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Solution
Q.1 Correct
Q.1 In-correct
Q.1 Unattempt
The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is
[31-Jan-2024 Shift 2]
The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is
[31-Jan-2024 Shift 2]
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt
Let A(a,b),B(3,4) and (−6,−8) respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of the point P(2a+3,7b+5) from the line 2x+3y−4=0 measured parallel to the line x−2y−1=0 is
[31-Jan-2024 Shift 2]
Let A(a,b),B(3,4) and (−6,−8) respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of the point P(2a+3,7b+5) from the line 2x+3y−4=0 measured parallel to the line x−2y−1=0 is
[31-Jan-2024 Shift 2]
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt
Let z1 and z2 be two complex number such that z1 +z2=5 and z13+z23=20+15i. Then |z14+z24| equals-
[31-Jan-2024 Shift 2]
Let z1 and z2 be two complex number such that z1 +z2=5 and z13+z23=20+15i. Then |z14+z24| equals-
[31-Jan-2024 Shift 2]
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt
Let a variable line passing through the centre of the circle x2+y2−16x−4y=0, meet the positive co-ordinate axes at the point A and B. Then the minimum value of OA+OB, where O is the origin, is equal to
[31-Jan-2024 Shift 2]
Let a variable line passing through the centre of the circle x2+y2−16x−4y=0, meet the positive co-ordinate axes at the point A and B. Then the minimum value of OA+OB, where O is the origin, is equal to
[31-Jan-2024 Shift 2]
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt
Let f,g:(0,∞)⟶R be two functions defined by f(x)=
x
∫
−x
(|t|−t2)e−t2‌dt and g(x)=
‌
∫
0
x2t1∕2e−t‌dt. Then the value of (f(√loge9)+g(√loge9)) is equal to
[31-Jan-2024 Shift 2]
Let f,g:(0,∞)⟶R be two functions defined by f(x)=
x
∫
−x
(|t|−t2)e−t2‌dt and g(x)=
‌
∫
0
x2t1∕2e−t‌dt. Then the value of (f(√loge9)+g(√loge9)) is equal to
[31-Jan-2024 Shift 2]
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt
Let (α,β,γ) be mirror image of the point (2,3,5) in the line ‌
x−1
2
−‌
y−2
3
−‌
z−3
4
.
Then 2α+3β+4γ is equal to
[31-Jan-2024 Shift 2]
Let (α,β,γ) be mirror image of the point (2,3,5) in the line ‌
x−1
2
−‌
y−2
3
−‌
z−3
4
.
Then 2α+3β+4γ is equal to
[31-Jan-2024 Shift 2]
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt
Let P be a parabola with vertex (2,3) and directrix 2x+y=6. Let an ellipse E:‌
x2
a2
+‌
y2
b2
=1,a>b of eccentricity ‌
1
√2
 pass through the focus of the parabola P. Then the square of the length of the latus rectum of E, is
[31-Jan-2024 Shift 2]
Let P be a parabola with vertex (2,3) and directrix 2x+y=6. Let an ellipse E:‌
x2
a2
+‌
y2
b2
=1,a>b of eccentricity ‌
1
√2
 pass through the focus of the parabola P. Then the square of the length of the latus rectum of E, is
[31-Jan-2024 Shift 2]
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt
The temperature T(t) of a body at time t=0 is 160∘ F and it decreases continuously as per the differential equation ‌
dT
dt
=−K(T−80), where K is positive constant. If T(15)=120∘F, then T(45) is equal to
[31-Jan-2024 Shift 2]
The temperature T(t) of a body at time t=0 is 160∘ F and it decreases continuously as per the differential equation ‌
dT
dt
=−K(T−80), where K is positive constant. If T(15)=120∘F, then T(45) is equal to
[31-Jan-2024 Shift 2]
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt
Let 2‌nd ‌,8‌th ‌ and 44‌th ‌, terms of a non-constant A.P. be respectively the 1‌st ‌,2‌nd ‌ and 3‌rd ‌ terms of G.P. If the first term of A.P. is 1 then the sum of first 20 terms is equal to-
[31-Jan-2024 Shift 2]
Let 2‌nd ‌,8‌th ‌ and 44‌th ‌, terms of a non-constant A.P. be respectively the 1‌st ‌,2‌nd ‌ and 3‌rd ‌ terms of G.P. If the first term of A.P. is 1 then the sum of first 20 terms is equal to-
[31-Jan-2024 Shift 2]
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt
Let ‌‌f:⟶R⟶(0,∞) be strictly increasing function such that
lim
x⟶∞
‌
f(7x)
f(x)
=1. Then, the value of
lim
x⟶∞
[‌
f(5x)
f(x)
−1] is equal to
[31-Jan-2024 Shift 2]
Let ‌‌f:⟶R⟶(0,∞) be strictly increasing function such that
lim
x⟶∞
‌
f(7x)
f(x)
=1. Then, the value of
lim
x⟶∞
[‌
f(5x)
f(x)
−1] is equal to
[31-Jan-2024 Shift 2]
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt
The area of the region enclosed by the parabola y=4x−x2 and 3y=(x−4)2 is equal to
[31-Jan-2024 Shift 2]
The area of the region enclosed by the parabola y=4x−x2 and 3y=(x−4)2 is equal to
[31-Jan-2024 Shift 2]
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt
Let the mean and the variance of 6 observation a, b, 68,44,48,60 be 55 and 194 , respectively if a>b, then a+3b is
[31-Jan-2024 Shift 2]
