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Solution
Q.1 Correct
Q.1 In-correct
Q.1 Unattempt
If E, M, J and G respectively denote energy, mass, angular momentum and universal gravitational constant, the quantity, which has the same dimensions as the dimensions of
EJ2
M5G2

©
If E, M, J and G respectively denote energy, mass, angular momentum and universal gravitational constant, the quantity, which has the same dimensions as the dimensions of
EJ2
M5G2

©
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt
The work done in moving an object from origin to a point whose position vector is r=3
^
i
+2
^
j
−5
^
k
 by a force F=2
^
i
−
^
j
−
^
k
 is
©
The work done in moving an object from origin to a point whose position vector is r=3
^
i
+2
^
j
−5
^
k
 by a force F=2
^
i
−
^
j
−
^
k
 is
©
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt
A particle is projected from the ground with an initial speed of v at an angle of projection θ. The average velocity of the particle between its time of projection and time it reaches highest point of trajectory is
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A particle is projected from the ground with an initial speed of v at an angle of projection θ. The average velocity of the particle between its time of projection and time it reaches highest point of trajectory is
©
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt
Two wooden blocks of masses M and m are placed on a smooth horizontal surface as shown in figure. If a force P is applied to the system as shown in figure such that the mass m remains stationary with respect to block of mass M, then the magnitude of the force P is


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Two wooden blocks of masses M and m are placed on a smooth horizontal surface as shown in figure. If a force P is applied to the system as shown in figure such that the mass m remains stationary with respect to block of mass M, then the magnitude of the force P is


©
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt
A ball at rest is dropped from a height of 12. It losses 25% of its kinetic energy on striking the ground and bounces back to a height ‘h’. Then value of ‘h’ is
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A ball at rest is dropped from a height of 12. It losses 25% of its kinetic energy on striking the ground and bounces back to a height ‘h’. Then value of ‘h’ is
©
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt
Two bodies of mass 4kg and 5kg are moving along east and north directions with velocities 5m∕s and 3m∕s respectively. Magnitude of the velocity of centre of mass of the system is
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Two bodies of mass 4kg and 5kg are moving along east and north directions with velocities 5m∕s and 3m∕s respectively. Magnitude of the velocity of centre of mass of the system is
©
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt
A mass of 2.9 kg is suspended from a string of length 50 cm and is at rest. Another body of mass 100 g, which is moving horizontally with a velocity of 150 m/s strikes and sticks to it. Subsequently when the string makes an angle of 60° with the vertical, the tension in the string is (g = 10 m /s‌2)
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A mass of 2.9 kg is suspended from a string of length 50 cm and is at rest. Another body of mass 100 g, which is moving horizontally with a velocity of 150 m/s strikes and sticks to it. Subsequently when the string makes an angle of 60° with the vertical, the tension in the string is (g = 10 m /s‌2)
©
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt
The upper half of an inclined plane with an angle of inclination ϕ, is smooth while the lower half is rough. A body starting from rest at the top of the inclined plane comes to rest at the bottom of the inclined plane. Then the coefficient of frictionfor the lower half is
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The upper half of an inclined plane with an angle of inclination ϕ, is smooth while the lower half is rough. A body starting from rest at the top of the inclined plane comes to rest at the bottom of the inclined plane. Then the coefficient of frictionfor the lower half is
©
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt
Moment of inertia of a body about an axis is 4 kg-m‌2 . The body is initially at rest and a torque of 8 N-m starts acting on it along the same axis. Work done by the torque in 20 s, in joules, is
©
Moment of inertia of a body about an axis is 4 kg-m‌2 . The body is initially at rest and a torque of 8 N-m starts acting on it along the same axis. Work done by the torque in 20 s, in joules, is
©
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt
A uniform circular disc of radius R, lying on a frictionless horizontal plane is rotating with an angular velocity 'ω' about is its own axis. Another identical circular disc is gently placed on the top of the first disc coaxially. The loss in rotational kinetic energy due to friction between the two discs, as they acquire common angular velocity is ( I is moment of inertia of the disc)
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A uniform circular disc of radius R, lying on a frictionless horizontal plane is rotating with an angular velocity 'ω' about is its own axis. Another identical circular disc is gently placed on the top of the first disc coaxially. The loss in rotational kinetic energy due to friction between the two discs, as they acquire common angular velocity is ( I is moment of inertia of the disc)
©
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt
The gravitational force acting on a particle, due to a solid sphere of uniform density and radius R, at a distance of 3R from the centre of the sphere is F1. A spherical hole of radius ( R∕2 ) is now made in the sphere as shown in the figure. The sphere with hole now exerts a force F2 on the same particle. Ratio of F1 and F2 is




The gravitational force acting on a particle, due to a solid sphere of uniform density and radius R, at a distance of 3R from the centre of the sphere is F1. A spherical hole of radius ( R∕2 ) is now made in the sphere as shown in the figure. The sphere with hole now exerts a force F2 on the same particle. Ratio of F1 and F2 is



©
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt
Two particles A and B of masses ' m ' and 2m ' are suspended from massless springs of force constants K1 and K2. During their oscillation, if their maximum velocities are equal, then the ratio of amplitudes of A and B is
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Two particles A and B of masses ' m ' and 2m ' are suspended from massless springs of force constants K1 and K2. During their oscillation, if their maximum velocities are equal, then the ratio of amplitudes of A and B is
©
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt
A tension of 20N is applied to a copper wire of cross sectional area 0.01cm2, Young's modulus of copper is 1.1×1011N∕m2 and Poisson's ratio is 0.32. The decrease in cross sectional area of the wire is
©
A tension of 20N is applied to a copper wire of cross sectional area 0.01cm2, Young's modulus of copper is 1.1×1011N∕m2 and Poisson's ratio is 0.32. The decrease in cross sectional area of the wire is
©
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt
A capillary tube of radius ' r ' is immersed in water and water rises to a height of ' h '. Mass of water in the capillary tube is 5×10−3kg. The same capillary tube is now immersed in a liquid whose surface tension is √2 times the surface tension of water. The angle of contact between the capillary tube and this liquid is 45°. The mass of liquid which rises into the capillary tube now is, (in kg )
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A capillary tube of radius ' r ' is immersed in water and water rises to a height of ' h '. Mass of water in the capillary tube is 5×10−3kg. The same capillary tube is now immersed in a liquid whose surface tension is √2 times the surface tension of water. The angle of contact between the capillary tube and this liquid is 45°. The mass of liquid which rises into the capillary tube now is, (in kg )
©
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt
The terminal velocity of a liquid drop of radius ' r ' falling through air is v. If two such drops are combined to form a bigger drop, the terminal velocity with which the bigger drop falls through air is (ignore any buoyant force due to air)
©
The terminal velocity of a liquid drop of radius ' r ' falling through air is v. If two such drops are combined to form a bigger drop, the terminal velocity with which the bigger drop falls through air is (ignore any buoyant force due to air)
©
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt
A glass flask of volume one litre is filled completely with mercury at 0°C. The flask is now heated to 100°C. Coefficient of volume expansion of mercury is 1.82×10−4∕°C andcoefficient of linear expansion of glass is 0.1×10−4∕°C . During this process, amount of mercury which overflows is
©
A glass flask of volume one litre is filled completely with mercury at 0°C. The flask is now heated to 100°C. Coefficient of volume expansion of mercury is 1.82×10−4∕°C andcoefficient of linear expansion of glass is 0.1×10−4∕°C . During this process, amount of mercury which overflows is
©
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt
On a temperature scale Y, water freezes at −160°Y and boils at −50°Y. On this Y scale, a temperature of 340K is
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On a temperature scale Y, water freezes at −160°Y and boils at −50°Y. On this Y scale, a temperature of 340K is
©
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt
Three moles of an ideal monoatomic gas undergoes a cyclic process as shown in the figure. The temperature of the gas in different states marked as 1, 2, 3 and 4 are 400 K, 700 K, 2500 K and 1100 K respectively. The work done by the gas during the process 1-2-3-4-1 is (universal gas constant is R)


