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Solution
Q.1 Correct
Q.1 In-correct
Q.1 Unattempt
Let D = R - {0 , 1} and f : D → D , g : D → D and h : D → D be three functions defined by
f (x) =
1
x
 ; g (x) = 1 - x and h (x) =
1
1−x
. If j : D → D is such that
(g o j o f) (x) = j (x) fot all x ∊ D, then which one of the following is j (x) ?
©
Let D = R - {0 , 1} and f : D → D , g : D → D and h : D → D be three functions defined by
f (x) =
1
x
 ; g (x) = 1 - x and h (x) =
1
1−x
. If j : D → D is such that
(g o j o f) (x) = j (x) fot all x ∊ D, then which one of the following is j (x) ?
©
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt
The maximum value of the function f (x) = tan(x+
2π
3
) - tan (x+
π
6
) + cos (x+
π
6
) in [−
5π
12
,−
π
3
] is
©
The maximum value of the function f (x) = tan(x+
2π
3
) - tan (x+
π
6
) + cos (x+
π
6
) in [−
5π
12
,−
π
3
] is
©
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt
12+(12+22) + (12+22+32) + ... + (12+22+...+n2) =
©
12+(12+22) + (12+22+32) + ... + (12+22+...+n2) =
©
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt
if
|
a+b+2cab
c2a+b+cb
caa+2b+c
|
= 2 , then a3+b3+c3 - 3abc =
©
if
|
a+b+2cab
c2a+b+cb
caa+2b+c
|
= 2 , then a3+b3+c3 - 3abc =
©
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt
If k is one of the roots of the equation x2 - 25x + 24 = 0 such that A = [
121
323
11k
] is a non-singular matrix, then A−1 =
©
If k is one of the roots of the equation x2 - 25x + 24 = 0 such that A = [
121
323
11k
] is a non-singular matrix, then A−1 =
©
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt
A value of b for which the rank of the matrix A = [
11−10
44−31
b222
99b3
] is 3 , is
©
A value of b for which the rank of the matrix A = [
11−10
44−31
b222
99b3
] is 3 , is
©
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt
If z = x - iy and z
1
3
 = a + ib, then
(
x
a
+
y
b
)
a2+b2
 =
©
If z = x - iy and z
1
3
 = a + ib, then
(
x
a
+
y
b
)
a2+b2
 =
©
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt
The equation whose solutions are the non-zero solutions of the equation
−
z
 = iz2 , is
©
The equation whose solutions are the non-zero solutions of the equation
−
z
 = iz2 , is
©
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt
If x , y ∊ R and x2 + y + 4i and - 3 + x2yi are conjugate to each other (|x|+|y|)2 =
©
If x , y ∊ R and x2 + y + 4i and - 3 + x2yi are conjugate to each other (|x|+|y|)2 =
©
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt
6
Σ
k=1
(sin‌
2πk
7
−icos
2πk
7
) =
©
6
Σ
k=1
(sin‌
2πk
7
−icos
2πk
7
) =
©
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt
If a satisfies the equation √
x
2x+1
 + √
2x+1
x
 = 2 , then the roots of the equation α2x2 + 4αx + 3 = 0 are
©
If a satisfies the equation √
x
2x+1
 + √
2x+1
x
 = 2 , then the roots of the equation α2x2 + 4αx + 3 = 0 are
©
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt
Let/ f (x) = x2 + 2x + 2 , g (x) = −x2 + 2x - 1 and a , b be the extreme values of f (x) , g (x) respectively. If c is the extreme value of
f
g
 (x) (for x ≠ 1), then a + 2b + 5c + 4 =
©
Let/ f (x) = x2 + 2x + 2 , g (x) = −x2 + 2x - 1 and a , b be the extreme values of f (x) , g (x) respectively. If c is the extreme value of
f
g
 (x) (for x ≠ 1), then a + 2b + 5c + 4 =
©
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt
The set of all real numbers satisfying the in equation x2 - |x + 2| + x > 0 is
©
The set of all real numbers satisfying the in equation x2 - |x + 2| + x > 0 is
©
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt
If α , β , γ are the roots of x3−6x2 + 11x - 6 = 0 , then the equation having the roots α2+β2,β2+γ2 and γ2+α2 is
©
If α , β , γ are the roots of x3−6x2 + 11x - 6 = 0 , then the equation having the roots α2+β2,β2+γ2 and γ2+α2 is
©
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt
If the number of elements in the sets G and A are 3 and 4 respectively, then match the items of List I with those of List II.
List - I List - II
A) The number of non bijective functions from G x G to G I) 24
B) The number of bijective functions from A to A II) 0
C) Hie number of functions from G to G x A III) 1728
D) The number of surjective functions from A to A x A V) 19683

The correct match is
©
If the number of elements in the sets G and A are 3 and 4 respectively, then match the items of List I with those of List II.
List - I List - II
A) The number of non bijective functions from G x G to G I) 24
B) The number of bijective functions from A to A II) 0
C) Hie number of functions from G to G x A III) 1728
D) The number of surjective functions from A to A x A V) 19683

The correct match is
©
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt
There are 20 straight lilies in a plane such that no two of them are parallel and no three of them are concurrent. If their points of intersection are joined, then the number of new line segments formed are
©
There are 20 straight lilies in a plane such that no two of them are parallel and no three of them are concurrent. If their points of intersection are joined, then the number of new line segments formed are
©
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt
Let a0,a1,a2 , ... an ∊ R be in an arithmetic progression and let C0,c1,C2 , ... Cn be the binomial coefficients. Then
n
Σ
k=0
ak.Ck =
©
Let a0,a1,a2 , ... an ∊ R be in an arithmetic progression and let C0,c1,C2 , ... Cn be the binomial coefficients. Then
n
Σ
k=0
ak.Ck =
©
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt
If x =
3
10
+
3.7
10.15
+
3.7.9
10.15.20
 + ... , then 5x + 8 =
©
If x =
3
10
+
3.7
10.15
+
3.7.9
10.15.20
 + ... , then 5x + 8 =
©
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt
if
x4
(x−1)(x−2)(x−3)
 = x + k +
A
x−1
+
B
x−2
+
C
x−3
 , then k + A - B + C =
©
if
x4
(x−1)(x−2)(x−3)
 = x + k +
A
x−1
+
B
x−2
+
C
x−3
 , then k + A - B + C =
©
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt
cosec 48° + cosec 96° + cosec 192° + cosec 384° =
©
cosec 48° + cosec 96° + cosec 192° + cosec 384° =
©
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt
sin4
π
8
+sin4
2π
8
 + sin4
3π
8
+sin4
4π
8
 + sin4
5π
8
+sin4
6π
8
 + sin4
7π
8
 =
©
sin4
π
8
+sin4
2π
8
 + sin4
3π
8
+sin4
4π
8
 + sin4
5π
8
+sin4
6π
8
 + sin4
7π
8
 =
©
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt
If x : y : z = tan (
π
15
+α) : tan (
π
15
+β) : tan (
π
15
+γ) ,

then
z+x
z−1
sin2 (γ - α) +
x+y
x−y
sin2(α−β) +
y+z
y−z
sin2(β−γ)
©
If x : y : z = tan (
π
15
+α) : tan (
π
15
+β) : tan (
π
15
+γ) ,