Let the mean and the variance of 6 observation a, b, 68,44,48,60 be 55 and 194 , respectively if a>b, then a+3b is
[31-Jan-2024 Shift 2]
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt
If the function f:(−∞,−1]⟶(a,b] defined by f(x)=ex3−3x+1 is one-one and onto, then the distance of the point P(2b+4,a+2) from the line x+e−3y=4 is :
[31-Jan-2024 Shift 2]
If the function f:(−∞,−1]⟶(a,b] defined by f(x)=ex3−3x+1 is one-one and onto, then the distance of the point P(2b+4,a+2) from the line x+e−3y=4 is :
[31-Jan-2024 Shift 2]
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt
Consider the function f:(0,∞)⟶R defined by f(x)=e−|logex|. If m and n be respectively the number of points at which f is not continuous and f is not differentiable, then m+n is
[31-Jan-2024 Shift 2]
Consider the function f:(0,∞)⟶R defined by f(x)=e−|logex|. If m and n be respectively the number of points at which f is not continuous and f is not differentiable, then m+n is
[31-Jan-2024 Shift 2]
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt
The number of solutions, of the equation esin‌x−2e−sin‌x=2 is
[31-Jan-2024 Shift 2]
The number of solutions, of the equation esin‌x−2e−sin‌x=2 is
[31-Jan-2024 Shift 2]
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt
If a=sin−1(sin(5)) and b=cos−1(cos(5)), then a2+b2 is equal to
[31-Jan-2024 Shift 2]
If a=sin−1(sin(5)) and b=cos−1(cos(5)), then a2+b2 is equal to
[31-Jan-2024 Shift 2]
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt
If for some m,n;‌6Cm+2(‌6Cm+1)+‌6Cm+2>‌8C3 and ‌n−1P3:‌nP4=1:8, then ‌nPm+1+‌n+1Cm is equal to
[31-Jan-2024 Shift 2]
If for some m,n;‌6Cm+2(‌6Cm+1)+‌6Cm+2>‌8C3 and ‌n−1P3:‌nP4=1:8, then ‌nPm+1+‌n+1Cm is equal to
[31-Jan-2024 Shift 2]
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt
A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is-
[31-Jan-2024 Shift 2]
A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is-
[31-Jan-2024 Shift 2]
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt
Let A be a 3×3 real matrix such that
A(
1
0
1
)=2(
1
0
1
),A(
−1
0
1
)=4(
−1
0
1
), A(
0
1
0
)=2(
0
1
0
)‌. ‌
Then, the system (A−3I)(
x
y
z
)=(
1
2
3
) has
[31-Jan-2024 Shift 2]
Let A be a 3×3 real matrix such that
A(
1
0
1
)=2(
1
0
1
),A(
−1
0
1
)=4(
−1
0
1
), A(
0
1
0
)=2(
0
1
0
)‌. ‌
Then, the system (A−3I)(
x
y
z
)=(
1
2
3
) has
[31-Jan-2024 Shift 2]
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt
The shortest distance between lines L1 and L2, where L1:‌
x−1
2
=‌
y+1
−3
=‌
z+4
2
 and L2 is the line passing through the points A(−4,4,3)⋅B(−1,6,3) and perpendicular to the line ‌
x−3
−2
=‌
y
3
=‌
z−1
1
, is
[31-Jan-2024 Shift 2]
The shortest distance between lines L1 and L2, where L1:‌
x−1
2
=‌
y+1
−3
=‌
z+4
2
 and L2 is the line passing through the points A(−4,4,3)⋅B(−1,6,3) and perpendicular to the line ‌
x−3
−2
=‌
y
3
=‌
z−1
1
, is
[31-Jan-2024 Shift 2]
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt
|‌
120
π3
‌
π
∫
0
‌
x2sin‌x‌cos‌x
sin‌4x+cos4x
‌dx| is equal to___
[31-Jan-2024 Shift 2]
|‌
120
π3
‌
π
∫
0
‌
x2sin‌x‌cos‌x
sin‌4x+cos4x
‌dx| is equal to___
[31-Jan-2024 Shift 2]
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt
Let a,b,c be the length of three sides of a triangle satisfying the condition (a2+b2)x2−2b(a+c). x+(b2+c2)=0. If the set of all possible values of x is the interval (α,β), then 12(α2+β2) is equal to____
[31-Jan-2024 Shift 2]
Let a,b,c be the length of three sides of a triangle satisfying the condition (a2+b2)x2−2b(a+c). x+(b2+c2)=0. If the set of all possible values of x is the interval (α,β), then 12(α2+β2) is equal to____
[31-Jan-2024 Shift 2]
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt
Let A(−2,−1),B(1,0),C(α,β) and D(γ,δ) be the vertices of a parallelogram ABCD. If the point C lies on 2x−y=5 and the point D lies on 3x−2y=6, then the value of |α+β+γ+δ| is equal to____
[31-Jan-2024 Shift 2]
Let A(−2,−1),B(1,0),C(α,β) and D(γ,δ) be the vertices of a parallelogram ABCD. If the point C lies on 2x−y=5 and the point D lies on 3x−2y=6, then the value of |α+β+γ+δ| is equal to____
[31-Jan-2024 Shift 2]
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt
Let the coefficient of xr in the expansion of
(x+3)n−1+(x+3)n−2(x+2)+
(x+3)n−3(x+2)2+......+(x+2)n−1
be αr. If
n
∑
r=0
αr=βn−γn,β,γ∈N, then the value of β2+γ2 equals
[31-Jan-2024 Shift 2]
Let the coefficient of xr in the expansion of
(x+3)n−1+(x+3)n−2(x+2)+
(x+3)n−3(x+2)2+......+(x+2)n−1
be αr. If
n
∑
r=0
αr=βn−γn,β,γ∈N, then the value of β2+γ2 equals
[31-Jan-2024 Shift 2]
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt
Let A be a 3×3 matrix and det(A)=2. If
n=det
(adj(adj(.......(adj‌A))))
‌
╰───────🡫──────╯
2024−‌ times ‌