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Three moles of an ideal monoatomic gas undergoes a cyclic process as shown in the figure. The temperature of the gas in different states marked as 1, 2, 3 and 4 are 400 K, 700 K, 2500 K and 1100 K respectively. The work done by the gas during the process 1-2-3-4-1 is (universal gas constant is R)


©
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt
Efficiency of a heat engine whose sink is at temperature of 300 K is 40%. To increase the efficiency to 60%, keeping the sink temperature constant, the source temperature must be increased by
©
Efficiency of a heat engine whose sink is at temperature of 300 K is 40%. To increase the efficiency to 60%, keeping the sink temperature constant, the source temperature must be increased by
©
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt
Two bodies A and B of equal surface area have thermal emissivities of 0.01 and 0.81 respectively. The two bodies are radiating energy at the same rate. Maximum energy is radiated from the two bodies A and B at wavelengths λA and λB respectively. Difference in these two wavelengths is 1µm. If the temperature of the body A is 5802K, then value of λB is
©
Two bodies A and B of equal surface area have thermal emissivities of 0.01 and 0.81 respectively. The two bodies are radiating energy at the same rate. Maximum energy is radiated from the two bodies A and B at wavelengths λA and λB respectively. Difference in these two wavelengths is 1µm. If the temperature of the body A is 5802K, then value of λB is
©
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt
An air column in a tube 32 cm long, closed at one end, is in resonance with a tuning fork. The air column in another tube, open at both ends, of length 66 cm is in resonance with another tuning fork. When these two tuning forks are sounded together, they produce 8 beats per second. Then the frequencies of the two tuning forks are, (Consider fundamental frequencies only)
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An air column in a tube 32 cm long, closed at one end, is in resonance with a tuning fork. The air column in another tube, open at both ends, of length 66 cm is in resonance with another tuning fork. When these two tuning forks are sounded together, they produce 8 beats per second. Then the frequencies of the two tuning forks are, (Consider fundamental frequencies only)
©
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt
A source of sound of frequency 640Hz is moving at a velocity of
100
3
m∕s along a road, and is at an instant 30m away from a point A on the road (as shown in figure). A person standing at O,40m away from the road hears sound of apparent frequency v′. The value of v′ is (velocity of sound =340m∕s )



©
A source of sound of frequency 640Hz is moving at a velocity of
100
3
m∕s along a road, and is at an instant 30m away from a point A on the road (as shown in figure). A person standing at O,40m away from the road hears sound of apparent frequency v′. The value of v′ is (velocity of sound =340m∕s )



©
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt
The two surfaces of a concave lens, made of glass of refractive index 1.5 have the same radii of curvature R. It is now immersed in a medium of refractive index 1.75, then the lens
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The two surfaces of a concave lens, made of glass of refractive index 1.5 have the same radii of curvature R. It is now immersed in a medium of refractive index 1.75, then the lens
©
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt
A microscope consists of an objective of focal length 1.9 cm and eye piece of focal length 5 cm. The two lenses are kept at a distance of 10.5 cm. If the image is to be formed at the least distance of distinct vision, the distance at which the object is to be placed before the objective is (least distance of distinct vision is 25 cm)
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A microscope consists of an objective of focal length 1.9 cm and eye piece of focal length 5 cm. The two lenses are kept at a distance of 10.5 cm. If the image is to be formed at the least distance of distinct vision, the distance at which the object is to be placed before the objective is (least distance of distinct vision is 25 cm)
©
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt
Fresnel diffraction is produced due to light rays falling on a small obstacle. The intensity of light at a point on a screen beyond an obstacle depends on
©
Fresnel diffraction is produced due to light rays falling on a small obstacle. The intensity of light at a point on a screen beyond an obstacle depends on
©
Q.26 Correct
Q.26 In-correct
Q.26 Unattempt
A short bar magnet having magnetic moment 4Am2, placed in a vibrating magnetometer, vibrates with a time period of 8s. Another short bar magnet having a magnetic moment 8Am2 vibrates with a time period of 6s. If the moment of inertia of the second magnet is 9×10−2kg−m2 , the moment of inertia of the first magnet is
(assume that both magnets are kept in the same uniform magnetic induction field.)
©
A short bar magnet having magnetic moment 4Am2, placed in a vibrating magnetometer, vibrates with a time period of 8s. Another short bar magnet having a magnetic moment 8Am2 vibrates with a time period of 6s. If the moment of inertia of the second magnet is 9×10−2kg−m2 , the moment of inertia of the first magnet is
(assume that both magnets are kept in the same uniform magnetic induction field.)
©
Q.27 Correct
Q.27 In-correct
Q.27 Unattempt
Two short bar magnets have their magnetic moments 1.2Am2 and 1.0Am2. They are placed on a horizontal table parallel to each other at a distance of 20cm between their centres, such that their north poles pointing towards geographic south. They have common magnetic equatorial line. Horizontal component of earth's field is 3.6×10−5T. Then, the resultant horizontal magnetic induction at mid point of the line joining their centers is (
µ0
4π
=10−7N∕m)
©
Two short bar magnets have their magnetic moments 1.2Am2 and 1.0Am2. They are placed on a horizontal table parallel to each other at a distance of 20cm between their centres, such that their north poles pointing towards geographic south. They have common magnetic equatorial line. Horizontal component of earth's field is 3.6×10−5T. Then, the resultant horizontal magnetic induction at mid point of the line joining their centers is (
µ0
4π
=10−7N∕m)
©
Q.28 Correct
Q.28 In-correct
Q.28 Unattempt
A deflection magnetometer is adjusted and a magnet of magnetic moment M is placed on it in the usual manner and the observed deflection is θ. The period of oscillation of the needle before settling of the deflection is T. When the magnet is removed, the period of oscillation of the needle is T0 before settling to 0°−0°. If the earth's induced magnetic field is BH , the relation between T and T0 is
©
A deflection magnetometer is adjusted and a magnet of magnetic moment M is placed on it in the usual manner and the observed deflection is θ. The period of oscillation of the needle before settling of the deflection is T. When the magnet is removed, the period of oscillation of the needle is T0 before settling to 0°−0°. If the earth's induced magnetic field is BH , the relation between T and T0 is
©
Q.29 Correct
Q.29 In-correct
Q.29 Unattempt
Two metal plates each of area 'A' form a parallel plate capacitor with air in between the plates. The distance between the plates is ' d '. A metal plate of thickness
d
2
 and ofsame area A is inserted between the plates to form two capacitors of capacitances C1 and C2 as shown in the figure. If the effective capacitance of the two capacitors is C′ and the capacitance of the capacitor initially is C, then
C′
C
 is

