulus will be:
[11 Jan. 2019 II]
If speed (V), acceleration (A) and force (F) are considered as fundamental units, the dimension of Young's modulus will be:
[11 Jan. 2019 II]
Q.166 Correct
Q.166 In-correct
Q.166 Unattempt
A quantity f is given by f=√
hc5
G
 where c is speed of light, G universal gravitational constant and h is the Planck's constant. Dimension of f is that of :
[ 9 Jan. 2019 I]
A quantity f is given by f=√
hc5
G
 where c is speed of light, G universal gravitational constant and h is the Planck's constant. Dimension of f is that of :
[ 9 Jan. 2019 I]
Q.167 Correct
Q.167 In-correct
Q.167 Unattempt
Expression for time in terms of G (universal gravitational constant), h (Planck's constant) and c (speed of light) is proportional to:
[9 Jan. 2019 II]
Expression for time in terms of G (universal gravitational constant), h (Planck's constant) and c (speed of light) is proportional to:
[9 Jan. 2019 II]
Q.168 Correct
Q.168 In-correct
Q.168 Unattempt
The dimensions of stopping potential V0 in photoelectric effect in units of Planck's constant ' h ', speed of light ' c ' and Gravitational constant ' G ' and ampere A is:
[8 Jan. 2019 I]
The dimensions of stopping potential V0 in photoelectric effect in units of Planck's constant ' h ', speed of light ' c ' and Gravitational constant ' G ' and ampere A is:
[8 Jan. 2019 I]
Q.169 Correct
Q.169 In-correct
Q.169 Unattempt
The dimensions of
B2
2µ0
, where B is magnetic field and µ0 is the magnetic permeability of vacuum, is:
[8 Jan. 2019 II]
The dimensions of
B2
2µ0
, where B is magnetic field and µ0 is the magnetic permeability of vacuum, is:
[8 Jan. 2019 II]
Q.170 Correct
Q.170 In-correct
Q.170 Unattempt
The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure 5 µm diameter of a wire is:
[12 Jan. 2019 I]
The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure 5 µm diameter of a wire is:
[12 Jan. 2019 I]
Q.171 Correct
Q.171 In-correct
Q.171 Unattempt
The diameter and height of a cylinder are measured by a meter scale to be 12.6 ± 0.1 cm and 34.2 ± 0.1 cm, respectively. What will be the value of its volume in appropriate significant figures?
[10 Jan. 2019 II]
The diameter and height of a cylinder are measured by a meter scale to be 12.6 ± 0.1 cm and 34.2 ± 0.1 cm, respectively. What will be the value of its volume in appropriate significant figures?
[10 Jan. 2019 II]
Q.172 Correct
Q.172 In-correct
Q.172 Unattempt
The pitch and the number of divisions, on the circular scale for a given screw gauge are 0.5 mm and 100 respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies 3 division below the mean line.
The readings of the main scale and the circular scale, for a thin sheet, are 5.5 mm and 48 respectively, the thickness of the sheet is:
[9 Jan. 2019 II]
The pitch and the number of divisions, on the circular scale for a given screw gauge are 0.5 mm and 100 respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies 3 division below the mean line.
The readings of the main scale and the circular scale, for a thin sheet, are 5.5 mm and 48 respectively, the thickness of the sheet is:
[9 Jan. 2019 II]
Q.173 Correct
Q.173 In-correct
Q.173 Unattempt
Which of the following combinations has the dimension of electrical resistance (∈0 is the permittivity of vacuum and µ0 is the permeability of vacuum)?
[12 April 2019 I]
Which of the following combinations has the dimension of electrical resistance (∈0 is the permittivity of vacuum and µ0 is the permeability of vacuum)?
[12 April 2019 I]
Q.174 Correct
Q.174 In-correct
Q.174 Unattempt
In the formula X=5YZ2 , X and Z have dimensions of capacitance and magnetic field, respectively. What are the dimensions of Y in SI units ?
[10 April 2019 II]
In the formula X=5YZ2 , X and Z have dimensions of capacitance and magnetic field, respectively. What are the dimensions of Y in SI units ?
