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Solution
Q.1 Correct
Q.1 In-correct
Q.1 Unattempt
If f(x)={
x3sin‌(‌
1
x
)		‌x≠0
0‌x=0
., then
If f(x)={
x3sin‌(‌
1
x
)		‌x≠0
0‌x=0
., then
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt
If A(3,1,−1),B(‌
5
3
,‌
7
3
,‌
1
3
),C(2,2,1) and D(‌
10
3
,‌
2
3
,‌
−1
3
) are the vertices of a quadrilateral ABCD, then its area is
If A(3,1,−1),B(‌
5
3
,‌
7
3
,‌
1
3
),C(2,2,1) and D(‌
10
3
,‌
2
3
,‌
−1
3
) are the vertices of a quadrilateral ABCD, then its area is
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt
π∕4
∫
0
‌
cos2xsin‌2x
(cos3x+sin‌3x)2
‌dx is equal to
π∕4
∫
0
‌
cos2xsin‌2x
(cos3x+sin‌3x)2
‌dx is equal to
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt
The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On respectively, it was found that an observation by mistake was taken 8 instead of 12 . The correct standard deviation is
The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On respectively, it was found that an observation by mistake was taken 8 instead of 12 . The correct standard deviation is
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt
The function f(x)=‌
x2+2x−15
x2−4x+9
,x∈R is
The function f(x)=‌
x2+2x−15
x2−4x+9
,x∈R is
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt
Let A={n∈[100,700]∩N:n is neither a multiple of 3 nor a multiple of 4}. Then the number of elements in A is
Let A={n∈[100,700]∩N:n is neither a multiple of 3 nor a multiple of 4}. Then the number of elements in A is
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt
Let C be the circle of minimum area touching the parabola y=6−x2 and the lines y=√3|x|. Then, which one of the following points lies on the circle C?
Let C be the circle of minimum area touching the parabola y=6−x2 and the lines y=√3|x|. Then, which one of the following points lies on the circle C?
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt
For α,β∈R and a natural number n, let Ar=|
r1‌
n2
2
+α
2r2n2−β
3r−23‌
n(3n−1)
2
|. Then 2A10−A8 is
For α,β∈R and a natural number n, let Ar=|
r1‌
n2
2
+α
2r2n2−β
3r−23‌
n(3n−1)
2
|. Then 2A10−A8 is
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt
The shortest distance between the lines ‌
x−3
2
=‌
y+15
−7
=‌
z−9
5
 and ‌
x+1
2
=‌
y−1
1
=‌
z−9
−3
 is
The shortest distance between the lines ‌
x−3
2
=‌
y+15
−7
=‌
z−9
5
 and ‌
x+1
2
=‌
y−1
1
=‌
z−9
−3
 is
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt
A company has two plants A and B to manufacture motorcycles. 60% motorcycles are manufactured at plant A and the remaining are manufactured at plant B. 80% of the motorcycles manufactured at plant A are rated of the standard quality, while 90% of the motorcycles manufactured at plant B are rated of the standard quality. A motorcycle picked up randomly from the total production is found to be of the standard quality. If p is the probability that it was manufactured at plant B, then 126p is
A company has two plants A and B to manufacture motorcycles. 60% motorcycles are manufactured at plant A and the remaining are manufactured at plant B. 80% of the motorcycles manufactured at plant A are rated of the standard quality, while 90% of the motorcycles manufactured at plant B are rated of the standard quality. A motorcycle picked up randomly from the total production is found to be of the standard quality. If p is the probability that it was manufactured at plant B, then 126p is
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt
Let, α,β be the distinct roots of the equation x2−(t2−5t+6)x+1=0,t∈R and an=αn+βn. Then the minimum value of ‌
a2023+a2025
a2024
 is
Let, α,β be the distinct roots of the equation x2−(t2−5t+6)x+1=0,t∈R and an=αn+βn. Then the minimum value of ‌
a2023+a2025
a2024
 is
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt
Let the relations R1 and R2 on the set X={1,2,3,...,20} be given by R1={(x,y):2x−3y=2} and R2={(x,y):−5x+4y=0}. If M and N be the minimum number of elements required to be added in R1 and R2, respectively, in order to make the relations symmetric, then M+N equals
Let the relations R1 and R2 on the set X={1,2,3,...,20} be given by R1={(x,y):2x−3y=2} and R2={(x,y):−5x+4y=0}. If M and N be the minimum number of elements required to be added in R1 and R2, respectively, in order to make the relations symmetric, then M+N equals
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt
Let a variable line of slope m>0 passing through the point (4,−9) intersect the coordinate axes at the points A and B. the minimum value of the sum of the distances of A and B from the origin is