©
Two metal plates each of area 'A' form a parallel plate capacitor with air in between the plates. The distance between the plates is ' d '. A metal plate of thickness
d
2
 and ofsame area A is inserted between the plates to form two capacitors of capacitances C1 and C2 as shown in the figure. If the effective capacitance of the two capacitors is C′ and the capacitance of the capacitor initially is C, then
C′
C
 is

©
Q.30 Correct
Q.30 In-correct
Q.30 Unattempt
In the circuit shown in the figure, the current ‘I’ is



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In the circuit shown in the figure, the current ‘I’ is



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Q.31 Correct
Q.31 In-correct
Q.31 Unattempt
In the meter bridge experiment, the length AB of the wire is 1 m. The resistors X and Y have values 5 Ω and 2 Ω respectively. When a shunt resistance S is connected to X, the balancing point is found to be 0.625 m from A. Then, the resistance of the shunt is


©
In the meter bridge experiment, the length AB of the wire is 1 m. The resistors X and Y have values 5 Ω and 2 Ω respectively. When a shunt resistance S is connected to X, the balancing point is found to be 0.625 m from A. Then, the resistance of the shunt is


©
Q.32 Correct
Q.32 In-correct
Q.32 Unattempt
The ends of an element of zinc wire are kept at a small temperature difference ∆T and a small current (I) is passed through the wire.
Then, the heat developed per unit time
©
The ends of an element of zinc wire are kept at a small temperature difference ∆T and a small current (I) is passed through the wire.
Then, the heat developed per unit time
©
Q.33 Correct
Q.33 In-correct
Q.33 Unattempt
A series LCR circuit is connected across a source of alternating emf of changing frequency and resonates at frequency f0. Keeping capacitance constant, if the inductance (L) is increased by √3 times and resistance is increased (R) by 1.4 times, the resonant frequency now is
©
A series LCR circuit is connected across a source of alternating emf of changing frequency and resonates at frequency f0. Keeping capacitance constant, if the inductance (L) is increased by √3 times and resistance is increased (R) by 1.4 times, the resonant frequency now is
©
Q.34 Correct
Q.34 In-correct
Q.34 Unattempt
The sensitivity of a galvanometer that measures current is decreased by
1
40
 times by using shunt resistance of 10Ω. Then, the value of the resistance of the galvanometer is
©
The sensitivity of a galvanometer that measures current is decreased by
1
40
 times by using shunt resistance of 10Ω. Then, the value of the resistance of the galvanometer is
©
Q.35 Correct
Q.35 In-correct
Q.35 Unattempt
Initially a photon of wavelength λ1 falls on photocathode and emits an electron of maximum energy E1. If the wavelength of the incident photon is changed to λ2, the maximum energy of the electron emitted becomes E2. Then value of hc(h= Planck's constant, c= velocity of light) is
©
Initially a photon of wavelength λ1 falls on photocathode and emits an electron of maximum energy E1. If the wavelength of the incident photon is changed to λ2, the maximum energy of the electron emitted becomes E2. Then value of hc(h= Planck's constant, c= velocity of light) is
©
Q.36 Correct
Q.36 In-correct
Q.36 Unattempt
The work function of a metal is 2eV. If a radiation of wavelength 3000Å is incident on it, the maximum kinetic energy of the emitted photoelectrons is (Planck's constant h=6.6×10−34Js; velocity of quad light c=3×108m∕s;1eV=1.6×10−19J)
©
The work function of a metal is 2eV. If a radiation of wavelength 3000Å is incident on it, the maximum kinetic energy of the emitted photoelectrons is (Planck's constant h=6.6×10−34Js; velocity of quad light c=3×108m∕s;1eV=1.6×10−19J)
©
Q.37 Correct
Q.37 In-correct
Q.37 Unattempt
The radius of ‌72Te125 nucleus is 6 fermi. The radius of 13Al27 nucleus in meters is
©
The radius of ‌72Te125 nucleus is 6 fermi. The radius of 13Al27 nucleus in meters is
©
Q.38 Correct
Q.38 In-correct
Q.38 Unattempt
AU235 nuclear reactor generates energy at a rate of 3.70×107J∕s. Each fission liberates 185MeV useful energy. If the reactor has to operate for 144×104s, then, the mass of the fuel needed is (Assume Avogadro's number =6×1023mol−1,1eV=1.6×10−19J)
©
AU235 nuclear reactor generates energy at a rate of 3.70×107J∕s. Each fission liberates 185MeV useful energy. If the reactor has to operate for 144×104s, then, the mass of the fuel needed is (Assume Avogadro's number =6×1023mol−1,1eV=1.6×10−19J)
©
Q.39 Correct
Q.39 In-correct
Q.39 Unattempt
The base current in a transistor circuit changes from 45 µA to 140 µA. Accordingly, the collector current changes from 0.2 mA to 0.400 mA. The gain in current is
©
The base current in a transistor circuit changes from 45 µA to 140 µA. Accordingly, the collector current changes from 0.2 mA to 0.400 mA. The gain in current is
©
Q.40 Correct
Q.40 In-correct
Q.40 Unattempt
Of the following, NAND gate is
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Of the following, NAND gate is
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Q.41 Correct
Q.41 In-correct
Q.41 Unattempt
The number of radial nodes of 3s and 2 p orbitals respectively are
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The number of radial nodes of 3s and 2 p orbitals respectively are
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Q.42 Correct
Q.42 In-correct
Q.42 Unattempt
The basis of quantum mechanical model of an atom is
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The basis of quantum mechanical model of an atom is
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Q.43 Correct
Q.43 In-correct
Q.43 Unattempt
The number of elements present in the fourth period is
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The number of elements present in the fourth period is
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Q.44 Correct
Q.44 In-correct
Q.44 Unattempt
Identify the correct set.
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Identify the correct set.
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Q.45 Correct
Q.45 In-correct
Q.45 Unattempt
Which one of the following statements is correct?
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Which one of the following statements is correct?
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Q.46 Correct
Q.46 In-correct
Q.46 Unattempt
Which one of the following is an example of disproportionation reaction?
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Which one of the following is an example of disproportionation reaction?
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Q.47 Correct
Q.47 In-correct
Q.47 Unattempt
At T(K), the ratio of kinetic energies of 4g of H2(g) and 8g of O2(g) is
©
At T(K), the ratio of kinetic energies of 4g of H2(g) and 8g of O2(g) is
©
Q.48 Correct
Q.48 In-correct
Q.48 Unattempt
Which one of the following is an isotonic pair of solutions?
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Which one of the following is an isotonic pair of solutions?
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Q.49 Correct
Q.49 In-correct
Q.49 Unattempt
The vapour pressure in mm of Hg, of an aqueous solution obtained by adding 18g of glucose (C6H12O6) to 180g of water at 100°C is
©
The vapour pressure in mm of Hg, of an aqueous solution obtained by adding 18g of glucose (C6H12O6) to 180g of water at 100°C is
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Q.50 Correct
Q.50 In-correct
Q.50 Unattempt
During the electrolysis of copper sulphate aqueous solution using copper electrode, the reaction takine place at the cathode is
©
During the electrolysis of copper sulphate aqueous solution using copper electrode, the reaction takine place at the cathode is
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Q.51 Correct
Q.51 In-correct
Q.51 Unattempt
The extent of charge of lead accumulator is determined by
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The extent of charge of lead accumulator is determined by
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Q.52 Correct
Q.52 In-correct
Q.52 Unattempt
The number of octahedral and tetrahedral holes respectively present in a hexagonal close packed (hcp) crystal of ‘ ’ X atoms are
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The number of octahedral and tetrahedral holes respectively present in a hexagonal close packed (hcp) crystal of ‘ ’ X atoms are
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Q.53 Correct
Q.53 In-correct
Q.53 Unattempt
Which one of the following plots is correct for a first order reaction?
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Which one of the following plots is correct for a first order reaction?
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Q.54 Correct
Q.54 In-correct
Q.54 Unattempt
The degree of ionization of 0.10 M lactic acid is 4.0% H3C−
H
|
C
|
OH(aq)
−COOH⇌H+(aq) +H3C−
H
|
C
|
OH(aq)
−COO−
The value of Kc is
©
The degree of ionization of 0.10 M lactic acid is 4.0% H3C−
H
|
C
|
OH(aq)
−COOH⇌H+(aq) +H3C−
H
|
C
|
OH(aq)
−COO−
The value of Kc is
©
Q.55 Correct
Q.55 In-correct
Q.55 Unattempt
The pH of a buffer solution made by mixing 25mL of 0.02MNH4OH and 25mL of 0.2MNH4Cl at 25° is (pKb of NH4OH=4.8)
©
The pH of a buffer solution made by mixing 25mL of 0.02MNH4OH and 25mL of 0.2MNH4Cl at 25° is (pKb of NH4OH=4.8)
©
Q.56 Correct
Q.56 In-correct
Q.56 Unattempt
For which one of the following reactions, the entropy change is positive?
©
For which one of the following reactions, the entropy change is positive?
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Q.57 Correct
Q.57 In-correct
Q.57 Unattempt
Match the following.
   List I    List II
 (A)  Solid dispersed in liquid  (I)  Emulsion
 (B)   Liquid dispersed in liquid  (II)   Foam
 (C)  Gas dispersed in liquid  (III)   Gel
 (D)  Liquid dispersed in solid  (IV)  Sol
     (V)  Aerosol