then
z+x
z−1
sin2 (γ - α) +
x+y
x−y
sin2(α−β) +
y+z
y−z
sin2(β−γ)
©
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt
Let [x] denote the largest integer < x. If the number of solutions of
sin x √4cos2x =
2+x−[x]
1−x+[x]
 is k , then for x ∊ [
π
4
,
π
2
] , then value of ktan2x
©
Let [x] denote the largest integer < x. If the number of solutions of
sin x √4cos2x =
2+x−[x]
1−x+[x]
 is k , then for x ∊ [
π
4
,
π
2
] , then value of ktan2x
©
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt
If α and β are the least and the greatest values of f (x) = (sin−1x)2+(cos−1x)2 for all x ∊ R respectively, then 8 (α + β) =
©
If α and β are the least and the greatest values of f (x) = (sin−1x)2+(cos−1x)2 for all x ∊ R respectively, then 8 (α + β) =
©
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt
If x ∊ (−
π
2
,
π
2
) , then log sec x =
©
If x ∊ (−
π
2
,
π
2
) , then log sec x =
©
Q.26 Correct
Q.26 In-correct
Q.26 Unattempt
The area (in square units) of Δ ABC if ∠A = 75° , ∠B = 45° and a = 2 (√3+1) is
©
The area (in square units) of Δ ABC if ∠A = 75° , ∠B = 45° and a = 2 (√3+1) is
©
Q.27 Correct
Q.27 In-correct
Q.27 Unattempt
In a Δ ABC , if 3a = b + c , then cot
B
2
 cot
C
2
 =
©
In a Δ ABC , if 3a = b + c , then cot
B
2
 cot
C
2
 =
©
Q.28 Correct
Q.28 In-correct
Q.28 Unattempt
In a ΔABC , if
2r2r3
r2−r1
 = r3−r1 , then
r1(r2+r3)
√r1r2+r2r3+r3r1
 =
©
In a ΔABC , if
2r2r3
r2−r1
 = r3−r1 , then
r1(r2+r3)
√r1r2+r2r3+r3r1
 =
©
Q.29 Correct
Q.29 In-correct
Q.29 Unattempt
If 3
^
i
−2
^
j
−
^
k
 , 2
^
i
+3
^
j
−4
^
k
 , −
^
i
+
^
j
+2
^
k
 and 4
^
i
+5
^
j
+λ
^
k
 are respectively the position vectors of four coplanar points P , Q , R and S then λ =
©
If 3
^
i
−2
^
j
−
^
k
 , 2
^
i
+3
^
j
−4
^
k
 , −
^
i
+
^
j
+2
^
k
 and 4
^
i
+5
^
j
+λ
^
k
 are respectively the position vectors of four coplanar points P , Q , R and S then λ =
©
Q.30 Correct
Q.30 In-correct
Q.30 Unattempt
If
→
OA
 = 2
^
i
+2
^
j
+
^
k
 ,
→
OB
 = 2
^
i
+4
^
j
+4
^
k
 and the length of the internal bisector of ∠BOA of triangle AOB is k. then 9k2 =
©
If
→
OA
 = 2
^
i
+2
^
j
+
^
k
 ,
→
OB
 = 2
^
i
+4
^
j
+4
^
k
 and the length of the internal bisector of ∠BOA of triangle AOB is k. then 9k2 =
©
Q.31 Correct
Q.31 In-correct
Q.31 Unattempt
If
−
a
+x
−
b
+y
−
c
 =
−
0
 ,
−
a
×
−
b
+
−
b
×
−
c
+
−
c
×
−
a
 = 6 (
−
b
×
−
c
) , then the locus of the point (x. y) is
©
If
−
a
+x
−
b
+y
−
c
 =
−
0
 ,
−
a
×
−
b
+
−
b
×
−
c
+
−
c
×
−
a
 = 6 (
−
b
×
−
c
) , then the locus of the point (x. y) is
©
Q.32 Correct
Q.32 In-correct
Q.32 Unattempt
Let A = (α , 1 , 2α) , B = (3 , 1 , 2) and
→
C
 = 4
^
i
−
^
j
+3
^
k
. If
→
AB
×
→
C
 = 6
^
i
+9
^
j
−5
^
k
 , then α2 + α + 5 =
©
Let A = (α , 1 , 2α) , B = (3 , 1 , 2) and
→
C
 = 4
^
i
−
^
j
+3
^
k
. If
→
AB
×
→
C
 = 6
^
i
+9
^
j
−5
^
k
 , then α2 + α + 5 =
©
Q.33 Correct
Q.33 In-correct
Q.33 Unattempt
The shortest distance between the skew lines
→
r
 = (6
^
i
+2
^
j
+2
^
k
) + t (
^
i
−2
^
j
+2
^
k
) and
→
r
 = (−4
^
i
−
^
k
) + s (3
^
i
−2
^
j
−2
^
k
)
©
The shortest distance between the skew lines
→
r
 = (6
^
i
+2
^
j
+2
^
k
) + t (
^
i
−2
^
j
+2
^
k
) and
→
r
 = (−4
^
i
−
^
k
) + s (3
^
i
−2
^
j
−2
^
k
)
©
Q.34 Correct
Q.34 In-correct
Q.34 Unattempt
If
−
a
 makes an acute angle with
→
b
,
→
r
.
→
a
 = 0 and
→
r
×
→
b
 =
→
c
×
→
b
 , then
→
r
 =
©
If
−
a
 makes an acute angle with
→
b
,
→
r
.
→
a
 = 0 and
→
r
×
→
b
 =
→
c
×
→
b
 , then
→
r
 =
©
Q.35 Correct
Q.35 In-correct
Q.35 Unattempt
For a data consisting of 15 observations x1 , i = 1 , 2 , 3 , ... , 15 the following results are obtained:
15
Σ
i=1
xi = 170 ;
15
Σ
i=1
xi2 = 2830. If one of the observation namely 20 was found wrong and was replaced by its collect value 30. then the corrected variance is
©
For a data consisting of 15 observations x1 , i = 1 , 2 , 3 , ... , 15 the following results are obtained:
15
Σ
i=1
xi = 170 ;
15
Σ
i=1
xi2 = 2830. If one of the observation namely 20 was found wrong and was replaced by its collect value 30. then the corrected variance is
©
Q.36 Correct
Q.36 In-correct
Q.36 Unattempt
The mean deviation about the mean for the following data is
Class interval 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70
Frequency 4 6 16 28 16 6 4
 
©
The mean deviation about the mean for the following data is
Class interval 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70
Frequency 4 6 16 28 16 6 4
 
©
Q.37 Correct
Q.37 In-correct
Q.37 Unattempt
A and B each select one number at random from the distinct numbers 1. 2. 3..... n and the probability that the number selected by A is less than the number selected by B is
1009
2019
. Now. the probability that the number selected by B is the number immediately next to the number selected by A is
©
A and B each select one number at random from the distinct numbers 1. 2. 3..... n and the probability that the number selected by A is less than the number selected by B is
1009
2019
. Now. the probability that the number selected by B is the number immediately next to the number selected by A is
©
Q.38 Correct
Q.38 In-correct
Q.38 Unattempt
There are 3 bags A. B and C. Bag A contains 2 white and 3 black balls, bag B contains 4 white and 2 black balls and Bag C contains 3 white and 2 black balls. If a ball is drawn at random from a randomly chosen bag. then the probability that the ball drawn is black, is
©
There are 3 bags A. B and C. Bag A contains 2 white and 3 black balls, bag B contains 4 white and 2 black balls and Bag C contains 3 white and 2 black balls. If a ball is drawn at random from a randomly chosen bag. then the probability that the ball drawn is black, is
©
Q.39 Correct
Q.39 In-correct
Q.39 Unattempt
The following table shows the probability of selecting the boxes A. B and C and the number of balls of different colours contained in them
Box Number of ballsProbability
WhiteGreen Red
A 1 2 3
1
2
B 2 3 1
1
3
C 3 1 2
1
6

A box is selected at random and a ball is drawn from it. If it is given that the ball drawn is green, then the probability that it has come from box C is
©
The following table shows the probability of selecting the boxes A. B and C and the number of balls of different colours contained in them
Box Number of ballsProbability
WhiteGreen Red
A 1 2 3
1
2
B 2 3 1
1
3
C 3 1 2
1
6