Let a variable line of slope m>0 passing through the point (4,−9) intersect the coordinate axes at the points A and B. the minimum value of the sum of the distances of A and B from the origin is
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt
The interval in which the function f(x)=xx,x>0, is strictly increasing is
The interval in which the function f(x)=xx,x>0, is strictly increasing is
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt
A circle in inscribed in an equilateral triangle of side of length 12. If the area and perimeter of any square inscribed in this circle are m and n, respectively, then m+n2 is equal to
A circle in inscribed in an equilateral triangle of side of length 12. If the area and perimeter of any square inscribed in this circle are m and n, respectively, then m+n2 is equal to
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt
The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is
The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt
Let y=y(x) be the solution of the differential equation (1+x2)‌
dy
dx
+y=etan−1x,y(1)=0. Then y(0) is
Let y=y(x) be the solution of the differential equation (1+x2)‌
dy
dx
+y=etan−1x,y(1)=0. Then y(0) is
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt
Let y=y(x) be the solution of the differential equation (2xlogex)‌
dy
dx
+2y=‌
3
x
logex,x>0 and y(e−1)=0. Then, y(e) is equal to
Let y=y(x) be the solution of the differential equation (2xlogex)‌
dy
dx
+2y=‌
3
x
logex,x>0 and y(e−1)=0. Then, y(e) is equal to
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt
Let the area of the region enclosed by the curves y=3x,2y=27−3x and y=3x−x√x be A. Then 10A is equal to
Let the area of the region enclosed by the curves y=3x,2y=27−3x and y=3x−x√x be A. Then 10A is equal to
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt
Let f:(−∞,∞)−{0}⟶R be a differentiable function such that f′(1)=
lim
a⟶∞
a2f(‌
1
a
). Then
lim
a⟶∞
‌
a(a+1)
2
tan−1(‌
1
a
)+a2−2logea is equal to
Let f:(−∞,∞)−{0}⟶R be a differentiable function such that f′(1)=
lim
a⟶∞
a2f(‌
1
a
). Then
lim
a⟶∞
‌
a(a+1)
2
tan−1(‌
1
a
)+a2−2logea is equal to
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt
Let αβγ=45;α,β,γ∈R. If x(α,1,2)+y(1,β,2) +z(2,3,γ)=(0,0,0) for some x,y,z∈R,xyz≠ 0 , then 6α+4β+γ is equal to _______.
Let αβγ=45;α,β,γ∈R. If x(α,1,2)+y(1,β,2) +z(2,3,γ)=(0,0,0) for some x,y,z∈R,xyz≠ 0 , then 6α+4β+γ is equal to _______.
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt
Let a conic C pass through the point (4,−2) and P(x,y),x≥3, be any point on C. Let the slope of the line touching the conic C only at a single point P be half the slope of the line joining the points P and (3,−5). If the focal distance of the point (7,1) on C is d, then 12d equals ______.
Let a conic C pass through the point (4,−2) and P(x,y),x≥3, be any point on C. Let the slope of the line touching the conic C only at a single point P be half the slope of the line joining the points P and (3,−5). If the focal distance of the point (7,1) on C is d, then 12d equals ______.
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt
Let rk=‌
1
∫
0
(1−x7)k‌dx
1
∫
0
(1−x7)k+1‌dx
,k∈N. Then the value of
10
∑
k=1
‌
1
7(rk−1)
 is equal to _______.
Let rk=‌
1
∫
0
(1−x7)k‌dx
1
∫
0
(1−x7)k+1‌dx
,k∈N. Then the value of
10
∑
k=1
‌
1
7(rk−1)
 is equal to _______.
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt
Let x1,x2,x3,x4 be the solution of the equation 4x4+8x3−17x2−12x+9=0 and (4+x12)(4+x22)(4+x32)(4+x42)=‌
125
16
m‌. ‌
Then the value of m is _____.
Let x1,x2,x3,x4 be the solution of the equation 4x4+8x3−17x2−12x+9=0 and (4+x12)(4+x22)(4+x32)(4+x42)=‌
125
16
m‌. ‌
Then the value of m is _____.
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt
Let L1,L2 be the lines passing through the point P(0,1) and touching the parabola
9x2+12x+18y−14=0. Let Q and R be the points on the lines L1 and L2 such that the △PQR is an isosceles triangle with base QR. If the slopes of the lines QR are m1 and m2. then 16(m12+m22) is equal to _____.
Let L1,L2 be the lines passing through the point P(0,1) and touching the parabola
9x2+12x+18y−14=0. Let Q and R be the points on the lines L1 and L2 such that the △PQR is an isosceles triangle with base QR. If the slopes of the lines QR are m1 and m2. then 16(m12+m22) is equal to _____.
Q.26 Correct
Q.26 In-correct
Q.26 Unattempt
If the second, third and fourth terms in the expansion of (x+y)n are 135,30 and ‌
10
3
, respectively, then 6(n3+x2+y) is equal to _______.
If the second, third and fourth terms in the expansion of (x+y)n are 135,30 and ‌
10
3
, respectively, then 6(n3+x2+y) is equal to _______.
Q.27 Correct
Q.27 In-correct
Q.27 Unattempt