©
Match the following.
   List I    List II
 (A)  Solid dispersed in liquid  (I)  Emulsion
 (B)   Liquid dispersed in liquid  (II)   Foam
 (C)  Gas dispersed in liquid  (III)   Gel
 (D)  Liquid dispersed in solid  (IV)  Sol
     (V)  Aerosol

©
Q.58 Correct
Q.58 In-correct
Q.58 Unattempt
Observe the following statements
1. Heavy water is harmful for the growth of animals.
2. Heavy water reacts with Al4C3 and forms deuterated acetylene.
3. BaCl2.2D2O is an example of interstitial deuterate.
The correct statements are
©
Observe the following statements
1. Heavy water is harmful for the growth of animals.
2. Heavy water reacts with Al4C3 and forms deuterated acetylene.
3. BaCl2.2D2O is an example of interstitial deuterate.
The correct statements are
©
Q.59 Correct
Q.59 In-correct
Q.59 Unattempt
Solution " X " contains Na2CO3 and NaHCO3. 20mL of X when titrated using methyl orange indicator consumed 60mL of 0.1M HCl solution. In another experiment, 20mL of X solution when titrated using phenolphthalein consumed 20mL of 0.1M HCl solution. The concentrations (in molL−1 ) of Na2CO3 and NaHCO3 in X are respectively
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Solution " X " contains Na2CO3 and NaHCO3. 20mL of X when titrated using methyl orange indicator consumed 60mL of 0.1M HCl solution. In another experiment, 20mL of X solution when titrated using phenolphthalein consumed 20mL of 0.1M HCl solution. The concentrations (in molL−1 ) of Na2CO3 and NaHCO3 in X are respectively
©
Q.60 Correct
Q.60 In-correct
Q.60 Unattempt
Diborane reacts with HCl in the presence of AlCl3 and liberates
©
Diborane reacts with HCl in the presence of AlCl3 and liberates
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Q.61 Correct
Q.61 In-correct
Q.61 Unattempt
How many corners of SiO4 units are shared in the formation of three dimensional silicates?
©
How many corners of SiO4 units are shared in the formation of three dimensional silicates?
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Q.62 Correct
Q.62 In-correct
Q.62 Unattempt
Which one of the following is not correct?
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Which one of the following is not correct?
©
Q.63 Correct
Q.63 In-correct
Q.63 Unattempt
Na2S2O3 reacts with moist Cl2 to form Na2SO4,HCl and X. Which one of the following is X ?
©
Na2S2O3 reacts with moist Cl2 to form Na2SO4,HCl and X. Which one of the following is X ?
©
Q.64 Correct
Q.64 In-correct
Q.64 Unattempt
The role of copper diaphragm in Whytlaw-Gray’s method is
©
The role of copper diaphragm in Whytlaw-Gray’s method is
©
Q.65 Correct
Q.65 In-correct
Q.65 Unattempt
Liquid X is used in bubble chamber to detect neutral mesons and gamma photons. Then, X is
©
Liquid X is used in bubble chamber to detect neutral mesons and gamma photons. Then, X is
©
Q.66 Correct
Q.66 In-correct
Q.66 Unattempt
A compound absorbs light in the wavelength region 490–500 nm. Its complementary colour is
©
A compound absorbs light in the wavelength region 490–500 nm. Its complementary colour is
©
Q.67 Correct
Q.67 In-correct
Q.67 Unattempt
Which of the following is not added during the extraction of silver by cyanide process?
©
Which of the following is not added during the extraction of silver by cyanide process?
©
Q.68 Correct
Q.68 In-correct
Q.68 Unattempt
Cataract and skin cancer are caused by
©
Cataract and skin cancer are caused by
©
Q.69 Correct
Q.69 In-correct
Q.69 Unattempt
Which one of the following gives Prussian blue colour?
©
Which one of the following gives Prussian blue colour?
©
Q.70 Correct
Q.70 In-correct
Q.70 Unattempt
C2H6
450°C
─────▶
C2H4+H2
Above reaction is called as
©
C2H6
450°C
─────▶
C2H4+H2
Above reaction is called as
©
Q.71 Correct
Q.71 In-correct
Q.71 Unattempt
Assertion (A) — NH2 group of aniline is ortho, para directing in electrophilic substitutions.
Reason (R) — NH2 group stabilises the arenium ion formed by the ortho, para attack of the electrophile.
The correct answer is
©
Assertion (A) — NH2 group of aniline is ortho, para directing in electrophilic substitutions.
Reason (R) — NH2 group stabilises the arenium ion formed by the ortho, para attack of the electrophile.
The correct answer is
©
Q.72 Correct
Q.72 In-correct
Q.72 Unattempt
In which of the following properties, the two enantiomers of lactic acid differ from each other?
©
In which of the following properties, the two enantiomers of lactic acid differ from each other?
©
Q.73 Correct
Q.73 In-correct
Q.73 Unattempt
Heating chloroform with aqueous sodium hydroxide solution forms
©
Heating chloroform with aqueous sodium hydroxide solution forms
©
Q.74 Correct
Q.74 In-correct
Q.74 Unattempt
The products formed in the reaction of phenol with Br2 dissolved in CS2 at 0°C are
©
The products formed in the reaction of phenol with Br2 dissolved in CS2 at 0°C are
©
Q.75 Correct
Q.75 In-correct
Q.75 Unattempt
The structure of PCC is
©
The structure of PCC is
©
Q.76 Correct
Q.76 In-correct
Q.76 Unattempt
The pKa values of four carboxylic acids are given below. Identify the weakest carboxylic acid.