[10 April 2019 II]
Q.175 Correct
Q.175 In-correct
Q.175 Unattempt
In SI units, the dimensions of √
∈0
µ0
 is:
[8 April 2019 I ]
In SI units, the dimensions of √
∈0
µ0
 is:
[8 April 2019 I ]
Q.176 Correct
Q.176 In-correct
Q.176 Unattempt
In the density measurement of a cube, the mass and edge length are measured as (10.00 ± 0.10) kg and (0.10 ± 0.01) m, respectively. The error in the measurement of density is:
[9 April 2019 I]
In the density measurement of a cube, the mass and edge length are measured as (10.00 ± 0.10) kg and (0.10 ± 0.01) m, respectively. The error in the measurement of density is:
[9 April 2019 I]
Q.177 Correct
Q.177 In-correct
Q.177 Unattempt
The area of a square is 5.29 cm‌2. The area of 7 such squares taking into account the significant figures is:
[9 April 2019 II]
The area of a square is 5.29 cm‌2. The area of 7 such squares taking into account the significant figures is:
[9 April 2019 II]
Q.178 Correct
Q.178 In-correct
Q.178 Unattempt
In a simple pendulum experiment for determination of acceleration due to gravity (g), time taken for 20 oscillations is measured by using a watch of 1 second least count. The mean value of time taken comes out to be 30 s. The length of pendulum is measured by using a meter scale of least count 1 mm and the value obtained is 55.0 cm. The percentage error in the determination of g is close to :
[8 April 2019 II]
In a simple pendulum experiment for determination of acceleration due to gravity (g), time taken for 20 oscillations is measured by using a watch of 1 second least count. The mean value of time taken comes out to be 30 s. The length of pendulum is measured by using a meter scale of least count 1 mm and the value obtained is 55.0 cm. The percentage error in the determination of g is close to :
[8 April 2019 II]
Q.179 Correct
Q.179 In-correct
Q.179 Unattempt
The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants G, h and c. Which of the following correctly gives the Planck length?
[Online April 15, 2018]
The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants G, h and c. Which of the following correctly gives the Planck length?
[Online April 15, 2018]
Q.180 Correct
Q.180 In-correct
Q.180 Unattempt
The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is:
[2018]
The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is:
[2018]
Q.181 Correct
Q.181 In-correct
Q.181 Unattempt
The percentage errors in quantities P,Q,R and S are 0.5% 1%,3% and 1.5% respectively in the measurement of aphysical quantity A=
P3Q2
√RS
.
The maximum percentage error in the value of A will be
[Online April 16, 2018]
The percentage errors in quantities P,Q,R and S are 0.5% 1%,3% and 1.5% respectively in the measurement of aphysical quantity A=
P3Q2
√RS
.
The maximum percentage error in the value of A will be
[Online April 16, 2018]
Q.182 Correct
Q.182 In-correct
Q.182 Unattempt
The relative uncertainty in the period of a satellite orbiting around the earth is 10–2 . If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is
[Online April 16, 2018]
The relative uncertainty in the period of a satellite orbiting around the earth is 10–2 . If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is
[Online April 16, 2018]
Q.183 Correct
Q.183 In-correct
Q.183 Unattempt
The relative error in the determination of the surface area of a sphere is a. Then the relative error in the determination of its volume is
[Online April 15, 2018]
The relative error in the determination of the surface area of a sphere is a. Then the relative error in the determination of its volume is
[Online April 15, 2018]
Q.184 Correct
Q.184 In-correct
Q.184 Unattempt
In a screw gauge, 5 complete rotations of the screw cause it to move a linear distance of 0.25 cm. There are 100 circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of 4 main scale divisions and 30 circular scale divisions. Assuming negligible zero error, the thickness of the wire is:
[Online April 15, 2018]
In a screw gauge, 5 complete rotations of the screw cause it to move a linear distance of 0.25 cm. There are 100 circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of 4 main scale divisions and 30 circular scale divisions. Assuming negligible zero error, the thickness of the wire is:
[Online April 15, 2018]
Q.185 Correct
Q.185 In-correct
Q.185 Unattempt
Time (T), velocity (C) and angular momentum (h) are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be :
[Online April 8, 2017]
Time (T), velocity (C) and angular momentum (h) are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be :
[Online April 8, 2017]
Q.186 Correct
Q.186 In-correct
Q.186 Unattempt
The following observations were taken for determining surface tensiton T of water by capillary method :
Diameter of capilary, D=1.25×10−2m
rise of water, h=1.45×10−2m
Using g=9.80m∕s2 and the simplified relation T=
rhg
2
×103N∕m, the possible error in surface tension is closest to :
[2017]
The following observations were taken for determining surface tensiton T of water by capillary method :
Diameter of capilary, D=1.25×10−2m
rise of water, h=1.45×10−2m
Using g=9.80m∕s2 and the simplified relation T=
rhg
2
×103N∕m, the possible error in surface tension is closest to :
[2017]
Q.187 Correct
Q.187 In-correct
Q.187 Unattempt
A physical quantity P is described by the relation P=a
1
2
b2c3d−4
If the relative errors in the measurement of a, b, c and d respectively, are 2%, 1%, 3% and 5%, then the relative error in P will be :
[Online April 9, 2017]
A physical quantity P is described by the relation P=a
1
2
b2c3d−4
If the relative errors in the measurement of a, b, c and d respectively, are 2%, 1%, 3% and 5%, then the relative error in P will be :
[Online April 9, 2017]
Q.188 Correct
Q.188 In-correct
Q.188 Unattempt
A, B, C and D are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation AD = C ln (BD) holds true. Then which of the combination is not a meaningful quantity ?