Let the first term of a series be T1=6 and its r‌th ‌ term Tr=3Tr−1+6r,r=2,3,......,n. If the sum of the first n terms of this series is ‌
1
5
(n2−12n+39) (4.6n−5.3n+1). Then n is equal to ______.
Let the first term of a series be T1=6 and its r‌th ‌ term Tr=3Tr−1+6r,r=2,3,......,n. If the sum of the first n terms of this series is ‌
1
5
(n2−12n+39) (4.6n−5.3n+1). Then n is equal to ______.
Q.28 Correct
Q.28 In-correct
Q.28 Unattempt
For n∈N, if cot−13+cot−14+cot−15+cot1n=‌
π
4
, then n is equal to ______.
For n∈N, if cot−13+cot−14+cot−15+cot1n=‌
π
4
, then n is equal to ______.
Q.29 Correct
Q.29 In-correct
Q.29 Unattempt
Let P be the point (10,−2,−1) and Q be the foot of the perpendicular drawn from the point R(1,7,6) on the line passing through the points (2,−5,11) and (−6,7,−5). Then the length of the line segment PQ is equal to _______.
Let P be the point (10,−2,−1) and Q be the foot of the perpendicular drawn from the point R(1,7,6) on the line passing through the points (2,−5,11) and (−6,7,−5). Then the length of the line segment PQ is equal to _______.
Q.30 Correct
Q.30 In-correct
Q.30 Unattempt
30. Let
→
a
=2
^
i
−3
^
j
+4
^
k
,
→
b
=3
^
i
+4
^
j
−5
^
k
, and a vector
→
c
 be such that
→
a
×(
→
b
+
→
c
)+
→
b
×
→
c
=
^
i
+8
^
j
+13
^
k
. If
→
a
⋅
→
c
=13, then (24−
→
b
⋅
→
c
) is equal to ______.
30. Let
→
a
=2
^
i
−3
^
j
+4
^
k
,
→
b
=3
^
i
+4
^
j
−5
^
k
, and a vector
→
c
 be such that
→
a
×(
→
b
+
→
c
)+
→
b
×
→
c
=
^
i
+8
^
j
+13
^
k
. If
→
a
⋅
→
c
=13, then (24−
→
b
⋅
→
c
) is equal to ______.
Q.31 Correct
Q.31 In-correct
Q.31 Unattempt
To find the spring constant (k) of a spring experimentally, a student commits 2% positive error in the measurement of time and 1% negative error in measurement of mass. The percentage error in determining value of k is :
To find the spring constant (k) of a spring experimentally, a student commits 2% positive error in the measurement of time and 1% negative error in measurement of mass. The percentage error in determining value of k is :
Q.32 Correct
Q.32 In-correct
Q.32 Unattempt
A bullet of mass 50g is fired with a speed 100m∕ s on a plywood and emerges with 40m∕ s. The percentage loss of kinetic energy is :
A bullet of mass 50g is fired with a speed 100m∕ s on a plywood and emerges with 40m∕ s. The percentage loss of kinetic energy is :
Q.33 Correct
Q.33 In-correct
Q.33 Unattempt
The ratio of the shortest wavelength of Balmer series to the shortest wavelength of Lyman series for hydrogen atom is :
The ratio of the shortest wavelength of Balmer series to the shortest wavelength of Lyman series for hydrogen atom is :
Q.34 Correct
Q.34 In-correct
Q.34 Unattempt
To project a body of mass m from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is RE,g= acceleration due to gravity on the surface of earth) :
To project a body of mass m from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is RE,g= acceleration due to gravity on the surface of earth) :
Q.35 Correct
Q.35 In-correct
Q.35 Unattempt
Electromagnetic waves travel in a medium with speed of 1.5×108ms−1. The relative permeability of the medium is 2.0 . The relative permittivity will be :
Electromagnetic waves travel in a medium with speed of 1.5×108ms−1. The relative permeability of the medium is 2.0 . The relative permittivity will be :
Q.36 Correct
Q.36 In-correct
Q.36 Unattempt
Which of the following phenomena does not explain by wave nature of light.
(A) reflection
(B) diffraction
(C) photoelectric effect
(D) interference
(E) polarization
Choose the most appropriate answer from the options given below :
Which of the following phenomena does not explain by wave nature of light.
(A) reflection
(B) diffraction
(C) photoelectric effect
(D) interference
(E) polarization
Choose the most appropriate answer from the options given below :
Q.37 Correct
Q.37 In-correct
Q.37 Unattempt
While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is 1‌mm and circular scale reading is equal to 42 divisions. Pitch of screw gauge is 1‌mm and it has 100 divisions on circular scale. The diameter of the wire is ‌
x
50
‌mm. The value of x is :
While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is 1‌mm and circular scale reading is equal to 42 divisions. Pitch of screw gauge is 1‌mm and it has 100 divisions on circular scale. The diameter of the wire is ‌
x
50
‌mm. The value of x is :
Q.38 Correct
Q.38 In-correct
Q.38 Unattempt
σ is the uniform surface charge density of a thin spherical shell of radius R. The electric field at any point on the surface of the spherical shell is :
σ is the uniform surface charge density of a thin spherical shell of radius R. The electric field at any point on the surface of the spherical shell is :
Q.39 Correct
Q.39 In-correct