Then the remainder when n is divided by 9 is equal to______
[31-Jan-2024 Shift 2]
Let A be a 3×3 matrix and det(A)=2. If
n=det
(adj(adj(.......(adj‌A))))
‌
╰───────🡫──────╯
2024−‌ times ‌

Then the remainder when n is divided by 9 is equal to______
[31-Jan-2024 Shift 2]
Q.26 Correct
Q.26 In-correct
Q.26 Unattempt
Let
→
a
=3
^
i
+2
^
j
+
^
k
,
→
b
=2
^
i
−
^
j
+3
^
k
 and
→
c
 be a vector such that (
→
a
+
→
b
)×
→
c
=2(
→
a
×
→
b
)+24
^
j
−6
^
k
 and (
→
a
−
→
b
+
^
i
)⋅
→
c
=−3. Then |
→
c
|2 is equal to____
[31-Jan-2024 Shift 2]
Let
→
a
=3
^
i
+2
^
j
+
^
k
,
→
b
=2
^
i
−
^
j
+3
^
k
 and
→
c
 be a vector such that (
→
a
+
→
b
)×
→
c
=2(
→
a
×
→
b
)+24
^
j
−6
^
k
 and (
→
a
−
→
b
+
^
i
)⋅
→
c
=−3. Then |
→
c
|2 is equal to____
[31-Jan-2024 Shift 2]
Q.27 Correct
Q.27 In-correct
Q.27 Unattempt
If
lim
x⟶0
‌
ax2ex−bloge(1+x)+cxe−x
x2sin‌x
=1, then 16(a2+b2+c2) is equal to_____
[31-Jan-2024 Shift 2]
If
lim
x⟶0
‌
ax2ex−bloge(1+x)+cxe−x
x2sin‌x
=1, then 16(a2+b2+c2) is equal to_____
[31-Jan-2024 Shift 2]
Q.28 Correct
Q.28 In-correct
Q.28 Unattempt
A line passes through A(4,−6,−2) and B(16,−2,4). The point P(a,b,c) where a,b,c are non-negative integers, on the line AB lies at a distance of 21 units, from the point A. The distance between the points P(a,b,c) and Q(4,−12,3) is equal to
[31-Jan-2024 Shift 2]
A line passes through A(4,−6,−2) and B(16,−2,4). The point P(a,b,c) where a,b,c are non-negative integers, on the line AB lies at a distance of 21 units, from the point A. The distance between the points P(a,b,c) and Q(4,−12,3) is equal to
[31-Jan-2024 Shift 2]
Q.29 Correct
Q.29 In-correct
Q.29 Unattempt
Let y=y(x) be the solution of the differential equation
sec2x‌dx+(e2ytan2x+tan‌x)dy=0
0<x<‌
π
2
,y(‌
π
4
)=0.‌ If ‌y(‌
π
6
)=α
Then e8α is equal to
[31-Jan-2024 Shift 2]
Let y=y(x) be the solution of the differential equation
sec2x‌dx+(e2ytan2x+tan‌x)dy=0
0<x<‌
π
2
,y(‌
π
4
)=0.‌ If ‌y(‌
π
6
)=α
Then e8α is equal to
[31-Jan-2024 Shift 2]
Q.30 Correct
Q.30 In-correct
Q.30 Unattempt
Let A={1,2,3,........100}. Let R be a relation on A defined by (x,y)∈R if and only if 2x=3y. Let R1 be a symmetric relation on A such that R⊂R1 and the number of elements in R1 is n. Then, the minimum value of n is
[31-Jan-2024 Shift 2]
Let A={1,2,3,........100}. Let R be a relation on A defined by (x,y)∈R if and only if 2x=3y. Let R1 be a symmetric relation on A such that R⊂R1 and the number of elements in R1 is n. Then, the minimum value of n is
[31-Jan-2024 Shift 2]
Q.31 Correct
Q.31 In-correct
Q.31 Unattempt
A light string passing over a smooth light fixed pulley connects two blocks of masses m1 and m2. If the acceleration of the system is g∕8, then the ratio of masses is

[31-Jan-2024 Shift 2]
A light string passing over a smooth light fixed pulley connects two blocks of masses m1 and m2. If the acceleration of the system is g∕8, then the ratio of masses is