A box is selected at random and a ball is drawn from it. If it is given that the ball drawn is green, then the probability that it has come from box C is
©
Q.40 Correct
Q.40 In-correct
Q.40 Unattempt
If a random variable X has the probability distribution given by P (X = 0) = 3X3 , P (X = 2) = 5X - 10 C2 and P (X = 4) = 4C - 1 , then the variance of that distribution is
©
If a random variable X has the probability distribution given by P (X = 0) = 3X3 , P (X = 2) = 5X - 10 C2 and P (X = 4) = 4C - 1 , then the variance of that distribution is
©
Q.41 Correct
Q.41 In-correct
Q.41 Unattempt
A box contains 30 toys of same size in which 10 toys are white and all the remaining toys are blue. A toy is drawn at random horn the box and it is replaced in the box after noting down its colour. If 5 toys are drawn in tills way, then the probability of getting atmost 2 white toys is
©
A box contains 30 toys of same size in which 10 toys are white and all the remaining toys are blue. A toy is drawn at random horn the box and it is replaced in the box after noting down its colour. If 5 toys are drawn in tills way, then the probability of getting atmost 2 white toys is
©
Q.42 Correct
Q.42 In-correct
Q.42 Unattempt
For any value of θ, if the straight lines x sin θ + (1 - cos θ) y = a sin θ and x sin θ - (1 + cos θ) y + a sin θ = 0 intersect at P(θ). then the locus of P(θ) is a
©
For any value of θ, if the straight lines x sin θ + (1 - cos θ) y = a sin θ and x sin θ - (1 + cos θ) y + a sin θ = 0 intersect at P(θ). then the locus of P(θ) is a
©
Q.43 Correct
Q.43 In-correct
Q.43 Unattempt
A line L has intercepts a and b on the coordinate axes. When the axes are rotated through a given angle θ keeping the origin fixed, this line L has the intercepts and q. Then
©
A line L has intercepts a and b on the coordinate axes. When the axes are rotated through a given angle θ keeping the origin fixed, this line L has the intercepts and q. Then
©
Q.44 Correct
Q.44 In-correct
Q.44 Unattempt

If O is the origin and A and B are points on the line 3x - 4y + 25 = 0 such that  = 13. then the area of ΔOAB (in sq. units) is

If O is the origin and A and B are points on the line 3x - 4y + 25 = 0 such that  = 13. then the area of ΔOAB (in sq. units) is
©
Q.45 Correct
Q.45 In-correct
Q.45 Unattempt
If P (α, β) be a point on the line 3x + y = 0 such that the point P and the point Q (1.1) lie on either side of the line 3x = 4y + 8, then
©
If P (α, β) be a point on the line 3x + y = 0 such that the point P and the point Q (1.1) lie on either side of the line 3x = 4y + 8, then
©
Q.46 Correct
Q.46 In-correct
Q.46 Unattempt
Two vertices of a triangle are (5 , -1) and (- 2, 3). If the origin is the orthocentre of this triangle, then the coordinates of the third vertex of that triangle are
©
Two vertices of a triangle are (5 , -1) and (- 2, 3). If the origin is the orthocentre of this triangle, then the coordinates of the third vertex of that triangle are
©
Q.47 Correct
Q.47 In-correct
Q.47 Unattempt
The distance from the origin to the orthocentre of the triangle formed by the lines x + y - 1 = 0 and 6x2 - 13xy + 5y2 = 0 is
©
The distance from the origin to the orthocentre of the triangle formed by the lines x + y - 1 = 0 and 6x2 - 13xy + 5y2 = 0 is
©
Q.48 Correct
Q.48 In-correct
Q.48 Unattempt
The combined equation of two lines L and L1 is 2x2 + axy + 3y2 = 0 and the combined equation of two lines L and L2 is 2x2 + bxy - 3y2 = 0. If L1 and L2 are perpendicular, then a2+b2 =
©
The combined equation of two lines L and L1 is 2x2 + axy + 3y2 = 0 and the combined equation of two lines L and L2 is 2x2 + bxy - 3y2 = 0. If L1 and L2 are perpendicular, then a2+b2 =
©
Q.49 Correct
Q.49 In-correct
Q.49 Unattempt
The power of the point B(- 1. 1) with respect to the circle s = x2+y2 - 2x - 4y + 3 = 0 is p. If the length of the tangent drawn from B to the circle S = 0 is p. then the point (2.3) with respect to the circle S ' = 0 having centre at (p, r2)and passing through the origin
©
The power of the point B(- 1. 1) with respect to the circle s = x2+y2 - 2x - 4y + 3 = 0 is p. If the length of the tangent drawn from B to the circle S = 0 is p. then the point (2.3) with respect to the circle S ' = 0 having centre at (p, r2)and passing through the origin
©
Q.50 Correct
Q.50 In-correct
Q.50 Unattempt
If tangents are drawn to the circle x2+y2 = 12 at the points where it intersects the circle x2+y2 - 5x + 3y - 2 = 0, then the coordinates of the point of intersection of those
©
If tangents are drawn to the circle x2+y2 = 12 at the points where it intersects the circle x2+y2 - 5x + 3y - 2 = 0, then the coordinates of the point of intersection of those
©
Q.51 Correct
Q.51 In-correct
Q.51 Unattempt
If the point of intersection of the pair of the transverse common tangents and that of the pair of direct common tangents drawn to the circles x2+y2 - 14x + 6y + 33 = 0 andx2+y2 + 3x - 2y + 1 = 0 are T and D respectively, then the centre of the circle having  as diameter is
©