[Online April 10, 2016]
A, B, C and D are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation AD = C ln (BD) holds true. Then which of the combination is not a meaningful quantity ?
[Online April 10, 2016]
Q.189 Correct
Q.189 In-correct
Q.189 Unattempt
In the following 'I' refers to current and other symbols have their usual meaning, Choose the option that corresponds to the dimensions of electrical conductivity :
[Online April 9, 2016]
In the following 'I' refers to current and other symbols have their usual meaning, Choose the option that corresponds to the dimensions of electrical conductivity :
[Online April 9, 2016]
Q.190 Correct
Q.190 In-correct
Q.190 Unattempt
A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that wen the two jaws of the screw gauge are brought in contact, the 45th division coincides with the main scale line and the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is 0.5 mm and the 25th division coincides with the main scale line?
[2016]
A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that wen the two jaws of the screw gauge are brought in contact, the 45th division coincides with the main scale line and the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is 0.5 mm and the 25th division coincides with the main scale line?
[2016]
Q.191 Correct
Q.191 In-correct
Q.191 Unattempt
A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s, and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be:
[2016]
A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s, and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be:
[2016]
Q.192 Correct
Q.192 In-correct
Q.192 Unattempt
If electronic charge e, electron mass m, speed of light in vacuum c and Planck’s constant h are taken as fundamental quantities, the permeability of vacuum µ0 can be expressed in units of :
[Online April 11, 2015]
If electronic charge e, electron mass m, speed of light in vacuum c and Planck’s constant h are taken as fundamental quantities, the permeability of vacuum µ0 can be expressed in units of :
[Online April 11, 2015]
Q.193 Correct
Q.193 In-correct
Q.193 Unattempt
If the capacitance of a nanocapacitor is measured in terms of a unit ‘u’ made by combining the electric charge ‘e’, Bohr radius ‘a0’ , Planck’s constant ‘h’ and speed of light ‘c’ then:
[Online April 10, 2015]
If the capacitance of a nanocapacitor is measured in terms of a unit ‘u’ made by combining the electric charge ‘e’, Bohr radius ‘a0’ , Planck’s constant ‘h’ and speed of light ‘c’ then:
[Online April 10, 2015]
Q.194 Correct
Q.194 In-correct
Q.194 Unattempt
The period of oscillation of a simple pendulum is T=2π√
L
g
. Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1s resolution. The accuracy in the determination of g is :
[2015]
The period of oscillation of a simple pendulum is T=2π√
L
g
. Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1s resolution. The accuracy in the determination of g is :
[2015]
Q.195 Correct
Q.195 In-correct
Q.195 Unattempt
Diameter of a steel ball is measured using a Vernier callipers which has divisions of 0.1 cm on its main scale (MS) and 10 divisions of its vernier scale (VS) match 9 divisions on the main scale. Three such measurements for a ball are given as:


If the zero error is – 0.03 cm, then mean corrected diameter is:
[Online April 10, 2015]
Diameter of a steel ball is measured using a Vernier callipers which has divisions of 0.1 cm on its main scale (MS) and 10 divisions of its vernier scale (VS) match 9 divisions on the main scale. Three such measurements for a ball are given as:
[Online April 10, 2015]

If the zero error is – 0.03 cm, then mean corrected diameter is:
Q.196 Correct
Q.196 In-correct
Q.196 Unattempt
From the following combinations of physical constants (expressed through their usual symbols) the only combination, that would have the same value in different systems of units, is:
[Online April 12, 2014]
From the following combinations of physical constants (expressed through their usual symbols) the only combination, that would have the same value in different systems of units, is:
[Online April 12, 2014]
Q.197 Correct
Q.197 In-correct
Q.197 Unattempt
In terms of resistance R and time T, the dimensions of ratio
µ
ε
 of the permeability m and permittivity ε is:
[Online April 11, 2014]
In terms of resistance R and time T, the dimensions of ratio
µ
ε
 of the permeability m and permittivity ε is:
[Online April 11, 2014]
Q.198 Correct
Q.198 In-correct
Q.198 Unattempt
The current voltage relation of a diode is given by I=(e1000V∕T−1)‌mA, where the applied voltage V is in volts and the temperature T is in degree kelvin. If a student makes an error measuring ±0.01V while measuring the current of 5 mA at 300 K, what will be the error in the value of current in mA?