[31-Jan-2024 Shift 2]
Q.32 Correct
Q.32 In-correct
Q.32 Unattempt
A uniform magnetic field of 2×10−3T acts along positive Y-direction. A rectangular loop of sides 20 cm and 10‌cm with current of 5A is Y−Z plane. The current is in anticlockwise sense with reference to negative X axis. Magnitude and direction of the torque is :
[31-Jan-2024 Shift 2]
A uniform magnetic field of 2×10−3T acts along positive Y-direction. A rectangular loop of sides 20 cm and 10‌cm with current of 5A is Y−Z plane. The current is in anticlockwise sense with reference to negative X axis. Magnitude and direction of the torque is :
[31-Jan-2024 Shift 2]
Q.33 Correct
Q.33 In-correct
Q.33 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.34 Correct
Q.34 In-correct
Q.34 Unattempt
Force between two point charges q1 and q2 placed in vacuum at ' r ' cm apart is F. Force between them when placed in a medium having dielectric K=5 at ' r∕5 ' cm apart will be:
[31-Jan-2024 Shift 2]
Force between two point charges q1 and q2 placed in vacuum at ' r ' cm apart is F. Force between them when placed in a medium having dielectric K=5 at ' r∕5 ' cm apart will be:
[31-Jan-2024 Shift 2]
Q.35 Correct
Q.35 In-correct
Q.35 Unattempt
An AC voltage V=20sin‌200πt is applied to a series LCR circuit which drives a current I=10sin‌(200πt+‌
π
3
). The average power dissipated is:
[31-Jan-2024 Shift 2]
An AC voltage V=20sin‌200πt is applied to a series LCR circuit which drives a current I=10sin‌(200πt+‌
π
3
). The average power dissipated is:
[31-Jan-2024 Shift 2]
Q.36 Correct
Q.36 In-correct
Q.36 Unattempt
When unpolarized light is incident at an angle of 60∘ on a transparent medium from air. The reflected ray is completely polarized. The angle of refraction in the medium is
[31-Jan-2024 Shift 2]
When unpolarized light is incident at an angle of 60∘ on a transparent medium from air. The reflected ray is completely polarized. The angle of refraction in the medium is
[31-Jan-2024 Shift 2]
Q.37 Correct
Q.37 In-correct
Q.37 Unattempt
The speed of sound in oxygen at S.T.P. will be approximately:
(Given, R=8.3JK−1,γ=1.4 )
[31-Jan-2024 Shift 2]
The speed of sound in oxygen at S.T.P. will be approximately:
(Given, R=8.3JK−1,γ=1.4 )
[31-Jan-2024 Shift 2]
Q.38 Correct
Q.38 In-correct
Q.38 Unattempt
A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature T. Neglecting all vibrational modes, the total internal energy of the system is
[31-Jan-2024 Shift 2]
A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature T. Neglecting all vibrational modes, the total internal energy of the system is
[31-Jan-2024 Shift 2]
Q.39 Correct
Q.39 In-correct
Q.39 Unattempt
The resistance per centimeter of a meter bridge wire is r, with XΩ resistance in left gap. Balancing length from left end is at 40‌cm with 25Ω resistance in right gap. Now the wire is replaced by another wire of 2r resistance per centimeter. The new balancing length for same settings will be at
[31-Jan-2024 Shift 2]
The resistance per centimeter of a meter bridge wire is r, with XΩ resistance in left gap. Balancing length from left end is at 40‌cm with 25Ω resistance in right gap. Now the wire is replaced by another wire of 2r resistance per centimeter. The new balancing length for same settings will be at
[31-Jan-2024 Shift 2]
Q.40 Correct
Q.40 In-correct
Q.40 Unattempt
Given below are two statements:
Statement I: Electromagnetic waves carry energy as they travel through space and this energy is equally shared by the electric and magnetic fields.
Statement II: When electromagnetic waves strike a surface, a pressure is exerted on the surface.
In the light of the above statements, choose the most appropriate answer from the options given below:
[31-Jan-2024 Shift 2]
Given below are two statements:
Statement I: Electromagnetic waves carry energy as they travel through space and this energy is equally shared by the electric and magnetic fields.
Statement II: When electromagnetic waves strike a surface, a pressure is exerted on the surface.
In the light of the above statements, choose the most appropriate answer from the options given below:
[31-Jan-2024 Shift 2]
Q.41 Correct
Q.41 In-correct
Q.41 Unattempt
In a photoelectric effect experiment a light of frequency 1.5 times the threshold frequency is made to fall on the surface of photosensitive material. Now if the frequency is halved and intensity is doubled, the number of photo electrons emitted will be:
[31-Jan-2024 Shift 2]
In a photoelectric effect experiment a light of frequency 1.5 times the threshold frequency is made to fall on the surface of photosensitive material. Now if the frequency is halved and intensity is doubled, the number of photo electrons emitted will be:
[31-Jan-2024 Shift 2]
Q.42 Correct
Q.42 In-correct
Q.42 Unattempt
A block of mass 5‌kg is placed on a rough inclined surface as shown in the figure.
If
→
F
1 is the force required to just move the block up the inclined plane and
→
F
2 is the force required to just prevent the block from sliding down, then the value of |
→
F
1|−|
→
F
2| is : [Use g=10m∕ s2 ]
[31-Jan-2024 Shift 2]
A block of mass 5‌kg is placed on a rough inclined surface as shown in the figure.