If the point of intersection of the pair of the transverse common tangents and that of the pair of direct common tangents drawn to the circles x2+y2 - 14x + 6y + 33 = 0 andx2+y2 + 3x - 2y + 1 = 0 are T and D respectively, then the centre of the circle having  as diameter is
©
Q.52 Correct
Q.52 In-correct
Q.52 Unattempt
If the circles x2+y2 + 2λx + 2 = 0 and x2+y2 + 4y + 2 = 0 touch each other , then λ =
©
If the circles x2+y2 + 2λx + 2 = 0 and x2+y2 + 4y + 2 = 0 touch each other , then λ =
©
Q.53 Correct
Q.53 In-correct
Q.53 Unattempt
The equation of the circle whose diameter is the common chord of the circles x2+y2 + 2x + 3y + 1 = 0 and x2+y2 + 4x + 3y + 2 = 0 is
©
The equation of the circle whose diameter is the common chord of the circles x2+y2 + 2x + 3y + 1 = 0 and x2+y2 + 4x + 3y + 2 = 0 is
©
Q.54 Correct
Q.54 In-correct
Q.54 Unattempt
If the focus of a parabola divides a focal chord of the parabola into segments of lengths 5. 3 units, then the length of the latus rectum of that parabola is
©
If the focus of a parabola divides a focal chord of the parabola into segments of lengths 5. 3 units, then the length of the latus rectum of that parabola is
©
Q.55 Correct
Q.55 In-correct
Q.55 Unattempt
The angle between the tangents drawn to the parabola y2 = 4 from the point (1, 4) is
©
The angle between the tangents drawn to the parabola y2 = 4 from the point (1, 4) is
©
Q.56 Correct
Q.56 In-correct
Q.56 Unattempt
If the tangent drawn to the parabola y2 = 4x at (t2,2t) is the normal to the ellipse 4x2+5y2 = 20 at (√5cosθ,2sinθ) , then
©
If the tangent drawn to the parabola y2 = 4x at (t2,2t) is the normal to the ellipse 4x2+5y2 = 20 at (√5cosθ,2sinθ) , then
©
Q.57 Correct
Q.57 In-correct
Q.57 Unattempt
If the tangents drawn from a point P to the ellipse 4x2+9y2 - 24x + 36y = 0 are perpendicular, then the locus of P is
©
If the tangents drawn from a point P to the ellipse 4x2+9y2 - 24x + 36y = 0 are perpendicular, then the locus of P is
©
Q.58 Correct
Q.58 In-correct
Q.58 Unattempt
The locus of the midpoints of the chords of the circle x2+y2 = 16 which are the tangents to the hyperbola 9x2−16y2 = 144 is
©
The locus of the midpoints of the chords of the circle x2+y2 = 16 which are the tangents to the hyperbola 9x2−16y2 = 144 is
©
Q.59 Correct
Q.59 In-correct
Q.59 Unattempt
A (3 , 2 , -1) , B (4 , 1 , 1) , C (6 , 2 , 5) are three points. If D , E , F are three points which divide BC. CA. AB respectively in the same ratio 2:1. then the centroid of ΔDEF is
©
A (3 , 2 , -1) , B (4 , 1 , 1) , C (6 , 2 , 5) are three points. If D , E , F are three points which divide BC. CA. AB respectively in the same ratio 2:1. then the centroid of ΔDEF is
©
Q.60 Correct
Q.60 In-correct
Q.60 Unattempt
If A = (1 , 8 , 4) , B = (2 , -3 , 1) , then the direction cosines of a normal to the plane AOB is
©
If A = (1 , 8 , 4) , B = (2 , -3 , 1) , then the direction cosines of a normal to the plane AOB is
©
Q.61 Correct
Q.61 In-correct
Q.61 Unattempt
If the two lines
x−1
2
 =
y+1
3
 =
z−1
4
 and
x−3
1
 =
y−k
2
 =
z
1
 have a point in common, then k =
©
If the two lines
x−1
2
 =
y+1
3
 =
z−1
4
 and
x−3
1
 =
y−k
2
 =
z
1
 have a point in common, then k =
©
Q.62 Correct
Q.62 In-correct
Q.62 Unattempt
lim
x→0
x2(tan2x−2tanx)2
(1−cos2x)4
 =
©
lim
x→0
x2(tan2x−2tanx)2
(1−cos2x)4
 =
©
Q.63 Correct
Q.63 In-correct
Q.63 Unattempt
lim
x→∞
 (
6x2−cos3x
x2+5
−
5x3+3
√x6+2
) =
©
lim
x→∞
 (
6x2−cos3x
x2+5
−
5x3+3
√x6+2
) =
©
Q.64 Correct
Q.64 In-correct
Q.64 Unattempt
The number of discontinuities in IR for the function f (x) =
x−1
x3+6x2+11x+6
 is
©
The number of discontinuities in IR for the function f (x) =
x−1
x3+6x2+11x+6
 is
©
Q.65 Correct
Q.65 In-correct
Q.65 Unattempt
d
dx
(log(√x+√x2+a2)) =
©
d
dx
(log(√x+√x2+a2)) =
©
Q.66 Correct
Q.66 In-correct
Q.66 Unattempt
if f (x) = cot−1(
xx−x−x
2
) , then f' (1) =
©
if f (x) = cot−1(
xx−x−x
2
) , then f' (1) =
©
Q.67 Correct
Q.67 In-correct
Q.67 Unattempt
If a ≠ 0 , x = a (t + sin t) and y = a (1 - cos t) , then
d2y
dx2
 at t =
2π
3
 is
©
If a ≠ 0 , x = a (t + sin t) and y = a (1 - cos t) , then
d2y
dx2
 at t =
2π
3
 is
©
Q.68 Correct
Q.68 In-correct
Q.68 Unattempt
The number of tangents to the curve y2 (x - a) = x2 (x + a) (a > 0) that are parallel to the X - axis is
©
The number of tangents to the curve y2 (x - a) = x2 (x + a) (a > 0) that are parallel to the X - axis is
©
Q.69 Correct
Q.69 In-correct
Q.69 Unattempt
If f (x) = (2k +1) x - 3 - ke−x+2ex is monotonically increasing for all x ∊ R then the least value of k is
©
If f (x) = (2k +1) x - 3 - ke−x+2ex is monotonically increasing for all x ∊ R then the least value of k is
©
Q.70 Correct
Q.70 In-correct
Q.70 Unattempt
If the function f (x) = ax3+bx2 + 11x - 6 satisfies the conditions of Rolle's theorem in [1 , 3] and f' (2+
1
√3
) = 0 , then a + b =
©
If the function f (x) = ax3+bx2 + 11x - 6 satisfies the conditions of Rolle's theorem in [1 , 3] and f' (2+
1
√3
) = 0 , then a + b =
©
Q.71 Correct
Q.71 In-correct
Q.71 Unattempt
For a > 0. if the function (x) = 2x3−9ax2+12a2x + 1 attains its maximum value at p and minimum value at q such that p2 = q. then a =
©
For a > 0. if the function (x) = 2x3−9ax2+12a2x + 1 attains its maximum value at p and minimum value at q such that p2 = q. then a =
©
Q.72 Correct
Q.72 In-correct
Q.72 Unattempt
If ∫ cos x . cos 2x . cos 5x dx = A sin 2x + B sin 4x + C sin 6x + D sin 8x + k
(where k is the arbitrary constant of integration), then
1
B
+
1
C
 =
©
If ∫ cos x . cos 2x . cos 5x dx = A sin 2x + B sin 4x + C sin 6x + D sin 8x + k
(where k is the arbitrary constant of integration), then
1
B
+
1
C
 =
©
Q.73 Correct
Q.73 In-correct
Q.73 Unattempt
If ∫ ex(
x+2
x+4
)2 dx = f (x) + arbitrary constant, then f (x) =
©
If ∫ ex(
x+2
x+4
)2 dx = f (x) + arbitrary constant, then f (x) =
©
Q.74 Correct
Q.74 In-correct
Q.74 Unattempt
∫
dx
sinx+sin2x
 =
©
∫
dx
sinx+sin2x
 =
©
Q.75 Correct
Q.75 In-correct
Q.75 Unattempt
If In = ∫
sinnx
sinx
 dx for n = 1 , 2 , 3 , ... , then I6 =
©
If In = ∫
sinnx
sinx
 dx for n = 1 , 2 , 3 , ... , then I6 =
©
Q.76 Correct
Q.76 In-correct
Q.76 Unattempt
If
lim
n→∞
 [(1+
1
n2
)(1+
22
n2
)...(1+
n2
n2
)]
1
n
 = k , then log k =
©
If
lim
n→∞
 [(1+
1
n2
)(1+
22
n2
)...(1+
n2
n2
)]
1
n
 = k , then log k =
©
Q.77 Correct
Q.77 In-correct
Q.77 Unattempt
π
2
∫
0
sin3xcosxdx
sin4x+cos4x
 =
©
π
2
∫
0
sin3xcosxdx
sin4x+cos4x
 =
©
Q.78 Correct
Q.78 In-correct
Q.78 Unattempt
The curve y = ax2 + bx passes through the point (1 , 2) and lies above the X - axis for 0 ≤ x ≤ 8. If the area enclosed by this curve , the X - axis and the line x = 6 is 108 square units, then 2b - a =
©
The curve y = ax2 + bx passes through the point (1 , 2) and lies above the X - axis for 0 ≤ x ≤ 8. If the area enclosed by this curve , the X - axis and the line x = 6 is 108 square units, then 2b - a =
©
Q.79 Correct
Q.79 In-correct
Q.79 Unattempt
The differential equation of all parabolas whose axes are parallel to Y - axis is
©
The differential equation of all parabolas whose axes are parallel to Y - axis is
©
Q.80 Correct
Q.80 In-correct
Q.80 Unattempt
The solution of the equation
dy
dx
 + 2 y tan x = sin x satisfying y = 0 when x =
π
3
 , is
©
The solution of the equation
dy
dx
 + 2 y tan x = sin x satisfying y = 0 when x =
π
3
 , is
©
Q.81 Correct
Q.81 In-correct
Q.81 Unattempt
Two intervals of time are measured as Δ t1 = (2.00 ± 0.02) s and Δ t2 = (4.00 ± 0.02) s. The value of √(Δt1)(Δt2) with correct significant figures and error is
©
Two intervals of time are measured as Δ t1 = (2.00 ± 0.02) s and Δ t2 = (4.00 ± 0.02) s. The value of √(Δt1)(Δt2) with correct significant figures and error is
©
Q.82 Correct
Q.82 In-correct
Q.82 Unattempt
The speed of a particle changes from √5ms−1 to 2√5ms−1 in a time t. If the magnitude of change in its velocity is 5 ms−1, the angle between the initial and final velocities of the particle is
©
The speed of a particle changes from √5ms−1 to 2√5ms−1 in a time t. If the magnitude of change in its velocity is 5 ms−1, the angle between the initial and final velocities of the particle is
©
Q.83 Correct
Q.83 In-correct
Q.83 Unattempt
If the maximum height and range of a projectile are 3 m and 4 m respectively then the velocity of the projectile is
(Acceleration due to gravity =10 ms−2)
©
If the maximum height and range of a projectile are 3 m and 4 m respectively then the velocity of the projectile is
(Acceleration due to gravity =10 ms−2)
©
Q.84 Correct
Q.84 In-correct
Q.84 Unattempt
A body is projected at an angle other than 90° with the horizontal with some velocity. If the time of ascent of the bod}' is 1 s then the maximum height it can reach is
(Acceleration due to gravity = 10 ms−2)
©
A body is projected at an angle other than 90° with the horizontal with some velocity. If the time of ascent of the bod}' is 1 s then the maximum height it can reach is
(Acceleration due to gravity = 10 ms−2)
©
Q.85 Correct
Q.85 In-correct
Q.85 Unattempt
The position-time (x - t) graph of a moving body of mass 2 kg is shown in the figure. impulse on the body at t = 4 s is
 