©
The pKa values of four carboxylic acids are given below. Identify the weakest carboxylic acid.

©
Q.77 Correct
Q.77 In-correct
Q.77 Unattempt
Identify X and Y in the following reactions



©
Identify X and Y in the following reactions


©
Q.78 Correct
Q.78 In-correct
Q.78 Unattempt
Example of a biodegradable polymer pair is
©
Example of a biodegradable polymer pair is
©
Q.79 Correct
Q.79 In-correct
Q.79 Unattempt
The number of hydrogen bonds between guanine and cytosine; and between adenine and thymine in DNA is
©
The number of hydrogen bonds between guanine and cytosine; and between adenine and thymine in DNA is
©
Q.80 Correct
Q.80 In-correct
Q.80 Unattempt
Identify phenacetin from the following.
©
Identify phenacetin from the following.
©
Q.81 Correct
Q.81 In-correct
Q.81 Unattempt
If f(x)=(p−xn)1∕n,p>0 and n is a positive integer, then f[f(x)] is equal to
©
If f(x)=(p−xn)1∕n,p>0 and n is a positive integer, then f[f(x)] is equal to
©
Q.82 Correct
Q.82 In-correct
Q.82 Unattempt
The value of {x∈ℝ|[log(1.6)1−x2−(0.625)6(1+x)]∈ℝ} is
©
The value of {x∈ℝ|[log(1.6)1−x2−(0.625)6(1+x)]∈ℝ} is
©
Q.83 Correct
Q.83 In-correct
Q.83 Unattempt
If I is the identity matrix of order 2 and A=[
11
01
], then for n≥1, mathematical induction gives
©
If I is the identity matrix of order 2 and A=[
11
01
], then for n≥1, mathematical induction gives
©
Q.84 Correct
Q.84 In-correct
Q.84 Unattempt
If ‌nCr−1=330,‌nCr=462, and ‌nCr+1=462 then r is equal to
©
If ‌nCr−1=330,‌nCr=462, and ‌nCr+1=462 then r is equal to
©
Q.85 Correct
Q.85 In-correct
Q.85 Unattempt
10 men and 6 women are to be seated in a row so that no two women sit together. The number of ways they can be seated, is
©
10 men and 6 women are to be seated in a row so that no two women sit together. The number of ways they can be seated, is
©
Q.86 Correct
Q.86 In-correct
Q.86 Unattempt
If tn denotes the number of triangles formed with n points in a plane, no three of which are collinear and if tn+1−tn=36, then n is equal to
©
If tn denotes the number of triangles formed with n points in a plane, no three of which are collinear and if tn+1−tn=36, then n is equal to
©
Q.87 Correct
Q.87 In-correct
Q.87 Unattempt
The term independent of x(x>0,x≠1) in the expansion of [
(x+1)
(x2∕3−x1∕3+1)
−
(x−1)
(x−√x)
]10 is
©
The term independent of x(x>0,x≠1) in the expansion of [
(x+1)
(x2∕3−x1∕3+1)
−
(x−1)
(x−√x)
]10 is
©
Q.88 Correct
Q.88 In-correct
Q.88 Unattempt
If x is small, so that x2 and higher powers can be neglected, then the approximate value for
(1−2x)−1(1−3x)−2
(1−4x)−3
 is
©
If x is small, so that x2 and higher powers can be neglected, then the approximate value for
(1−2x)−1(1−3x)−2
(1−4x)−3
 is
©
Q.89 Correct
Q.89 In-correct
Q.89 Unattempt
If
1
x4+x2+1
=−
Ax+B
x2+x+1
+
Cx+D
x2−x+1
, then C+D is equal to
©
If
1
x4+x2+1
=−
Ax+B
x2+x+1
+
Cx+D
x2−x+1
, then C+D is equal to
©
Q.90 Correct
Q.90 In-correct
Q.90 Unattempt
1
2.3
+
1
4.5
+
1
6.7
+
1
8.9
+... is equal to
©
1
2.3
+
1
4.5
+
1
6.7
+
1
8.9
+... is equal to
©
Q.91 Correct
Q.91 In-correct
Q.91 Unattempt
If the harmonic mean between the roots of (5+√2)x2−bx+(8+2√5)=0 is 4, then the value of b is
©
If the harmonic mean between the roots of (5+√2)x2−bx+(8+2√5)=0 is 4, then the value of b is
©
Q.92 Correct
Q.92 In-correct
Q.92 Unattempt
The set of solutions satisfying both x2+5x+6≥0 and x2+3x−4<0 is
©
The set of solutions satisfying both x2+5x+6≥0 and x2+3x−4<0 is
©
Q.93 Correct
Q.93 In-correct
Q.93 Unattempt
If the roots of x3−42x2+336x−512=0, are in increasing geometric progression, then its common ratio is
©
If the roots of x3−42x2+336x−512=0, are in increasing geometric progression, then its common ratio is
©
Q.94 Correct
Q.94 In-correct
Q.94 Unattempt
If α and β are the roots of the equation x2−2x+4=0, then α9+β9 is equal to
©
If α and β are the roots of the equation x2−2x+4=0, then α9+β9 is equal to
©
Q.95 Correct
Q.95 In-correct
Q.95 Unattempt
If A=[
−85
24
] satisfies the equation x2+4x−p=0, then p is equal to
©
If A=[
−85
24
] satisfies the equation x2+4x−p=0, then p is equal to
©
Q.96 Correct
Q.96 In-correct
Q.96 Unattempt
|
x+2x+3x+5
x+4x+6x+9
x+8x+11x+15
| is equal to
©
|
x+2x+3x+5
x+4x+6x+9
x+8x+11x+15
| is equal to
©
Q.97 Correct
Q.97 In-correct
Q.97 Unattempt
The system of equations 3x+2y+z=6, 3x+4y+3z=14 and 6x+10y+8z=a , has infinite number of solutions, if a is equal to
©
The system of equations 3x+2y+z=6, 3x+4y+3z=14 and 6x+10y+8z=a , has infinite number of solutions, if a is equal to
©
Q.98 Correct
Q.98 In-correct
Q.98 Unattempt
The number of real values of t such that the system of homogeneous equations
tx+(t+1)y+(t−1)z=0
(t+1)x+ty+(t+2)z=0
(t−1)x+(t+2)y+tz=0
has non-trivial solutions is
©
The number of real values of t such that the system of homogeneous equations
tx+(t+1)y+(t−1)z=0
(t+1)x+ty+(t+2)z=0
(t−1)x+(t+2)y+tz=0
has non-trivial solutions is
©
Q.99 Correct
Q.99 In-correct
Q.99 Unattempt
(
1+i
1−i
)4+(
1−i
1+i
)4 is equal to
©
(
1+i
1−i
)4+(
1−i
1+i
)4 is equal to
©
Q.100 Correct
Q.100 In-correct
Q.100 Unattempt
If a complex number z satisfies |z2−1|=|z|2+1, then z lies on
©
If a complex number z satisfies |z2−1|=|z|2+1, then z lies on
©
Q.101 Correct
Q.101 In-correct
Q.101 Unattempt
If
(1+i)x−i
2+i
+
(1+2i)y+i
2−i
=1, then (x,y) isequal to
©
If
(1+i)x−i
2+i
+
(1+2i)y+i
2−i
=1, then (x,y) isequal to
©
Q.102 Correct
Q.102 In-correct
Q.102 Unattempt
The period of f(x)=cos(
x
3
)+sin(
x
2
) is
©
The period of f(x)=cos(
x
3
)+sin(
x
2
) is
©
Q.103 Correct
Q.103 In-correct
Q.103 Unattempt
If sin‌θ+cos‌θ=p and sin3θ+cos3θ=qthen p(p2−3) is equal to
©
If sin‌θ+cos‌θ=p and sin3θ+cos3θ=qthen p(p2−3) is equal to
©
Q.104 Correct
Q.104 In-correct
Q.104 Unattempt
If tan(π‌cos‌θ)=cot(π‌sin‌θ), then a value ofcos(θ−
π
4
) among the following is
©
If tan(π‌cos‌θ)=cot(π‌sin‌θ), then a value ofcos(θ−
π
4
) among the following is
©
Q.105 Correct
Q.105 In-correct
Q.105 Unattempt
The set of solutions of the system of equations
x+y=
2π
3
and cos‌x+cos‌y=
3
2
,
where x, y are real, is
©
The set of solutions of the system of equations
x+y=
2π
3
and cos‌x+cos‌y=
3
2
,
where x, y are real, is
©
Q.106 Correct
Q.106 In-correct
Q.106 Unattempt
If cos−1(
5
13
)+cos−1(
3
5
)=cos−1x, then x isequal to
©
If cos−1(
5
13
)+cos−1(
3
5
)=cos−1x, then x isequal to
©
Q.107 Correct
Q.107 In-correct
Q.107 Unattempt
tanh−1(
1
2
)+coth−1(2) is equal to
©
tanh−1(
1
2
)+coth−1(2) is equal to
©
Q.108 Correct
Q.108 In-correct
Q.108 Unattempt
In any ΔABC, r1r2+r2r3+r3r1 is equal to
©
In any ΔABC, r1r2+r2r3+r3r1 is equal to
©
Q.109 Correct
Q.109 In-correct
Q.109 Unattempt
If in a ΔABC,
1
a+c
+
1
b+c
=
3
a+b+c
, then ∠C is equal to
©
If in a ΔABC,
1
a+c
+
1
b+c
=
3
a+b+c
, then ∠C is equal to
©
Q.110 Correct