If
→
F
1 is the force required to just move the block up the inclined plane and
→
F
2 is the force required to just prevent the block from sliding down, then the value of |
→
F
1|−|
→
F
2| is : [Use g=10m∕ s2 ]
[31-Jan-2024 Shift 2]
Q.43 Correct
Q.43 In-correct
Q.43 Unattempt
By what percentage will the illumination of the lamp decrease if the current drops by 20% ?
[31-Jan-2024 Shift 2]
By what percentage will the illumination of the lamp decrease if the current drops by 20% ?
[31-Jan-2024 Shift 2]
Q.44 Correct
Q.44 In-correct
Q.44 Unattempt
If two vectors
→
A
 and
→
B
 having equal magnitude R are inclined at an angle θ, then
[31-Jan-2024 Shift 2]
If two vectors
→
A
 and
→
B
 having equal magnitude R are inclined at an angle θ, then
[31-Jan-2024 Shift 2]
Q.45 Correct
Q.45 In-correct
Q.45 Unattempt
The mass number of nucleus having radius equal to half of the radius of nucleus with mass number 192 is:
[31-Jan-2024 Shift 2]
The mass number of nucleus having radius equal to half of the radius of nucleus with mass number 192 is:
[31-Jan-2024 Shift 2]
Q.46 Correct
Q.46 In-correct
Q.46 Unattempt
The mass of the moon is
1
144
 times the mass of a planet and its diameter
1
16
 times the diameter of a planet. If the escape velocity on the planet is v, the escape velocity on the moon will be:
[31-Jan-2024 Shift 2]
The mass of the moon is
1
144
 times the mass of a planet and its diameter
1
16
 times the diameter of a planet. If the escape velocity on the planet is v, the escape velocity on the moon will be:
[31-Jan-2024 Shift 2]
Q.47 Correct
Q.47 In-correct
Q.47 Unattempt
A small spherical ball of radius r, falling through a viscous medium of negligible density has terminal velocity ' v '. Another ball of the same mass but of radius 2r, falling through the same viscous medium will have terminal velocity:
[31-Jan-2024 Shift 2]
A small spherical ball of radius r, falling through a viscous medium of negligible density has terminal velocity ' v '. Another ball of the same mass but of radius 2r, falling through the same viscous medium will have terminal velocity:
[31-Jan-2024 Shift 2]
Q.48 Correct
Q.48 In-correct
Q.48 Unattempt
A body of mass 2‌kg begins to move under the action of a time dependent force given by
→
F
=(6t
^
i
+6t2
^
j
)N. The power developed by the force at the time t is given by:
[31-Jan-2024 Shift 2]
A body of mass 2‌kg begins to move under the action of a time dependent force given by
→
F
=(6t
^
i
+6t2
^
j
)N. The power developed by the force at the time t is given by:
[31-Jan-2024 Shift 2]
Q.49 Correct
Q.49 In-correct
Q.49 Unattempt
The output of the given circuit diagram is

[31-Jan-2024 Shift 2]
The output of the given circuit diagram is

[31-Jan-2024 Shift 2]
Q.50 Correct
Q.50 In-correct
Q.50 Unattempt
Consider two physical quantities A and B related to each other as E=‌
B−x2
At
 where E,x and t have dimensions of energy, length and time respectively. The dimension of AB is
[31-Jan-2024 Shift 2]
Consider two physical quantities A and B related to each other as E=‌
B−x2
At
 where E,x and t have dimensions of energy, length and time respectively. The dimension of AB is
[31-Jan-2024 Shift 2]
Q.51 Correct
Q.51 In-correct
Q.51 Unattempt
In the following circuit, the battery has an emf of 2 V and an internal resistance of ‌
2
3
Ω. The power consumption in the entire circuit is_______ W.

[31-Jan-2024 Shift 2]
In the following circuit, the battery has an emf of 2 V and an internal resistance of ‌
2
3
Ω. The power consumption in the entire circuit is_______ W.

[31-Jan-2024 Shift 2]
Q.52 Correct
Q.52 In-correct
Q.52 Unattempt
Light from a point source in air falls on a convex curved surface of radius 20‌cm and refractive index 1.5. If the source is located at 100‌cm from the convex surface, the image will be formed at ______cm from the object.
[31-Jan-2024 Shift 2]
Light from a point source in air falls on a convex curved surface of radius 20‌cm and refractive index 1.5. If the source is located at 100‌cm from the convex surface, the image will be formed at ______cm from the object.
[31-Jan-2024 Shift 2]
Q.53 Correct
Q.53 In-correct
Q.53 Unattempt
The magnetic flux φ (in weber) linked with a closed circuit of resistance 8Ω varies with time (in seconds) as φ=5t2−36t+1. The induced current in the circuit at t=2 s is _____A.
[31-Jan-2024 Shift 2]
The magnetic flux φ (in weber) linked with a closed circuit of resistance 8Ω varies with time (in seconds) as φ=5t2−36t+1. The induced current in the circuit at t=2 s is _____A.
[31-Jan-2024 Shift 2]
Q.54 Correct
Q.54 In-correct
Q.54 Unattempt
Two blocks of mass 2‌kg and 4‌kg are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is 4.0×10−5 m and Young's modulus of the metal is 2.0×1011N∕m2. The longitudinal strain developed in the wire is ‌
1
απ
. The value of α is_____ [Use g=10m∕ s2 )

[31-Jan-2024 Shift 2]
Two blocks of mass 2‌kg and 4‌kg are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is 4.0×10−5 m and Young's modulus of the metal is 2.0×1011N∕m2. The longitudinal strain developed in the wire is ‌
1
απ
. The value of α is_____ [Use g=10m∕ s2 )
[31-Jan-2024 Shift 2]
Q.55 Correct
Q.55 In-correct
Q.55 Unattempt
A body of mass ' m ' is projected with a speed ' u ' making an angle of 45∘ with the ground. The angular momentum of the body about the point of projection, at the highest point is expressed as ‌
√2mu3
Xg
. The value of ' X ' is______
[31-Jan-2024 Shift 2]
A body of mass ' m ' is projected with a speed ' u ' making an angle of 45∘ with the ground. The angular momentum of the body about the point of projection, at the highest point is expressed as ‌
√2mu3
Xg
. The value of ' X ' is______
[31-Jan-2024 Shift 2]
Q.56 Correct
Q.56 In-correct
Q.56 Unattempt
Two circular coils P and Q of 100 turns each have same radius of π‌cm. The currents in P and R are 1A and 2 A respectively. P and Q are placed with their planes mutually perpendicular with their centers coincide. The resultant magnetic field induction at the center of the coils is √x‌mT, where x=____ [. Use µ0=4π×10−7TmA−1 ]
[31-Jan-2024 Shift 2]
Two circular coils P and Q of 100 turns each have same radius of π‌cm. The currents in P and R are 1A and 2 A respectively. P and Q are placed with their planes mutually perpendicular with their centers coincide. The resultant magnetic field induction at the center of the coils is √x‌mT, where x=____ [. Use µ0=4π×10−7TmA−1 ]
[31-Jan-2024 Shift 2]
Q.57 Correct
Q.57 In-correct
Q.57 Unattempt
The distance between charges +q and −q is 2l and between +2q and −2q is 4l. The electrostatic potential at point P at a distance r from centre O is −α[‌
ql
r2
]×109V, where the value of α is (Use ‌
1
4πε0
=9×109Nm2C−2)