 
The position-time (x - t) graph of a moving body of mass 2 kg is shown in the figure. impulse on the body at t = 4 s is
 
Q.86 Correct
Q.86 In-correct
Q.86 Unattempt

A block of mass ‘m’ is lying on a rough inclined plane having an inclination a = tan-1 (1/5). The inclined plane is moving horizontally with a constant acceleration of a = 2 ms-2 as shown in the figure. Hie minimum value of coefficient of friction so that the block remains stationary with respect to the inclined plane is (Acceleration due to gravity = 10 ms-2)

A block of mass ‘m’ is lying on a rough inclined plane having an inclination a = tan-1 (1/5). The inclined plane is moving horizontally with a constant acceleration of a = 2 ms-2 as shown in the figure. Hie minimum value of coefficient of friction so that the block remains stationary with respect to the inclined plane is (Acceleration due to gravity = 10 ms-2)
Q.87 Correct
Q.87 In-correct
Q.87 Unattempt
Potential energy of a body of mass 1 kg free to move along X-axis is given by U (x) = (
x2
2
−x) J. If the total mechanical energy of the body is 2 J. then the maximum speed of the body is (Assume only conservative force acts on the body)
©
Potential energy of a body of mass 1 kg free to move along X-axis is given by U (x) = (
x2
2
−x) J. If the total mechanical energy of the body is 2 J. then the maximum speed of the body is (Assume only conservative force acts on the body)
©
Q.88 Correct
Q.88 In-correct
Q.88 Unattempt
A cylindrical well of radius 2.5 m has water up to a height of 14 m horn the bottom. If the water level is at a depth of 6 m from the top of the well, then the time taken in minutes to empty the well using a motor of 10 HP is approximately
(Acceleration due to gravity = 10 ms−2)
©
A cylindrical well of radius 2.5 m has water up to a height of 14 m horn the bottom. If the water level is at a depth of 6 m from the top of the well, then the time taken in minutes to empty the well using a motor of 10 HP is approximately
(Acceleration due to gravity = 10 ms−2)
©
Q.89 Correct
Q.89 In-correct
Q.89 Unattempt
A fly wheel of mass 1 kg and radius vector (2
^
i
+
^
j
+2
^
k
) m is at rest. When a force (3
^
i
+2
^
j
−4
^
k
) N acts on it tangentially, it can rotate freely. Then its angular velocity after 4.5 s is
©
A fly wheel of mass 1 kg and radius vector (2
^
i
+
^
j
+2
^
k
) m is at rest. When a force (3
^
i
+2
^
j
−4
^
k
) N acts on it tangentially, it can rotate freely. Then its angular velocity after 4.5 s is
©
Q.90 Correct
Q.90 In-correct
Q.90 Unattempt
Three identical spheres each of diameter 2√3 m are kept on a horizontal surface such that each sphere touches the other two spheres. If one of the spheres is removed, then the shift in the position of the centre of mass of the system is
©
Three identical spheres each of diameter 2√3 m are kept on a horizontal surface such that each sphere touches the other two spheres. If one of the spheres is removed, then the shift in the position of the centre of mass of the system is
©
Q.91 Correct
Q.91 In-correct
Q.91 Unattempt

For a particle executing simple harmonic motion, the displacement-time (x - t) graph is as shown in the figure. The acceleration of the particle at t = 4/3 s is

For a particle executing simple harmonic motion, the displacement-time (x - t) graph is as shown in the figure. The acceleration of the particle at t =
4
3
s is
 
Q.92 Correct
Q.92 In-correct
Q.92 Unattempt
Two masses 90 kg and 160 kg are separated by a distance of 5 m. The magnitude of intensity of the gravitational field at a point which is at a distance 3 m from the 90 kg mass and 4 m from the 160 kg mass is
(Universal gravitational constant = 6.67 × 10−11Nm2Kg−2)
©
Two masses 90 kg and 160 kg are separated by a distance of 5 m. The magnitude of intensity of the gravitational field at a point which is at a distance 3 m from the 90 kg mass and 4 m from the 160 kg mass is
(Universal gravitational constant = 6.67 × 10−11Nm2Kg−2)
©
Q.93 Correct
Q.93 In-correct
Q.93 Unattempt
The following four wires are made of the same material. If same tension is applied to each, the wire having largest extension is
a) length 0.5 m. diameter 0.5 mm
b) length 1 m, diameter 1 mm
c) length 2 m. diameter 2 mm
d) length 3 m, diameter 3 mm

©
The following four wires are made of the same material. If same tension is applied to each, the wire having largest extension is
a) length 0.5 m. diameter 0.5 mm
b) length 1 m, diameter 1 mm
c) length 2 m. diameter 2 mm
d) length 3 m, diameter 3 mm

©
Q.94 Correct
Q.94 In-correct
Q.94 Unattempt

A liquid drop of density ρ is floating half immersed in a liquid of surface tension S and density p/2. If the surface tension S of liquid is numerically equal to 10 times of acceleration due to gravity, then the diameter of the drop is

A liquid drop of density ρ is floating half immersed in a liquid of surface tension S and density p/2. If the surface tension S of liquid is numerically equal to 10 times of acceleration due to gravity, then the diameter of the drop is
Q.95 Correct
Q.95 In-correct
Q.95 Unattempt
A block of metal is heated to a temperature much higher than the room temperature and placed in an evacuated cavity. The curve which correctly represents the rate of cooling
(T is temperature of the block and t is the time)
 
©
A block of metal is heated to a temperature much higher than the room temperature and placed in an evacuated cavity. The curve which correctly represents the rate of cooling
(T is temperature of the block and t is the time)
 