[2014]
The current voltage relation of a diode is given by I=(e1000V∕T−1)‌mA, where the applied voltage V is in volts and the temperature T is in degree kelvin. If a student makes an error measuring ±0.01V while measuring the current of 5 mA at 300 K, what will be the error in the value of current in mA?
[2014]
Q.199 Correct
Q.199 In-correct
Q.199 Unattempt
A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?
[2014]
A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?
[2014]
Q.200 Correct
Q.200 In-correct
Q.200 Unattempt
Match List - I (Event) with List-II (Order of the time interval for happening of the event) and select the correct option from the options given below the lists:

[Online April 19, 2014]
Match List - I (Event) with List-II (Order of the time interval for happening of the event) and select the correct option from the options given below the lists:

[Online April 19, 2014]
Q.201 Correct
Q.201 In-correct
Q.201 Unattempt
In the experiment of calibration of voltmeter, a standard cell of e.m.f. 1.1 volt is balanced against 440 cm of potential wire. The potential difference across the ends of resistance is found to balance against 220 cm of the wire. The corresponding reading of voltmeter is 0.5 volt. The error in the reading of voltmeter will be:
[Online April 12, 2014]
In the experiment of calibration of voltmeter, a standard cell of e.m.f. 1.1 volt is balanced against 440 cm of potential wire. The potential difference across the ends of resistance is found to balance against 220 cm of the wire. The corresponding reading of voltmeter is 0.5 volt. The error in the reading of voltmeter will be:
[Online April 12, 2014]
Q.202 Correct
Q.202 In-correct
Q.202 Unattempt
An experiment is performed to obtain the value of acceleration due to gravity g by using a simple pendulum of length L. In this experiment time for 100 oscillations is measured by using a watch of 1 second least count and the value is 90.0 seconds. The length L is measured by using a meter scale of least count 1 mm and the value is 20.0 cm. The error in the determination of g would be:
[Online April 9, 2014]
An experiment is performed to obtain the value of acceleration due to gravity g by using a simple pendulum of length L. In this experiment time for 100 oscillations is measured by using a watch of 1 second least count and the value is 90.0 seconds. The length L is measured by using a meter scale of least count 1 mm and the value is 20.0 cm. The error in the determination of g would be:
[Online April 9, 2014]
Q.203 Correct
Q.203 In-correct
Q.203 Unattempt
A metal sample carrying a current along X -axis with density Jx is subjected to a magnetic field Bz (along z-axis). The electric field Ey developed along Y-axis is directly proportional to Jx as well as Bz. The constant of proportionality has SI unit
[Online April 25, 2013]
A metal sample carrying a current along X -axis with density Jx is subjected to a magnetic field Bz (along z-axis). The electric field Ey developed along Y-axis is directly proportional to Jx as well as Bz. The constant of proportionality has SI unit
[Online April 25, 2013]
Q.204 Correct
Q.204 In-correct
Q.204 Unattempt
Let ∈0 denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then:
[2013]
Let ∈0 denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then:
[2013]
Q.205 Correct
Q.205 In-correct
Q.205 Unattempt
If the time period t of the oscillation of a drop of liquid of density d, radius r, vibrating under surface tension s is given by the formula t=√r2bscda∕2. It is observed that the time period is directly proportional to √
d
s
. The value of b should therefore be:
[ Online April 23, 2013]
If the time period t of the oscillation of a drop of liquid of density d, radius r, vibrating under surface tension s is given by the formula t=√r2bscda∕2. It is observed that the time period is directly proportional to √
d
s
. The value of b should therefore be:
[ Online April 23, 2013]
Q.206 Correct
Q.206 In-correct
Q.206 Unattempt
The dimensions of angular momentum, latent heat and capacitance are, respectively.
[Online April 22, 2013]
The dimensions of angular momentum, latent heat and capacitance are, respectively.
[Online April 22, 2013]
Q.207 Correct
Q.207 In-correct
Q.207 Unattempt
Given that K = energy, V = velocity, T = time. If they are chosen as the fundamental units, then what is dimensional formula for surface tension?
[Online May 7, 2012]
Given that K = energy, V = velocity, T = time. If they are chosen as the fundamental units, then what is dimensional formula for surface tension?
[Online May 7, 2012]
Q.208 Correct
Q.208 In-correct
Q.208 Unattempt
Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is
[2012]
Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is
[2012]
Q.209 Correct
Q.209 In-correct
Q.209 Unattempt
A spectrometer gives the following reading when used to measure the angle of a prism.