[31-Jan-2024 Shift 2]
The distance between charges +q and −q is 2l and between +2q and −2q is 4l. The electrostatic potential at point P at a distance r from centre O is −α[‌
ql
r2
]×109V, where the value of α is (Use ‌
1
4πε0
=9×109Nm2C−2)

[31-Jan-2024 Shift 2]
Q.58 Correct
Q.58 In-correct
Q.58 Unattempt
Two identical spheres each of mass 2‌kg and radius 50‌cm are fixed at the ends of a light rod so that the separation between the centers is 150‌cm. Then, moment of inertia of the system about an axis perpendicular to the rod and passing through its middle point is ‌
x
20
‌kg‌m2, where the value of x is___
[31-Jan-2024 Shift 2]
Two identical spheres each of mass 2‌kg and radius 50‌cm are fixed at the ends of a light rod so that the separation between the centers is 150‌cm. Then, moment of inertia of the system about an axis perpendicular to the rod and passing through its middle point is ‌
x
20
‌kg‌m2, where the value of x is___
[31-Jan-2024 Shift 2]
Q.59 Correct
Q.59 In-correct
Q.59 Unattempt
The time period of simple harmonic motion of mass M in the given figure is π√‌
αM
5K
, where the value of α is _____

[31-Jan-2024 Shift 2]
The time period of simple harmonic motion of mass M in the given figure is π√‌
αM
5K
, where the value of α is _____

[31-Jan-2024 Shift 2]
Q.60 Correct
Q.60 In-correct
Q.60 Unattempt
A nucleus has mass number A1 and volume V1. Another nucleus has mass number A2 and volume V2. If relation between mass number is A2=4A1, then ‌
V2
V1
=____
[31-Jan-2024 Shift 2]
A nucleus has mass number A1 and volume V1. Another nucleus has mass number A2 and volume V2. If relation between mass number is A2=4A1, then ‌
V2
V1
=____
[31-Jan-2024 Shift 2]
Q.61 Correct
Q.61 In-correct
Q.61 Unattempt
Choose the correct answer from the options given below :

[31-Jan-2024 Shift 2]
Choose the correct answer from the options given below :

[31-Jan-2024 Shift 2]
Q.62 Correct
Q.62 In-correct
Q.62 Unattempt
A sample of CaCO3 and MgCO3 weighed 2.21g is ignited to constant weight of 1.152g. The composition of mixture is :
(Given molar mass in gmol−1
CaCO3:100,MgCO3:84‌ ) ‌
[31-Jan-2024 Shift 2]
A sample of CaCO3 and MgCO3 weighed 2.21g is ignited to constant weight of 1.152g. The composition of mixture is :
(Given molar mass in gmol−1
CaCO3:100,MgCO3:84‌ ) ‌
[31-Jan-2024 Shift 2]
Q.63 Correct
Q.63 In-correct
Q.63 Unattempt
Identify A and B in the following reaction sequence.

[31-Jan-2024 Shift 2]
Identify A and B in the following reaction sequence.

[31-Jan-2024 Shift 2]
Q.64 Correct
Q.64 In-correct
Q.64 Unattempt
Given below are two statements :
Statement I: S8 solid undergoes disproportionation reaction under alkaline conditions to form S2− and S2O3‌2−
Statement II: ClO4−can undergo disproportionation reaction under acidic condition. In the light of the above statements, choose the most appropriate answer from the options given below :
[31-Jan-2024 Shift 2]
Given below are two statements :
Statement I: S8 solid undergoes disproportionation reaction under alkaline conditions to form S2− and S2O3‌2−
Statement II: ClO4−can undergo disproportionation reaction under acidic condition. In the light of the above statements, choose the most appropriate answer from the options given below :
[31-Jan-2024 Shift 2]
Q.65 Correct
Q.65 In-correct
Q.65 Unattempt
Identify major product ' P ' formed in the following reaction.

[31-Jan-2024 Shift 2]
Identify major product ' P ' formed in the following reaction.

[31-Jan-2024 Shift 2]
Q.66 Correct
Q.66 In-correct
Q.66 Unattempt
Major product of the following reaction is -

[31-Jan-2024 Shift 2]
Major product of the following reaction is -

[31-Jan-2024 Shift 2]
Q.67 Correct
Q.67 In-correct
Q.67 Unattempt
Identify structure of 2,3-dibromo-1-phenylpentane.
[31-Jan-2024 Shift 2]
Identify structure of 2,3-dibromo-1-phenylpentane.
[31-Jan-2024 Shift 2]
Q.68 Correct
Q.68 In-correct
Q.68 Unattempt
Select the option with correct property -
[31-Jan-2024 Shift 2]
Select the option with correct property -
[31-Jan-2024 Shift 2]
Q.69 Correct
Q.69 In-correct
Q.69 Unattempt
The azo-dye (Y) formed in the following reactions is Sulphanilic acid +NaNO2+CH3‌COOH⟶X