©
Q.96 Correct
Q.96 In-correct
Q.96 Unattempt
A solid copper sphere of density ρ. specific heat capacity C and radius r is initially at 200 K. It is suspended inside a chamber whose walls are at 0 K. The time required (in (is) for the temperature of the sphere to drop to 100 K is
(σ is Stefan's constant and all the quantities are in SI units)
©
A solid copper sphere of density ρ. specific heat capacity C and radius r is initially at 200 K. It is suspended inside a chamber whose walls are at 0 K. The time required (in (is) for the temperature of the sphere to drop to 100 K is
(σ is Stefan's constant and all the quantities are in SI units)
©
Q.97 Correct
Q.97 In-correct
Q.97 Unattempt
Match the temperatures of the source and sink (T1 and T2 respectively) of a Carnot heat engine given in List - I with the corresponding efficiencies given in List - II
List - IList - II
A) T1 = 500 K , t2 = 300 K I) 0.2
B) T1 = 500 K , T2 = 350 K II) 0.3
C) T1 = 800 K , T2 = 400 K III) 0.4
D) T1 = 450 K , T2 = 360 K IV) 0.5

©
Match the temperatures of the source and sink (T1 and T2 respectively) of a Carnot heat engine given in List - I with the corresponding efficiencies given in List - II
List - IList - II
A) T1 = 500 K , t2 = 300 K I) 0.2
B) T1 = 500 K , T2 = 350 K II) 0.3
C) T1 = 800 K , T2 = 400 K III) 0.4
D) T1 = 450 K , T2 = 360 K IV) 0.5

©
Q.98 Correct
Q.98 In-correct
Q.98 Unattempt
A hammer of mass 200 kg strikes a steel block of mass 200 g with a velocity 8 ms−1. If 23% of the energy is utilized to heat the steel block, the rise in temperature of the block is (specific heat capacity of steel = 460 J kg−1K−1)
©
A hammer of mass 200 kg strikes a steel block of mass 200 g with a velocity 8 ms−1. If 23% of the energy is utilized to heat the steel block, the rise in temperature of the block is (specific heat capacity of steel = 460 J kg−1K−1)
©
Q.99 Correct
Q.99 In-correct
Q.99 Unattempt
At a temperature of 314 K and a pressure of 100 kPa. the speed of sound in a gas is 1380 ms−1. The radius of each gas molecule is 0.5 A. The frequency of sound at which the wavelength of sound wave in the gas becomes equal to the mean free path of the gas molecules is
(Boltzmann Constant = 1.38 x 10−23JK−1)
©
At a temperature of 314 K and a pressure of 100 kPa. the speed of sound in a gas is 1380 ms−1. The radius of each gas molecule is 0.5 A. The frequency of sound at which the wavelength of sound wave in the gas becomes equal to the mean free path of the gas molecules is
(Boltzmann Constant = 1.38 x 10−23JK−1)
©
Q.100 Correct
Q.100 In-correct
Q.100 Unattempt
At a temperature of 27 °C. two identical organ pipes produce notes of frequency 140 Hz. If the temperature of one pipe is raised to 57.75 °C. the number of beats produced per second is
©
At a temperature of 27 °C. two identical organ pipes produce notes of frequency 140 Hz. If the temperature of one pipe is raised to 57.75 °C. the number of beats produced per second is
©
Q.101 Correct
Q.101 In-correct
Q.101 Unattempt
A source of sound "S' in the form of a block kept oil a smooth horizontal surface is connected to a spring, as shown in the figure. If the spring oscillates with an amplitude of 50 cm along horizontal between the wall and the observer O. the maximum frequency heard by the observer is 12.5% more than the minimum frequency heard by him. If the mass of the source of sound is 100 g. the force constant of the spring is (Speed of sound in air is 340 ms−1)
A source of sound "S' in the form of a block kept oil a smooth horizontal surface is connected to a spring, as shown in the figure. If the spring oscillates with an amplitude of 50 cm along horizontal between the wall and the observer O. the maximum frequency heard by the observer is 12.5% more than the minimum frequency heard by him. If the mass of the source of sound is 100 g. the force constant of the spring is (Speed of sound in air is 340 ms−1)
 
Q.102 Correct
Q.102 In-correct
Q.102 Unattempt
A girl of height 150 cm with her eye level at 140 cm stands in front of a plane minor of height 75 cm fixed to a wall. The lower edge of the mirror is at a height of 85 cm above her feet level. The height of her image the girl can see in the min or is
©
A girl of height 150 cm with her eye level at 140 cm stands in front of a plane minor of height 75 cm fixed to a wall. The lower edge of the mirror is at a height of 85 cm above her feet level. The height of her image the girl can see in the min or is
©
Q.103 Correct
Q.103 In-correct
Q.103 Unattempt

Unpolarised light from air incidents on the surface of a transparent medium of refractive index 1.414 such that the reflected light is completely polarised. Match the angles given in List - I with the corresponding values given in List - II.

Unpolarised light from air incidents on the surface of a transparent medium of refractive index 1.414 such that the reflected light is completely polarised. Match the angles given in List - I with the corresponding values given in List - II.
Q.104 Correct
Q.104 In-correct
Q.104 Unattempt
The electric field intensity at a point on the axis of an electric dipole in ah is 4 NC−1. Then the electric field intensity at a point on the equitorial hue which is at a distance equal to twice the distance on the axial line and if the dipole is in a medium of dielectric constant 4 is
©
The electric field intensity at a point on the axis of an electric dipole in ah is 4 NC−1. Then the electric field intensity at a point on the equitorial hue which is at a distance equal to twice the distance on the axial line and if the dipole is in a medium of dielectric constant 4 is
©
Q.105 Correct
Q.105 In-correct
Q.105 Unattempt

Two small spheres of each charge ‘q' mass 'm' and material density ‘d’ are suspended from a fixed point with the help of inextensible light thread. When the spheres are in ah. the angle between the threads is 90°. When the spheres are suspended in a liquid of density 2/3 d, the angle between the threads is 60°. The value of dielectric constant of the liquid is

Two small spheres of each charge ‘q' mass 'm' and material density ‘d’ are suspended from a fixed point with the help of inextensible light thread. When the spheres are in ah. the angle between the threads is 90°. When the spheres are suspended in a liquid of density 2/3 d, the angle between the threads is 60°. The value of dielectric constant of the liquid is
Q.106 Correct
Q.106 In-correct
Q.106 Unattempt
Hie potential difference (VA−VB) in the arrangement shown in figure is
(|q| = 1 µC , x = 2 cm , y = 3 cm)
 

 
Hie potential difference (VA−VB) in the arrangement shown in figure is
(|q| = 1 µC , x = 2 cm , y = 3 cm)
 