Q.110 In-correct
Q.110 Unattempt
A person observes the top of a tower from a point A on the ground. The elevation of the tower from this point is 60°. He moves 60m in the direction perpendicular to the line joining A and base of the tower. The angle of elevation of the tower from this point is 45°. Then, the height of the tower (in metres) is
©
A person observes the top of a tower from a point A on the ground. The elevation of the tower from this point is 60°. He moves 60m in the direction perpendicular to the line joining A and base of the tower. The angle of elevation of the tower from this point is 45°. Then, the height of the tower (in metres) is
©
Q.111 Correct
Q.111 In-correct
Q.111 Unattempt
The points whose position vectors are 2i+3j+4k,3i+4j+2k and 4i+2j+3k arethe vertices of
©
The points whose position vectors are 2i+3j+4k,3i+4j+2k and 4i+2j+3k arethe vertices of
©
Q.112 Correct
Q.112 In-correct
Q.112 Unattempt
P,Q,R and S are four points with the position vectors 3i−4j+5k,−4i+5j+kand −3i+4j+3k, respectively. Then, the line PQ meets the line RS at the point
©
P,Q,R and S are four points with the position vectors 3i−4j+5k,−4i+5j+kand −3i+4j+3k, respectively. Then, the line PQ meets the line RS at the point
©
Q.113 Correct
Q.113 In-correct
Q.113 Unattempt
If a≠0,b≠0,c≠0,a×b=0 and b×c=0then a×c is equal to
©
If a≠0,b≠0,c≠0,a×b=0 and b×c=0then a×c is equal to
©
Q.114 Correct
Q.114 In-correct
Q.114 Unattempt
The shortest distance between the lines r=3i+5j+7k+λ(i+2j+k)and r=−i−j−k+µ(7i−6j+k) is
©
The shortest distance between the lines r=3i+5j+7k+λ(i+2j+k)and r=−i−j−k+µ(7i−6j+k) is
©
Q.115 Correct
Q.115 In-correct
Q.115 Unattempt
A unit vector coplanar with i+j+3k and i+3j+k and perpendicular to i+j+k is
©
A unit vector coplanar with i+j+3k and i+3j+k and perpendicular to i+j+k is
©
Q.116 Correct
Q.116 In-correct
Q.116 Unattempt
If a and b are two non-zero perpendicular vectors, then a vector y satisfying equations a.y=c( where,c is scalar ) and a×y=b is
©
If a and b are two non-zero perpendicular vectors, then a vector y satisfying equations a.y=c( where,c is scalar ) and a×y=b is
©
Q.117 Correct
Q.117 In-correct
Q.117 Unattempt
Two numbers are chosen at random from {1,2,3,4,5,6,7,8} at a time. The probability that smaller of the two numbers is less than 4 is
©
Two numbers are chosen at random from {1,2,3,4,5,6,7,8} at a time. The probability that smaller of the two numbers is less than 4 is
©
Q.118 Correct
Q.118 In-correct
Q.118 Unattempt
Two fair dice are rolled. The probability of the sum of digits on their faces to be greater than or equal to 10 is
©
Two fair dice are rolled. The probability of the sum of digits on their faces to be greater than or equal to 10 is
©
Q.119 Correct
Q.119 In-correct
Q.119 Unattempt
A bag contains 2n+1 coins. It is known that n of these coins have a head on both sides, whereas the remaining n+1 coins are fair. A coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is
31
42
, then n is equal to
©
A bag contains 2n+1 coins. It is known that n of these coins have a head on both sides, whereas the remaining n+1 coins are fair. A coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is
31
42
, then n is equal to
©
Q.120 Correct
Q.120 In-correct
Q.120 Unattempt
The random variable takes the values 1,2,3, .....,m. If P(X=n)=
1
m
 to each n, then the variance of X is
©
The random variable takes the values 1,2,3, .....,m. If P(X=n)=
1
m
 to each n, then the variance of X is
©
Q.121 Correct
Q.121 In-correct
Q.121 Unattempt
If X is quad a poisson variate P(X=1)=2P(X=2), then P(X=3) is equal to
©
If X is quad a poisson variate P(X=1)=2P(X=2), then P(X=3) is equal to
©
Q.122 Correct
Q.122 In-correct
Q.122 Unattempt
The origin is translated to (1,2). The point (7,5) in the old system undergoes the following transformations successively.
I. Moves to the new point under the given translation of origin.
II. Translated through 2 units along the negative direction of the new X -axis.
III. Rotated through an angle
π
4
 about the origin of new system in the clockwise direction. The final position of the point (7,5) is
©
The origin is translated to (1,2). The point (7,5) in the old system undergoes the following transformations successively.
I. Moves to the new point under the given translation of origin.
II. Translated through 2 units along the negative direction of the new X -axis.
III. Rotated through an angle
π
4
 about the origin of new system in the clockwise direction. The final position of the point (7,5) is
©
Q.123 Correct
Q.123 In-correct
Q.123 Unattempt
If p and q are the perpendicular distances from the origin to the straight lines x‌sec‌θ−y‌cosec‌θ=aand x‌cos‌θ+y‌sin‌θ=a‌cos‌2‌θ, then
©
If p and q are the perpendicular distances from the origin to the straight lines x‌sec‌θ−y‌cosec‌θ=aand x‌cos‌θ+y‌sin‌θ=a‌cos‌2‌θ, then
©
Q.124 Correct
Q.124 In-correct
Q.124 Unattempt
If 2x+3y=5 is the perpendicular bisector of the line segment joining the points A(1,
1
3
) and B, then B is equal to
©
If 2x+3y=5 is the perpendicular bisector of the line segment joining the points A(1,
1
3
) and B, then B is equal to
©
Q.125 Correct
Q.125 In-correct
Q.125 Unattempt
If the points (1,2) and (3,4) lie on the same side of the straight line 3x−5y+a=0, then a lies in the set
©
If the points (1,2) and (3,4) lie on the same side of the straight line 3x−5y+a=0, then a lies in the set
©
Q.126 Correct
Q.126 In-correct
Q.126 Unattempt
The equation of the pair of lines passing through the origin whose sum and product of slopes are respectively the arithmetic mean and geometric mean of 4 and 9 is
©
The equation of the pair of lines passing through the origin whose sum and product of slopes are respectively the arithmetic mean and geometric mean of 4 and 9 is
©
Q.127 Correct
Q.127 In-correct
Q.127 Unattempt
The equation x2−5xy+py2+3x−8y+2=0 represents a pair of straight lines. If θ is the angle between them, then sin‌θ is equal to
©
The equation x2−5xy+py2+3x−8y+2=0 represents a pair of straight lines. If θ is the angle between them, then sin‌θ is equal to
©
Q.128 Correct
Q.128 In-correct
Q.128 Unattempt
If ax2+2hxy+by2+2gx +2fy+c=0 equation represents a pair of straight lines, then the square of the distance of their point of intersection from the origin is
©
If ax2+2hxy+by2+2gx +2fy+c=0 equation represents a pair of straight lines, then the square of the distance of their point of intersection from the origin is
©
Q.129 Correct
Q.129 In-correct
Q.129 Unattempt
The circle 4x2+4y2−12x −12y+9=0
©
The circle 4x2+4y2−12x −12y+9=0
©
Q.130 Correct
Q.130 In-correct
Q.130 Unattempt
For the circle C with the equation x2+y2−16x−12y+64=0 match the List I with the List II given below.