[31-Jan-2024 Shift 2]
The azo-dye (Y) formed in the following reactions is Sulphanilic acid +NaNO2+CH3‌COOH⟶X
[31-Jan-2024 Shift 2]
Q.70 Correct
Q.70 In-correct
Q.70 Unattempt
Given below are two statements:
Statement I: Aniline reacts with con. H2SO4 followed by heating at 453−473K gives p aminobenzene sulphonic acid, which gives blood red colour in the 'Lassaigne's test'.
Statement II: In Friedel - Craft's alkylation and acylation reactions, aniline forms salt with the AlCl3 catalyst. Due to this, nitrogen of aniline aquires a positive charge and acts as deactivating group.
In the light of the above statements, choose the correct answer from the options given below :
[31-Jan-2024 Shift 2]
Given below are two statements:
Statement I: Aniline reacts with con. H2SO4 followed by heating at 453−473K gives p aminobenzene sulphonic acid, which gives blood red colour in the 'Lassaigne's test'.
Statement II: In Friedel - Craft's alkylation and acylation reactions, aniline forms salt with the AlCl3 catalyst. Due to this, nitrogen of aniline aquires a positive charge and acts as deactivating group.
In the light of the above statements, choose the correct answer from the options given below :
[31-Jan-2024 Shift 2]
Q.71 Correct
Q.71 In-correct
Q.71 Unattempt
A(g)⇌B(g)+‌
C
2
(g)‌‌ The correct relationship between KP,α and equilibrium pressure P is
[31-Jan-2024 Shift 2]
A(g)⇌B(g)+‌
C
2
(g)‌‌ The correct relationship between KP,α and equilibrium pressure P is
[31-Jan-2024 Shift 2]
Q.72 Correct
Q.72 In-correct
Q.72 Unattempt
Choose the correct statements from the following
A. All group 16 elements form oxides of general formula EO2 and EO3 where E=S,Se,Te and Po. Both the types of oxides are acidic in nature.
B. TeO2 is an oxidising agent while SO2 is reducing in nature.
C. The reducing property decreases from H2S to H2‌Te down the group.
D. The ozone molecule contains five lone pairs of electrons.
Choose the correct answer from the options given below:
[31-Jan-2024 Shift 2]
Choose the correct statements from the following
A. All group 16 elements form oxides of general formula EO2 and EO3 where E=S,Se,Te and Po. Both the types of oxides are acidic in nature.
B. TeO2 is an oxidising agent while SO2 is reducing in nature.
C. The reducing property decreases from H2S to H2‌Te down the group.
D. The ozone molecule contains five lone pairs of electrons.
Choose the correct answer from the options given below:
[31-Jan-2024 Shift 2]
Q.73 Correct
Q.73 In-correct
Q.73 Unattempt
Identify the name reaction.

[31-Jan-2024 Shift 2]
Identify the name reaction.

[31-Jan-2024 Shift 2]
Q.74 Correct
Q.74 In-correct
Q.74 Unattempt
Which of the following is least ionic?
[31-Jan-2024 Shift 2]
Which of the following is least ionic?
[31-Jan-2024 Shift 2]
Q.75 Correct
Q.75 In-correct
Q.75 Unattempt
The fragrance of flowers is due to the presence of some steam volatile organic compounds called essential oils. These are generally insoluble in water at room temperature but are miscible with water vapour in vapour phase. A suitable method for the extraction of these oils from the flowers is -
[31-Jan-2024 Shift 2]
The fragrance of flowers is due to the presence of some steam volatile organic compounds called essential oils. These are generally insoluble in water at room temperature but are miscible with water vapour in vapour phase. A suitable method for the extraction of these oils from the flowers is -
[31-Jan-2024 Shift 2]
Q.76 Correct
Q.76 In-correct
Q.76 Unattempt
Given below are two statements :
Statement I: Group 13 trivalent halides get easily hydrolyzed by water due to their covalent nature.
Statement II: AlCl3 upon hydrolysis in acidified aqueous solution forms octahedral [Al(H2O)6]3+ ion.
In the light of the above statements, choose the correct answer from the options given below :
[31-Jan-2024 Shift 2]
Given below are two statements :
Statement I: Group 13 trivalent halides get easily hydrolyzed by water due to their covalent nature.
Statement II: AlCl3 upon hydrolysis in acidified aqueous solution forms octahedral [Al(H2O)6]3+ ion.
In the light of the above statements, choose the correct answer from the options given below :
[31-Jan-2024 Shift 2]
Q.77 Correct
Q.77 In-correct
Q.77 Unattempt
The four quantum numbers for the electron in the outer most orbital of potassium (atomic no. 19) are
[31-Jan-2024 Shift 2]
The four quantum numbers for the electron in the outer most orbital of potassium (atomic no. 19) are
[31-Jan-2024 Shift 2]
Q.78 Correct
Q.78 In-correct
Q.78 Unattempt
Choose the correct statements from the following
A. Mn2O7 is an oil at room temperature
B. V2O4 reacts with acid to give VO22+
C. CrO is a basic oxide
D. V2O5 does not react with acid
Choose the correct answer from the options given below :
[31-Jan-2024 Shift 2]
Choose the correct statements from the following
A. Mn2O7 is an oil at room temperature
B. V2O4 reacts with acid to give VO22+
C. CrO is a basic oxide
D. V2O5 does not react with acid
Choose the correct answer from the options given below :
[31-Jan-2024 Shift 2]
Q.79 Correct
Q.79 In-correct
Q.79 Unattempt
The correct order of reactivity in electrophilic substitution reaction of the following compounds is :

[31-Jan-2024 Shift 2]
The correct order of reactivity in electrophilic substitution reaction of the following compounds is :

[31-Jan-2024 Shift 2]
Q.80 Correct
Q.80 In-correct
Q.80 Unattempt
Consider the following elements.
Which of the following is/are true about A′,B′,C′ and D′ ?
A. Order of atomic radii: B′<A′<D′<C′
B. Order of metallic character : B′<A′<D′<C′
C. Size of the element : D′<C′<B′<A′
D. Order of ionic radii : B′+<A′+<D′+<C′+
Choose the correct answer from the options given below :
[31-Jan-2024 Shift 2]
Consider the following elements.