Q.107 Correct
Q.107 In-correct
Q.107 Unattempt
In a parallel plate capacitor the separation between plates is 3.y. This separation is filled by two layers of dielectrics, in which one layer has thickness and dielectric constant 3 K. the other layer is of thickness 2x and dielectric constant 5 K. If the plates of the capacitor are connected to a battery, then the ratio of potential difference across the dielectric layers is
©
In a parallel plate capacitor the separation between plates is 3.y. This separation is filled by two layers of dielectrics, in which one layer has thickness and dielectric constant 3 K. the other layer is of thickness 2x and dielectric constant 5 K. If the plates of the capacitor are connected to a battery, then the ratio of potential difference across the dielectric layers is
©
Q.108 Correct
Q.108 In-correct
Q.108 Unattempt
Assertion (A): When a wire of aluminium and another wire of silicon are heated from room temperature to 80 °C. the conductivity of aluminium increases and that of silicon decreases.
Reason (R) : Aluminium has positive temperature coefficient of resistivity and silicon has negative temperature coefficient of resistivity.
©
Assertion (A): When a wire of aluminium and another wire of silicon are heated from room temperature to 80 °C. the conductivity of aluminium increases and that of silicon decreases.
Reason (R) : Aluminium has positive temperature coefficient of resistivity and silicon has negative temperature coefficient of resistivity.
©
Q.109 Correct
Q.109 In-correct
Q.109 Unattempt
The walls of a closed cubical box of edge 60 cm are made of material of thickness 1 mm and thermal conductivity 4 x 10−4cals−1cm−1°C−1. The interior of the box is maintained 1000 °C above the outside temperature by a heater placed inside the box and connected across 400 V DC supply. The resistance of the heater is
©
The walls of a closed cubical box of edge 60 cm are made of material of thickness 1 mm and thermal conductivity 4 x 10−4cals−1cm−1°C−1. The interior of the box is maintained 1000 °C above the outside temperature by a heater placed inside the box and connected across 400 V DC supply. The resistance of the heater is
©
Q.110 Correct
Q.110 In-correct
Q.110 Unattempt
A galvanometer of resistance ‘G' Ω. is shunted by a resistance ‘S' Ω. To keep the main current in the circuit unchanged, the resistance to be connected in series with the galvanometer is
©
A galvanometer of resistance ‘G' Ω. is shunted by a resistance ‘S' Ω. To keep the main current in the circuit unchanged, the resistance to be connected in series with the galvanometer is
©
Q.111 Correct
Q.111 In-correct
Q.111 Unattempt
A proton and an α-particle are simultaneously projected in opposite directions into a region of uniform magnetic field of 2 mT perpendicular to the direction of the field. After some time it is found that the velocity of proton has changed in direction by 90°. Then at this tune, the angle between the velocity vectors of proton and a-particle is
©
A proton and an α-particle are simultaneously projected in opposite directions into a region of uniform magnetic field of 2 mT perpendicular to the direction of the field. After some time it is found that the velocity of proton has changed in direction by 90°. Then at this tune, the angle between the velocity vectors of proton and a-particle is
©
Q.112 Correct
Q.112 In-correct
Q.112 Unattempt
A bar- magnet placed in a uniform magnetic field making an angle θ with the field experiences a torque. If the angle made by the magnet with the field is doubled, the torque experienced by the magnet increases by 41.4%. The initial angle made by the magnet with the magnetic field is
©
A bar- magnet placed in a uniform magnetic field making an angle θ with the field experiences a torque. If the angle made by the magnet with the field is doubled, the torque experienced by the magnet increases by 41.4%. The initial angle made by the magnet with the magnetic field is
©
Q.113 Correct
Q.113 In-correct
Q.113 Unattempt
A metal rod AB of length 50 cm is moving at a velocity 8 ms−1 in a magnetic field of 2 T. If the field is at 60° with the plane of motion as shown in figure, then the potentials VA and VB are related by
 

 
A metal rod AB of length 50 cm is moving at a velocity 8 ms−1 in a magnetic field of 2 T. If the field is at 60° with the plane of motion as shown in figure, then the potentials VA and VB are related by
 
Q.114 Correct
Q.114 In-correct
Q.114 Unattempt
In the given electrical circuit, if the switch S is closed then the maximum energy stored in the inductor is
 

 
In the given electrical circuit, if the switch S is closed then the maximum energy stored in the inductor is
 
Q.115 Correct
Q.115 In-correct
Q.115 Unattempt
Which, of the following is/are the property properties of a monochromatic electromagnetic wave propagating in free space?
a) Electric and magnetic fields will have a phase difference
π
2
.
b) The energy of the wave is distributed equally between electric and magnetic fields.
c) The pressure exerted by the wave is the product of its speed and energy density.
d) The speed of the wave is equal to the ratio of magnetic field to the electric field.
©
Which, of the following is/are the property properties of a monochromatic electromagnetic wave propagating in free space?
a) Electric and magnetic fields will have a phase difference
π
2
.
b) The energy of the wave is distributed equally between electric and magnetic fields.
c) The pressure exerted by the wave is the product of its speed and energy density.
d) The speed of the wave is equal to the ratio of magnetic field to the electric field.
©
Q.116 Correct
Q.116 In-correct
Q.116 Unattempt
The maximum kinetic energy of a photoelectron liberated from the surface of lithium with work function 2.35 eVby electromagnetic radiation whose electric component varies with time as E = a [1 + cos (2πf1t)] cos 2πf2t (where 'a' is a constant) is
(f1 = 3.6 × 1015 Hz , f2 = 1.2 × 1015 Hz and Plank’s constant = 6.6 × 10−34 J-s)
©
The maximum kinetic energy of a photoelectron liberated from the surface of lithium with work function 2.35 eVby electromagnetic radiation whose electric component varies with time as E = a [1 + cos (2πf1t)] cos 2πf2t (where 'a' is a constant) is
(f1 = 3.6 × 1015 Hz , f2 = 1.2 × 1015 Hz and Plank’s constant = 6.6 × 10−34 J-s)
©
Q.117 Correct
Q.117 In-correct
Q.117 Unattempt
Magnetic moment due to the motion of the election in n energy state of hydrogen atom is proportional to_________
©
Magnetic moment due to the motion of the election in n energy state of hydrogen atom is proportional to_________
©
Q.118 Correct
Q.118 In-correct
Q.118 Unattempt

The rate of disintegration of a radioactive sample is ‘R‘ and the number of atoms present at any time 't' is ‘N'. When R/N is taken alone Y-axis and 't'is taken alone X-axis, the correct graph is

The rate of disintegration of a radioactive sample is ‘R‘ and the number of atoms present at any time 't' is ‘N'. When R/N is taken alone Y-axis and 't'is taken alone X-axis, the correct graph is
Q.119 Correct
Q.119 In-correct
Q.119 Unattempt
For an LED to emit light in visible region of electromagnetic spectrum, it can have energy band gap in the range of
(Plank’s constant = 6.6 × 10−34 J - s and speed of light = 3 × 108ms−1 in vacuum)
©
For an LED to emit light in visible region of electromagnetic spectrum, it can have energy band gap in the range of
(Plank’s constant = 6.6 × 10−34 J - s and speed of light = 3 × 108ms−1 in vacuum)
©
Q.120 Correct
Q.120 In-correct
Q.120 Unattempt
A transmitting antenna of height 20 m and the receiving antenna of height 'h' are separated by a distance of 40 km for satisfactory communication in line of sight mode. Then the value of 'h' is
(Given Radius of earth is 6400 km)
©
A transmitting antenna of height 20 m and the receiving antenna of height 'h' are separated by a distance of 40 km for satisfactory communication in line of sight mode. Then the value of 'h' is
(Given Radius of earth is 6400 km)
©
Q.121 Correct
Q.121 In-correct
Q.121 Unattempt
The energies of an electron in first orbit of He+ and in third orbit of Li2+ in J are respectively
©
The energies of an electron in first orbit of He+ and in third orbit of Li2+ in J are respectively
©
Q.122 Correct
Q.122 In-correct
Q.122 Unattempt
How many orbitals is/are possible with n = 3, l = 1, and m1 = -1 value?
©
How many orbitals is/are possible with n = 3, l = 1, and m1 = -1 value?
©
Q.123 Correct
Q.123 In-correct
Q.123 Unattempt
If four - elements with atomic numbers Z - 2. Z - 1. Z and Z + 1 are forming isoelectronic ions, the atomic number of the ion having largest size is
©
If four - elements with atomic numbers Z - 2. Z - 1. Z and Z + 1 are forming isoelectronic ions, the atomic number of the ion having largest size is
©
Q.124 Correct
Q.124 In-correct
Q.124 Unattempt
Identify the molecule in which the arrangement of electron pair s around the central atom is octahedral and shape is not octahedral
©
Identify the molecule in which the arrangement of electron pair s around the central atom is octahedral and shape is not octahedral
©
Q.125 Correct
Q.125 In-correct
Q.125 Unattempt
The wave functions of Is orbitals of two hydrogen atoms are ψA and ψB. ψA and ψB are linearly combined to form two molecular orbitals (σ and
*
σ
). Which of the following statements are collect?
I)
*
σ
 is equal to (ψA - ψB)
II) In a orbital, one nodal plane is present in between two nuclei
III) The energy of a orbital is lower than the energy of
*
σ
 orbital