 
The correct match is
©
For the circle C with the equation x2+y2−16x−12y+64=0 match the List I with the List II given below.


The correct match is
©
Q.131 Correct
Q.131 In-correct
Q.131 Unattempt
If the length of the tangent from (h,k) to the circle x2+y2=16 is twice the length of the tangent from the same point to the circle x2+y2+2x+2y=0, then
©
If the length of the tangent from (h,k) to the circle x2+y2=16 is twice the length of the tangent from the same point to the circle x2+y2+2x+2y=0, then
©
Q.132 Correct
Q.132 In-correct
Q.132 Unattempt
(a,0) and (b,0) are centres of two circles belonging to a coaxial system of which y -axis is the radical axis. If radius of one of the circles is ' r ', then the radius of the other circle is
©
(a,0) and (b,0) are centres of two circles belonging to a coaxial system of which y -axis is the radical axis. If radius of one of the circles is ' r ', then the radius of the other circle is
©
Q.133 Correct
Q.133 In-correct
Q.133 Unattempt
If the circle x2+y2+4x−6y+c=0 bisects the circumference of the circle x2+y2−6x+4y−12=0, then c is equal to
©
If the circle x2+y2+4x−6y+c=0 bisects the circumference of the circle x2+y2−6x+4y−12=0, then c is equal to
©
Q.134 Correct
Q.134 In-correct
Q.134 Unattempt
A circle of radius 4, drawn on a chord of the parabola y2=8x as diameter, touches the axis of the parabola. Then, the slope of the chord is
©
A circle of radius 4, drawn on a chord of the parabola y2=8x as diameter, touches the axis of the parabola. Then, the slope of the chord is
©
Q.135 Correct
Q.135 In-correct
Q.135 Unattempt
The mid-point of a chord of the ellipse x2+4y2−2x+20y=0 is (2,−4). The equation of the chord is
©
The mid-point of a chord of the ellipse x2+4y2−2x+20y=0 is (2,−4). The equation of the chord is
©
Q.136 Correct
Q.136 In-correct
Q.136 Unattempt
If the focii of the ellipse
x2
25
+
y2
16
=1 and the hyperbola
x2
4
−
y2
b2
=1 coincide, then b2 is equal to
©
If the focii of the ellipse
x2
25
+
y2
16
=1 and the hyperbola
x2
4
−
y2
b2
=1 coincide, then b2 is equal to
©
Q.137 Correct
Q.137 In-correct
Q.137 Unattempt
If x=9 is a chord of contact of the hyperbola x2−y2=9, then the equation of the tangent at one of the points of contact is
©
If x=9 is a chord of contact of the hyperbola x2−y2=9, then the equation of the tangent at one of the points of contact is
©
Q.138 Correct
Q.138 In-correct
Q.138 Unattempt
The perpendicular distance from the point (1,π) to the line joining (1,0°) and (1,
π
2
), (in polar coordinates) is
©
The perpendicular distance from the point (1,π) to the line joining (1,0°) and (1,
π
2
), (in polar coordinates) is
©
Q.139 Correct
Q.139 In-correct
Q.139 Unattempt
If D(2,1,0),E(2,0,0) and F(0,1,0) are mid-points of the sides BC,CA and AB of ΔABC, respectively. Then, the centroid of ΔABC is
©
If D(2,1,0),E(2,0,0) and F(0,1,0) are mid-points of the sides BC,CA and AB of ΔABC, respectively. Then, the centroid of ΔABC is
©
Q.140 Correct
Q.140 In-correct
Q.140 Unattempt
The direction ratios of the two lines AB and AC are 1,−1,−1 and 2,−1,1. The direction ratios of the normal to the plane ABC are
©
The direction ratios of the two lines AB and AC are 1,−1,−1 and 2,−1,1. The direction ratios of the normal to the plane ABC are
©
Q.141 Correct
Q.141 In-correct
Q.141 Unattempt
A plane passing through (−1,2,3) and whose normal makes equal angles with the coordinate axes is
©
A plane passing through (−1,2,3) and whose normal makes equal angles with the coordinate axes is
©
Q.142 Correct
Q.142 In-correct
Q.142 Unattempt
A variable plane passes through a fixed point (1,2,3). Then, the foot of the perpendicular from the origin to the plane lies on
©
A variable plane passes through a fixed point (1,2,3). Then, the foot of the perpendicular from the origin to the plane lies on
©
Q.143 Correct