Q.39 Unattempt
The value of unknown resistance (x) for which the potential difference between B and D will be zero in the arrangement shown, is :
The value of unknown resistance (x) for which the potential difference between B and D will be zero in the arrangement shown, is :
Q.40 Correct
Q.40 In-correct
Q.40 Unattempt
The specific heat at constant pressure of a real gas obeying PV2=RT equation is :
The specific heat at constant pressure of a real gas obeying PV2=RT equation is :
Q.41 Correct
Q.41 In-correct
Q.41 Unattempt
Choose the correct answer from the options given below :
Choose the correct answer from the options given below :
Q.42 Correct
Q.42 In-correct
Q.42 Unattempt
Given below are two statements :
Statement I : In an LCR series circuit, current is maximum at resonance.
Statement II : Current in a purely resistive circuit can never be less than that in a series LCR circuit when connected to same voltage source. In the light of the above statements, choose the correct from the options given below :
Given below are two statements :
Statement I : In an LCR series circuit, current is maximum at resonance.
Statement II : Current in a purely resistive circuit can never be less than that in a series LCR circuit when connected to same voltage source. In the light of the above statements, choose the correct from the options given below :
Q.43 Correct
Q.43 In-correct
Q.43 Unattempt
The correct truth table for the following logic circuit is :
The correct truth table for the following logic circuit is :
Q.44 Correct
Q.44 In-correct
Q.44 Unattempt
A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is :
A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is :
Q.45 Correct
Q.45 In-correct
Q.45 Unattempt
A light string passing over a smooth light pulley connects two blocks of masses m1 and m2 (where m2>m1 ). If the acceleration of the system is ‌
g
√2
, then the ratio of the masses ‌
m1
m2
 is :
A light string passing over a smooth light pulley connects two blocks of masses m1 and m2 (where m2>m1 ). If the acceleration of the system is ‌
g
√2
, then the ratio of the masses ‌
m1
m2
 is :
Q.46 Correct
Q.46 In-correct
Q.46 Unattempt
Four particles A, B, C, D of mass ‌
m
2
,m,2m,4m, have same momentum, respectively. The particle with maximum kinetic energy is :
Four particles A, B, C, D of mass ‌
m
2
,m,2m,4m, have same momentum, respectively. The particle with maximum kinetic energy is :
Q.47 Correct
Q.47 In-correct
Q.47 Unattempt
A train starting from rest first accelerates uniformly up to a speed of 80‌km∕h for time t, then it moves with a constant speed for time 3t. The average speed of the train for this duration of journey will be (in km∕h ) :
A train starting from rest first accelerates uniformly up to a speed of 80‌km∕h for time t, then it moves with a constant speed for time 3t. The average speed of the train for this duration of journey will be (in km∕h ) :
Q.48 Correct
Q.48 In-correct
Q.48 Unattempt
An element ∆l=∆x
^
i
 is placed at the origin and carries a large current I=10A. The magnetic field on the y-axis at a distance of 0.5m from the elements ∆x of 1‌cm length is :
An element ∆l=∆x
^
i
 is placed at the origin and carries a large current I=10A. The magnetic field on the y-axis at a distance of 0.5m from the elements ∆x of 1‌cm length is :
Q.49 Correct
Q.49 In-correct
Q.49 Unattempt
A small ball of mass m and density ρ is dropped in a viscous liquid of density ρ0. After sometime, the ball falls with constant velocity. The viscous force on the ball is :
A small ball of mass m and density ρ is dropped in a viscous liquid of density ρ0. After sometime, the ball falls with constant velocity. The viscous force on the ball is :
Q.50 Correct
Q.50 In-correct
Q.50 Unattempt
In photoelectric experiment energy of 2.48‌eV irradiates a photo sensitive material. The stopping potential was measured to be 0.5V. Work function of the photo sensitive material is :
In photoelectric experiment energy of 2.48‌eV irradiates a photo sensitive material. The stopping potential was measured to be 0.5V. Work function of the photo sensitive material is :
Q.51 Correct
Q.51 In-correct
Q.51 Unattempt
If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day of earth will be ______ hours 30 minutes.
If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day of earth will be ______ hours 30 minutes.
Q.52 Correct
Q.52 In-correct
Q.52 Unattempt
Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point P is ‌
xσ
E0
. The value of x is _____
(all quantities are measured in SI units).
Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point P is ‌
xσ
E0
. The value of x is _____