Which of the following is/are true about A′,B′,C′ and D′ ?
A. Order of atomic radii: B′<A′<D′<C′
B. Order of metallic character : B′<A′<D′<C′
C. Size of the element : D′<C′<B′<A′
D. Order of ionic radii : B′+<A′+<D′+<C′+
Choose the correct answer from the options given below :
[31-Jan-2024 Shift 2]
Q.81 Correct
Q.81 In-correct
Q.81 Unattempt
A diatomic molecule has a dipole moment of 1.2D. If the bond distance is 1Å, then fractional charge on each atom is ____×10−1‌esu.
(Given 1D=10−18 esu cm )
[31-Jan-2024 Shift 2]
A diatomic molecule has a dipole moment of 1.2D. If the bond distance is 1Å, then fractional charge on each atom is ____×10−1‌esu.
(Given 1D=10−18 esu cm )
[31-Jan-2024 Shift 2]
Q.82 Correct
Q.82 In-correct
Q.82 Unattempt
r=k[A] for a reaction, 50% of A is decomposed in 120 minutes. The time taken for 90% decomposition of A is ____ minutes.
[31-Jan-2024 Shift 2]
r=k[A] for a reaction, 50% of A is decomposed in 120 minutes. The time taken for 90% decomposition of A is ____ minutes.
[31-Jan-2024 Shift 2]
Q.83 Correct
Q.83 In-correct
Q.83 Unattempt
A compound (x) with molar mass 108gmol−1 undergoes acetylation to give product with molar mass 192gmol−1. The number of amino groups in the compound (x) is______
[31-Jan-2024 Shift 2]
A compound (x) with molar mass 108gmol−1 undergoes acetylation to give product with molar mass 192gmol−1. The number of amino groups in the compound (x) is______
[31-Jan-2024 Shift 2]
Q.84 Correct
Q.84 In-correct
Q.84 Unattempt
Number of isomeric products formed by monochlorination of 2-methylbutane in presence of sunlight is_______
[31-Jan-2024 Shift 2]
Number of isomeric products formed by monochlorination of 2-methylbutane in presence of sunlight is_______
[31-Jan-2024 Shift 2]
Q.85 Correct
Q.85 In-correct
Q.85 Unattempt
Number of moles of H+ions required by 1 mole of MnO4−to oxidise oxalate ion to CO2 is_____
[31-Jan-2024 Shift 2]
Number of moles of H+ions required by 1 mole of MnO4−to oxidise oxalate ion to CO2 is_____
[31-Jan-2024 Shift 2]
Q.86 Correct
Q.86 In-correct
Q.86 Unattempt
In the reaction of potassium dichromate, potassium chloride and sulfuric acid (conc.), the oxidation state of the chromium in the product is (+)___
[31-Jan-2024 Shift 2]
In the reaction of potassium dichromate, potassium chloride and sulfuric acid (conc.), the oxidation state of the chromium in the product is (+)___
[31-Jan-2024 Shift 2]
Q.87 Correct
Q.87 In-correct
Q.87 Unattempt
The molarity of 1L orthophosphoric acid (H3PO4) having 70% purity by weight (specific gravity 1.54gcm−3 ) is______ M.
(Molar mass of H3PO4=98gmol−1 )
[31-Jan-2024 Shift 2]
The molarity of 1L orthophosphoric acid (H3PO4) having 70% purity by weight (specific gravity 1.54gcm−3 ) is______ M.
(Molar mass of H3PO4=98gmol−1 )
[31-Jan-2024 Shift 2]
Q.88 Correct
Q.88 In-correct
Q.88 Unattempt
The values of conductivity of some materials at 298.15K−1Sm−1 are 2.1×103, 1.0×10−16,1.2×10,3.91,1.5×10−2, 1×10−7,1.0×103. The number of conductors among the materials is____
[31-Jan-2024 Shift 2]
The values of conductivity of some materials at 298.15K−1Sm−1 are 2.1×103, 1.0×10−16,1.2×10,3.91,1.5×10−2, 1×10−7,1.0×103. The number of conductors among the materials is____
[31-Jan-2024 Shift 2]
Q.89 Correct
Q.89 In-correct
Q.89 Unattempt
From the vitamins A,B1,B6,B12,C,D,E and K, the number vitamins that can be stored in our body is____
[31-Jan-2024 Shift 2]
From the vitamins A,B1,B6,B12,C,D,E and K, the number vitamins that can be stored in our body is____
[31-Jan-2024 Shift 2]
Q.90 Correct
Q.90 In-correct
Q.90 Unattempt
If 5 moles of an ideal gas expands from 10L to a volume of 100L at 300K under isothermal and reversible condition then work, w, is −xJ. The value of x is_____
(Given R=8.314JK−1mol−1 )
[31-Jan-2024 Shift 2]
If 5 moles of an ideal gas expands from 10L to a volume of 100L at 300K under isothermal and reversible condition then work, w, is −xJ. The value of x is_____
(Given R=8.314JK−1mol−1 )
[31-Jan-2024 Shift 2]
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