Q.143 In-correct
Q.143 Unattempt
Let f be a non-zero real valued continuous function satisfying f(x+y)=f(x).f(y) for all x,y∈R. If f(2)=9, then f(6) is equal to
©
Let f be a non-zero real valued continuous function satisfying f(x+y)=f(x).f(y) for all x,y∈R. If f(2)=9, then f(6) is equal to
©
Q.144 Correct
Q.144 In-correct
Q.144 Unattempt
lim
x→0
tan3x−sin3x
x5
 is equal to
©
lim
x→0
tan3x−sin3x
x5
 is equal to
©
Q.145 Correct
Q.145 In-correct
Q.145 Unattempt
If f(x)=
1
1+
1
x
 and g(x)=
1
1+
1
f(x)
, then g′(2)is equal to
©
If f(x)=
1
1+
1
x
 and g(x)=
1
1+
1
f(x)
, then g′(2)is equal to
©
Q.146 Correct
Q.146 In-correct
Q.146 Unattempt
If √
y
x
+√
x
y
=2, then
dy
dx
 is equal to
©
If √
y
x
+√
x
y
=2, then
dy
dx
 is equal to
©
Q.147 Correct
Q.147 In-correct
Q.147 Unattempt
If
d
dx
[(x+1)(x2+1)(x4+1)(x8+1)] =(15xp−16xq+1)(x−1)−2, then (p,q) is equal to
©
If
d
dx
[(x+1)(x2+1)(x4+1)(x8+1)] =(15xp−16xq+1)(x−1)−2, then (p,q) is equal to
©
Q.148 Correct
Q.148 In-correct
Q.148 Unattempt
If cos−1(
y
b
)=2‌log(
x
2
), where x>0, then x2
d2y
dx2
+x
dy
dx
 is equal to
©
If cos−1(
y
b
)=2‌log(
x
2
), where x>0, then x2
d2y
dx2
+x
dy
dx
 is equal to
©
Q.149 Correct
Q.149 In-correct
Q.149 Unattempt
The relation between pressure p and volume V is given by pV1∕4= constant. If the percentage decrease in volume is
1
2
, then the percentage increase in pressure is
©
The relation between pressure p and volume V is given by pV1∕4= constant. If the percentage decrease in volume is
1
2
, then the percentage increase in pressure is
©
Q.150 Correct
Q.150 In-correct
Q.150 Unattempt
If the curves x2+py2=1 and qx2+y2=1 are orthogonal to each other, then
©
If the curves x2+py2=1 and qx2+y2=1 are orthogonal to each other, then
©
Q.151 Correct
Q.151 In-correct
Q.151 Unattempt
The focal length of a mirror is given by
2
f
=
1
v
−
1
u
. In finding the values of u and v, the errors are equal to ' p '. Then, the relative error in f is
©
The focal length of a mirror is given by
2
f
=
1
v
−
1
u
. In finding the values of u and v, the errors are equal to ' p '. Then, the relative error in f is
©
Q.152 Correct
Q.152 In-correct
Q.152 Unattempt
If u=log(x3+y3+z3−3xyz),then (x+y+z)(ux+uy+uz) is equal to
©
If u=log(x3+y3+z3−3xyz),then (x+y+z)(ux+uy+uz) is equal to
©
Q.153 Correct
Q.153 In-correct
Q.153 Unattempt
∫ex(
2+sin‌2‌x
1+cos‌2‌x
)dx is equal to
©
∫ex(
2+sin‌2‌x
1+cos‌2‌x
)dx is equal to
©
Q.154 Correct
Q.154 In-correct
Q.154 Unattempt
∫
x−sin‌x
1+cos‌x
dx=x‌tan(
x
2
) +p‌log|sec(
x
2
)|+C then p is equal to
©
∫
x−sin‌x
1+cos‌x
dx=x‌tan(
x
2
) +p‌log|sec(
x
2
)|+C then p is equal to
©
Q.155 Correct
Q.155 In-correct
Q.155 Unattempt
If ∫
dx
x(log‌x−2)(log‌x−3)
=I+C, then I isequal to
©
If ∫
dx
x(log‌x−2)(log‌x−3)
=I+C, then I isequal to
©
Q.156 Correct
Q.156 In-correct
Q.156 Unattempt
If
b
∫
0
dx
1+x2
=
∞
∫
b
dx
1+x2
, then b is equal to
©
If
b
∫
0
dx
1+x2
=
∞
∫
b
dx
1+x2
, then b is equal to
©
Q.157 Correct
Q.157 In-correct
Q.157 Unattempt
The area (in sq units) bounded by the curves x=−2y2 and x=1−3y2 is
©
The area (in sq units) bounded by the curves x=−2y2 and x=1−3y2 is
©
Q.158 Correct
Q.158 In-correct
Q.158 Unattempt
The approximate value of
3
∫
1
dx
2+3x
 using Simpson's rule and dividing the interval [1,3] into two equal parts is
©
The approximate value of
3
∫
1
dx
2+3x
 using Simpson's rule and dividing the interval [1,3] into two equal parts is
©
Q.159 Correct
Q.159 In-correct
Q.159 Unattempt
An integrating factor of the equation (1+y+x2y)dx+(x+x3)dy=0 is
©
An integrating factor of the equation (1+y+x2y)dx+(x+x3)dy=0 is
©
Q.160 Correct
Q.160 In-correct
Q.160 Unattempt
The solution of the differential equation
dy
dx
−2y‌tan‌2‌x=ex‌sec‌2‌x is
©
The solution of the differential equation
dy
dx
−2y‌tan‌2‌x=ex‌sec‌2‌x is
©
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