(all quantities are measured in SI units).
Q.53 Correct
Q.53 In-correct
Q.53 Unattempt
A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of energy of big drop is ‌
10
x
. The value of x is ______.
A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of energy of big drop is ‌
10
x
. The value of x is ______.
Q.54 Correct
Q.54 In-correct
Q.54 Unattempt
When a dc voltage of 1100V is applied to an inductor, a dc current of 5A flows through it. When an ac voltage of 200V peak value is connected to inductor, its inductive reactance is found to be 20√3Ω. The power dissipated in the circuit is ______ W.
When a dc voltage of 1100V is applied to an inductor, a dc current of 5A flows through it. When an ac voltage of 200V peak value is connected to inductor, its inductive reactance is found to be 20√3Ω. The power dissipated in the circuit is ______ W.
Q.55 Correct
Q.55 In-correct
Q.55 Unattempt
The refractive index of prism is µ=√3 and the ratio of the angle of minimum deviation to the angle of prism is one. The value of angle of prism is _______ ∘.
The refractive index of prism is µ=√3 and the ratio of the angle of minimum deviation to the angle of prism is one. The value of angle of prism is _______ ∘.
Q.56 Correct
Q.56 In-correct
Q.56 Unattempt
A wire of resistance R and radius r is stretched till its radius became r∕2. If new resistance of the stretched wire is x, then value of x is ______.
A wire of resistance R and radius r is stretched till its radius became r∕2. If new resistance of the stretched wire is x, then value of x is ______.
Q.57 Correct
Q.57 In-correct
Q.57 Unattempt
Radius of a certain orbit of hydrogen atom is 8.48 Å. If energy of electron in this orbit is E∕x, then x= _____.
(Given a0=0.529Å,E= energy of electron in ground state)
Radius of a certain orbit of hydrogen atom is 8.48 Å. If energy of electron in this orbit is E∕x, then x= _____.
(Given a0=0.529Å,E= energy of electron in ground state)
Q.58 Correct
Q.58 In-correct
Q.58 Unattempt
A circular coil having 200 turns, 2.5×10−4m2 area and carrying 100µA current is placed in a uniform magnetic field of 1T. Initially the magnetic dipole moment (
→
M
) was directed along
→
B
. Amount of work, required to rotate the coil through 90∘ from its initial orientation such that
→
M
 becomes perpendicular to
→
B
, is ______ µJ.
A circular coil having 200 turns, 2.5×10−4m2 area and carrying 100µA current is placed in a uniform magnetic field of 1T. Initially the magnetic dipole moment (
→
M
) was directed along
→
B
. Amount of work, required to rotate the coil through 90∘ from its initial orientation such that
→
M
 becomes perpendicular to
→
B
, is ______ µJ.
Q.59 Correct
Q.59 In-correct
Q.59 Unattempt
A particle is doing simple harmonic motion of amplitude 0.06m and time period 3.14 s. The maximum velocity of the particle is ______ cm∕ s.
A particle is doing simple harmonic motion of amplitude 0.06m and time period 3.14 s. The maximum velocity of the particle is ______ cm∕ s.
Q.60 Correct
Q.60 In-correct
Q.60 Unattempt
For three vectors
→
A
=(−x
^
i
−6
^
j
−2
^
k
),
→
B
=(−
^
i
+4
^
j
+3
^
k
)‌‌ and ‌‌
→
C
=(−8
^
i
−
^
j
+3
^
k
),‌‌ if
→
A
⋅(
→
B
×
→
C
)=0, them value of x is _______.
For three vectors
→
A
=(−x
^
i
−6
^
j
−2
^
k
),
→
B
=(−
^
i
+4
^
j
+3
^
k
)‌‌ and ‌‌
→
C
=(−8
^
i
−
^
j
+3
^
k
),‌‌ if
→
A
⋅(
→
B
×
→
C
)=0, them value of x is _______.
Q.61 Correct
Q.61 In-correct
Q.61 Unattempt
Functional group present in sulphonic acid is:
Functional group present in sulphonic acid is:
Q.62 Correct
Q.62 In-correct
Q.62 Unattempt
Given below are two statements :
Statement I : Picric acid is 2, 4, 6-trinitrotoluene.
Statement II : Phenol-2, 4-disulphuric acid is treated with conc. HNO3 to get picric acid.
In the light of the above statement, choose the most appropriate answer from the options given below :
Given below are two statements :
Statement I : Picric acid is 2, 4, 6-trinitrotoluene.
Statement II : Phenol-2, 4-disulphuric acid is treated with conc. HNO3 to get picric acid.
In the light of the above statement, choose the most appropriate answer from the options given below :
Q.63 Correct
Q.63 In-correct
Q.63 Unattempt
Which of the following is metamer of the given compound (X) ?
Which of the following is metamer of the given compound (X) ?
Q.64 Correct
Q.64 In-correct
Q.64 Unattempt
DNA molecule contains 4 bases whoes structure are shown below. One of the structure is not correct, identify the incorrect base structure.
DNA molecule contains 4 bases whoes structure are shown below. One of the structure is not correct, identify the incorrect base structure.
Q.65 Correct
Q.65 In-correct
Q.65 Unattempt
Match List I with List II :