Main scale reading : 58.5 degree
Vernier scale reading : 09 divisions
Given that 1 division on main scale corresponds to 0.5
degree. Total divisions on the Vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data is
[2012]
A spectrometer gives the following reading when used to measure the angle of a prism.
Main scale reading : 58.5 degree
Vernier scale reading : 09 divisions
Given that 1 division on main scale corresponds to 0.5
degree. Total divisions on the Vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data is
[2012]
Q.210 Correct
Q.210 In-correct
Q.210 Unattempt
N divisions on the main scale of a vernier calliper coincide with (N + 1) divisions of the vernier scale. If each division of main scale is ‘a’ units, then the least count of the instrument is
[Online May 19, 2012]
N divisions on the main scale of a vernier calliper coincide with (N + 1) divisions of the vernier scale. If each division of main scale is ‘a’ units, then the least count of the instrument is
[Online May 19, 2012]
Q.211 Correct
Q.211 In-correct
Q.211 Unattempt
A student measured the diameter of a wire using a screw gauge with the least count 0.001 cm and listed the measurements. The measured value should be recorded as
[Online May 12, 2012]
A student measured the diameter of a wire using a screw gauge with the least count 0.001 cm and listed the measurements. The measured value should be recorded as
[Online May 12, 2012]
Q.212 Correct
Q.212 In-correct
Q.212 Unattempt
A screw gauge gives the following reading when used to measure the diameter of a wire.
Main scale reading : 0 mm
Circular scale reading : 52 divisions
Given that 1mm on main scale corresponds to 100 divisions of the circular scale. The diameter of wire from the above data is
[2011]
A screw gauge gives the following reading when used to measure the diameter of a wire.
Main scale reading : 0 mm
Circular scale reading : 52 divisions
Given that 1mm on main scale corresponds to 100 divisions of the circular scale. The diameter of wire from the above data is
[2011]
Q.213 Correct
Q.213 In-correct
Q.213 Unattempt
The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1×10–3 are
[2010]
The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1×10–3 are
[2010]
Q.214 Correct
Q.214 In-correct
Q.214 Unattempt
In an experiment the angles are required to be measured using an instrument, 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half- a degree (= 0.5°), then the least count of the instrument is:
[2009]
In an experiment the angles are required to be measured using an instrument, 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half- a degree (= 0.5°), then the least count of the instrument is:
[2009]
Q.215 Correct
Q.215 In-correct
Q.215 Unattempt
The dimensions of magnetic field in M, L, T and C (coulomb) is given as
[2008]
The dimensions of magnetic field in M, L, T and C (coulomb) is given as
[2008]
Q.216 Correct
Q.216 In-correct
Q.216 Unattempt
A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 ms‌–1. The magnitude of its momentum is recorded as
[2008]
A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 ms‌–1. The magnitude of its momentum is recorded as
[2008]
Q.217 Correct
Q.217 In-correct
Q.217 Unattempt
Two full turns of the circular scale of a screw gauge cover a distance of 1mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of – 0.03 mm. While measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is
[2008]
Two full turns of the circular scale of a screw gauge cover a distance of 1mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of – 0.03 mm. While measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is
[2008]
Q.218 Correct
Q.218 In-correct
Q.218 Unattempt
Which of the following units denotes the dimension
ML2
Q2
, where Q denotes the electric charge?
[2006]
Which of the following units denotes the dimension
ML2
Q2
, where Q denotes the electric charge?
[2006]
Q.219 Correct
Q.219 In-correct
Q.219 Unattempt
Out of the following pair, which one does NOT have identical dimensions ?
[2005]
Out of the following pair, which one does NOT have identical dimensions ?
[2005]
Q.220 Correct
Q.220 In-correct
Q.220 Unattempt
Which one of the following represents the correct dimensions of the coefficient of viscosity?
[2004]
Which one of the following represents the correct dimensions of the coefficient of viscosity?
[2004]
Q.221 Correct
Q.221 In-correct
Q.221 Unattempt
Dimensions of
1
µoεo
, where symbols have their usual meaning, are
[2003]
Dimensions of
1
µoεo
, where symbols have their usual meaning, are
[2003]
Q.222 Correct
Q.222 In-correct
Q.222 Unattempt
The physical quantities not having same dimensions are
[2003]
The physical quantities not having same dimensions are
[2003]
Q.223 Correct
Q.223 In-correct
Q.223 Unattempt
Identify the pair whose dimensions are equal
[2002]
Identify the pair whose dimensions are equal
[2002]
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