Choose the correct answer from the options given below :
Match List I with List II :

Choose the correct answer from the options given below :
Q.66 Correct
Q.66 In-correct
Q.66 Unattempt
Given below are two statements :
Statement I : Gallium is used in the manufacturing of thermometers.
Statement II : A thermometer containing gallium is useful for measuring the freezing point ( 256K ) of brine solution.
In the light of the above statement, choose the correct answer from the options given below :
Given below are two statements :
Statement I : Gallium is used in the manufacturing of thermometers.
Statement II : A thermometer containing gallium is useful for measuring the freezing point ( 256K ) of brine solution.
In the light of the above statement, choose the correct answer from the options given below :
Q.67 Correct
Q.67 In-correct
Q.67 Unattempt
Which of the following statements are correct ?
A. Glycerol is purified by vacuum distillation because it decomposes at its normal boiling point.
B. Aniline can be purified by steam distillation as aniline is miscible in water.
C. Ethanol can be separated from ethanol water mixture by azeotropic distillation because it forms azeotrope.
D. An organic compound is pure, if mixed M.P. is remained same.
Choose the most appropriate answer from the options given below :
Which of the following statements are correct ?
A. Glycerol is purified by vacuum distillation because it decomposes at its normal boiling point.
B. Aniline can be purified by steam distillation as aniline is miscible in water.
C. Ethanol can be separated from ethanol water mixture by azeotropic distillation because it forms azeotrope.
D. An organic compound is pure, if mixed M.P. is remained same.
Choose the most appropriate answer from the options given below :
Q.68 Correct
Q.68 In-correct
Q.68 Unattempt
Match List I with List II :

Choose the correct answer from the options given below :
Match List I with List II :

Choose the correct answer from the options given below :
Q.69 Correct
Q.69 In-correct
Q.69 Unattempt
In Reimer - Tiemann reaction, phenol is converted into salicylaldehyde through an intermediate. The structure of intermediate is ______.
In Reimer - Tiemann reaction, phenol is converted into salicylaldehyde through an intermediate. The structure of intermediate is ______.
Q.70 Correct
Q.70 In-correct
Q.70 Unattempt
Which of the following material is not a semiconductor.
Which of the following material is not a semiconductor.
Q.71 Correct
Q.71 In-correct
Q.71 Unattempt
Consider the following complexes.

The correct order of A, B, C and D in terms of wavenumber of light absorbed is :
Consider the following complexes.

The correct order of A, B, C and D in terms of wavenumber of light absorbed is :
Q.72 Correct
Q.72 In-correct
Q.72 Unattempt
Match List I with List II :

Choose the correct answer from the options given below :
Match List I with List II :

Choose the correct answer from the options given below :
Q.73 Correct
Q.73 In-correct
Q.73 Unattempt
The electron affinity value are negative for :
A. Be⟶Be−
B. N⟶N−
C. O⟶O2−
D. Na⟶Na−
E. Al⟶Al−
Choose the most appropriate answer from the options given below :
The electron affinity value are negative for :
A. Be⟶Be−
B. N⟶N−
C. O⟶O2−
D. Na⟶Na−
E. Al⟶Al−
Choose the most appropriate answer from the options given below :
Q.74 Correct
Q.74 In-correct
Q.74 Unattempt
The number of element from the following that do not belong to lanthanoids is :
Eu,Cm,Er,Tb,Yb and Lu
The number of element from the following that do not belong to lanthanoids is :
Eu,Cm,Er,Tb,Yb and Lu
Q.75 Correct
Q.75 In-correct
Q.75 Unattempt
The density of ' x ' M solution (' x ' molar) of NaOH is 1.12gmL−1. while in molality, the concentration of the solution is 3m ( 3 molal). Then x is (Given : Molar mass of NaOH is 40g∕mol )
The density of ' x ' M solution (' x ' molar) of NaOH is 1.12gmL−1. while in molality, the concentration of the solution is 3m ( 3 molal). Then x is (Given : Molar mass of NaOH is 40g∕mol )
Q.76 Correct
Q.76 In-correct
Q.76 Unattempt
Which among the following aldehydes is most reactive towards nucleophilic addition reactions?
Which among the following aldehydes is most reactive towards nucleophilic addition reactions?
Q.77 Correct
Q.77 In-correct
Q.77 Unattempt
At −20∘C and 1‌atm pressure, a cylinder is filled with equal number of H2.I2 and HI molecules for the reaction H2(g)+I2(g)⇌2‌HI(g),∣ the KP for the process is x×10−1⋅x= ________.
At −20∘C and 1‌atm pressure, a cylinder is filled with equal number of H2.I2 and HI molecules for the reaction H2(g)+I2(g)⇌2‌HI(g),∣ the KP for the process is x×10−1⋅x= ________.
Q.78 Correct
Q.78 In-correct
Q.78 Unattempt
Match List I with List II :

Choose the correct answer from the options given below :
Match List I with List II :

Choose the correct answer from the options given below :
Q.79 Correct
Q.79 In-correct
Q.79 Unattempt
A conductivity cell with two electrodes (dark side) are half filled with infinitely dilute aqueous solution of a weak electrolyte. If volume is doubled by adding more water at constant temperature, the molar conductivity of the cell will-
A conductivity cell with two electrodes (dark side) are half filled with infinitely dilute aqueous solution of a weak electrolyte. If volume is doubled by adding more water at constant temperature, the molar conductivity of the cell will-
Q.80 Correct
Q.80 In-correct
Q.80 Unattempt
Consider the dissociation of the weak acid HX as given below
HX(aq)⇌H+(aq)+X−(aq),Ka=1.2×10−5
[Ka:. dissociation constant ]
The osmotic pressure of 0.03M aqueous solution of HX at 300K is _______ ×10−2 bar (nearest integer).
[Given : R=0.083L‌bar‌Mol−1‌K−1 ]
Consider the dissociation of the weak acid HX as given below
HX(aq)⇌H+(aq)+X−(aq),Ka=1.2×10−5
[Ka:. dissociation constant ]
The osmotic pressure of 0.03M aqueous solution of HX at 300K is _______ ×10−2 bar (nearest integer).
[Given : R=0.083L‌bar‌Mol−1‌K−1 ]
Q.81 Correct
Q.81 In-correct
Q.81 Unattempt
The difference in the 'spin-only' magnetic moment values of KMnO4 and the manganese product formed during titration of KMnO4 against oxalic acid in acidic medium is _______ BM. (nearest integer)
The difference in the 'spin-only' magnetic moment values of KMnO4 and the manganese product formed during titration of KMnO4 against oxalic acid in acidic medium is _______ BM. (nearest integer)
Q.82 Correct
Q.82 In-correct
Q.82 Unattempt
Time required for 99.9% completion of a first order reaction is ______ time the time required for completion of 90% reaction.(nearest integer).
Time required for 99.9% completion of a first order reaction is ______ time the time required for completion of 90% reaction.(nearest integer).
Q.83 Correct
Q.83 In-correct
Q.83 Unattempt
Number of molecules from the following which can exhibit hydrogen bonding is ______ . (nearest integer)
Number of molecules from the following which can exhibit hydrogen bonding is ______ . (nearest integer)
Q.84 Correct
Q.84 In-correct
Q.84 Unattempt
9.3g of pure aniline upon diazotisation followed by coupling with phenol gives an orange dye. The mass of orange dye produced (assume 100\% yield/ conversion) is _____ g. (nearest integer)
9.3g of pure aniline upon diazotisation followed by coupling with phenol gives an orange dye. The mass of orange dye produced (assume 100\% yield/ conversion) is _____ g. (nearest integer)
Q.85 Correct
Q.85 In-correct
Q.85 Unattempt
The major product of the following reaction is P.
CH3C≡C−CH3
(i)‌Na∕liq.NH3
─────────▶
‌ (ii)dil. ‌KMnO4
273K
′P′
Number of oxygen atoms present in product ' P ' is ______ (nearest integer).
The major product of the following reaction is P.
CH3C≡C−CH3
(i)‌Na∕liq.NH3
─────────▶
‌ (ii)dil. ‌KMnO4
273K
′P′
Number of oxygen atoms present in product ' P ' is ______ (nearest integer).
Q.86 Correct
Q.86 In-correct
Q.86 Unattempt
Frequency of the de-Broglie wave of election in Bohr's first orbit of hydrogen atom is ______ ×1013‌Hz (nearest integer).
[Given : RH (Rydberg constant) =2.18×10−18J.
h( Plank's constant )=6.6×10−34 J.s. ]
Frequency of the de-Broglie wave of election in Bohr's first orbit of hydrogen atom is ______ ×1013‌Hz (nearest integer).
[Given : RH (Rydberg constant) =2.18×10−18J.
h( Plank's constant )=6.6×10−34 J.s. ]
Q.87 Correct
Q.87 In-correct
Q.87 Unattempt
The major products from the following reaction sequence are product A and product B.

The total sum of π electrons in product A and product B are ______ (nearest integer)
The major products from the following reaction sequence are product A and product B.

The total sum of π electrons in product A and product B are ______ (nearest integer)
Q.88 Correct
Q.88 In-correct
Q.88 Unattempt
Among CrO,Cr2O3 and CrO3, the sum of spin-only magnetic moment values of basic and amphoteric oxides is ______ 10−2‌BM (nearest integer).
(Given atomic number of Cr is 24 )
Among CrO,Cr2O3 and CrO3, the sum of spin-only magnetic moment values of basic and amphoteric oxides is ______ 10−2‌BM (nearest integer).
(Given atomic number of Cr is 24 )
Q.89 Correct
Q.89 In-correct
Q.89 Unattempt

Match List I with List II :


Choose the correct answer from the options given below :

Match List I with List II :


Choose the correct answer from the options given below :
Q.90 Correct
Q.90 In-correct
Q.90 Unattempt
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