©
The wave functions of Is orbitals of two hydrogen atoms are ψA and ψB. ψA and ψB are linearly combined to form two molecular orbitals (σ and
*
σ
). Which of the following statements are collect?
I)
*
σ
 is equal to (ψA - ψB)
II) In a orbital, one nodal plane is present in between two nuclei
III) The energy of a orbital is lower than the energy of
*
σ
 orbital

©
Q.126 Correct
Q.126 In-correct
Q.126 Unattempt
The variation of vapour pressure (b) as a function of temperature (a) is studied for C5H5OC2H5,CCl4 and H2O at 760 nun Hg and is shown in the figure below. The boiling temperatures of C5H5OC2H5,CCl4 and H2O are 308. 350 and 373 K respectively. Curves A, B, C respectively correspond to
 
 
The variation of vapour pressure (b) as a function of temperature (a) is studied for C5H5OC2H5,CCl4 and H2O at 760 nun Hg and is shown in the figure below. The boiling temperatures of C5H5OC2H5,CCl4 and H2O are 308. 350 and 373 K respectively. Curves A, B, C respectively correspond to
 
Q.127 Correct
Q.127 In-correct
Q.127 Unattempt
30.0 mL of the given HCl solution requires 20.0 mL of 0.1 M sodium carbonate solution for complete neutralisation. What is the volume of this HCl solution required to neutralise 30.0 mL of 0.2 M NaOH solution?
©
30.0 mL of the given HCl solution requires 20.0 mL of 0.1 M sodium carbonate solution for complete neutralisation. What is the volume of this HCl solution required to neutralise 30.0 mL of 0.2 M NaOH solution?
©
Q.128 Correct
Q.128 In-correct
Q.128 Unattempt
The heat required to rise the temperature of 54 g of aluminium from 40 °C to 60 °C in J is
(molar heat capacity of aluminium in this temperature range is 24 J mol−1K−1; atomic weight of Al is 27)
©
The heat required to rise the temperature of 54 g of aluminium from 40 °C to 60 °C in J is
(molar heat capacity of aluminium in this temperature range is 24 J mol−1K−1; atomic weight of Al is 27)
©
Q.129 Correct
Q.129 In-correct
Q.129 Unattempt
The equilibrium constant at 850 K for the reaction
N2(g) + O2(g) ⇌ 2NO(g) | is 0.5 625. The equilibrium concentration of NO(g) is 3.0 × 10−7 M. If the equilibrium concentrations of N2(g) and O2(g) are equal, the concentration of N2(g) in M is
©
The equilibrium constant at 850 K for the reaction
N2(g) + O2(g) ⇌ 2NO(g) | is 0.5 625. The equilibrium concentration of NO(g) is 3.0 × 10−7 M. If the equilibrium concentrations of N2(g) and O2(g) are equal, the concentration of N2(g) in M is
©
Q.130 Correct
Q.130 In-correct
Q.130 Unattempt
The solubility product of a sparingly soluble salt A2B is 3.2 × 10−11. Its solubility in mol L−1 is
©
The solubility product of a sparingly soluble salt A2B is 3.2 × 10−11. Its solubility in mol L−1 is
©
Q.131 Correct
Q.131 In-correct
Q.131 Unattempt
What is the volume (in mL) of 20 vol H2O2 required to completely react with 500 mL of 0.02 M acidified KMnO4 solution?
©
What is the volume (in mL) of 20 vol H2O2 required to completely react with 500 mL of 0.02 M acidified KMnO4 solution?
©
Q.132 Correct
Q.132 In-correct
Q.132 Unattempt
KO2 reacts with water to form A. B and C. B forms C when it reacts with iodine in basic medium. What are B and C respectively?
©
KO2 reacts with water to form A. B and C. B forms C when it reacts with iodine in basic medium. What are B and C respectively?
©
Q.133 Correct
Q.133 In-correct
Q.133 Unattempt
Identify the correct statements from the following :
I) Ga2O3 is an amphoteric oxide.
II) The dimer of aluminium chloride has three Al-Cl-Al bridge bonds,
III) Boron is very hard refractory solid of high melting temperature.
©
Identify the correct statements from the following :
I) Ga2O3 is an amphoteric oxide.
II) The dimer of aluminium chloride has three Al-Cl-Al bridge bonds,
III) Boron is very hard refractory solid of high melting temperature.
©
Q.134 Correct
Q.134 In-correct
Q.134 Unattempt
Which one of the following methods is used to prepare carbon monoxide on commercial scale?
©
Which one of the following methods is used to prepare carbon monoxide on commercial scale?
©
Q.135 Correct
Q.135 In-correct
Q.135 Unattempt
Match the following.
List - I List - II
A)Insecticide I) COD
B) K2Cr2O7 / 50% H2SO4 II) PAN
C) Bleaching of cloths and paper III) Na3AsO3
D) Eye Irritant IV) BOD
  V) H2O2

The correct answer is
©
Match the following.
List - I List - II
A)Insecticide I) COD
B) K2Cr2O7 / 50% H2SO4 II) PAN
C) Bleaching of cloths and paper III) Na3AsO3
D) Eye Irritant IV) BOD
  V) H2O2

The correct answer is
©
Q.136 Correct
Q.136 In-correct
Q.136 Unattempt
For which of the following. Kjeldahl's method is not used for the estimation of nitrogen?
(I) Aniline
(II) Azobenzene
(III) Nitrobenzene
(IV) Pyridine
 
©
For which of the following. Kjeldahl's method is not used for the estimation of nitrogen?
(I) Aniline
(II) Azobenzene
(III) Nitrobenzene
(IV) Pyridine
 
©
Q.137 Correct
Q.137 In-correct
Q.137 Unattempt
Identify the compound, which has maximum number of no bond resonance structures
©
Identify the compound, which has maximum number of no bond resonance structures
©
Q.138 Correct
Q.138 In-correct
Q.138 Unattempt
Wliicli of the following statements are correct?
I) In nitrating mixture nitric acid participates as an acid
II) σ complex is the intermediate substance in electrophilic substitution of benzene
III) Benzene on Friedel-Crafts alkylation with 11-propyl chloride gives isopropyl benzene
©
Wliicli of the following statements are correct?
I) In nitrating mixture nitric acid participates as an acid
II) σ complex is the intermediate substance in electrophilic substitution of benzene
III) Benzene on Friedel-Crafts alkylation with 11-propyl chloride gives isopropyl benzene
©
Q.139 Correct
Q.139 In-correct
Q.139 Unattempt
Which one of the following functional groups is not meta directing?
©
Which one of the following functional groups is not meta directing?
©
Q.140 Correct
Q.140 In-correct
Q.140 Unattempt
If the radius of an atom of an element which forms a body centered cubic unit cell is 173.2 pm. the volume of unit cell in cm3 is
©
If the radius of an atom of an element which forms a body centered cubic unit cell is 173.2 pm. the volume of unit cell in cm3 is
©
Q.141 Correct
Q.141 In-correct
Q.141 Unattempt
A solution is prepared by dissolving 10 g of a non-volatile solute (molar mass. ‘M‘ g mol−1) in 360 g of water. What is the molar mass in g mol−1 of solute if the relative lowering of vapour pressure of solution is 5 × 10−3?
©
A solution is prepared by dissolving 10 g of a non-volatile solute (molar mass. ‘M‘ g mol−1) in 360 g of water. What is the molar mass in g mol−1 of solute if the relative lowering of vapour pressure of solution is 5 × 10−3?
©
Q.142 Correct
Q.142 In-correct
Q.142 Unattempt
x g of MgSO4 (t = 1.8) is in 2.5 L of solution has an osmotic pressure of 2.463 atm. at 27 °C. What is the value of x in g?
©
x g of MgSO4 (t = 1.8) is in 2.5 L of solution has an osmotic pressure of 2.463 atm. at 27 °C. What is the value of x in g?
©
Q.143 Correct
Q.143 In-correct
Q.143 Unattempt
The electrode potentials for
M2+ (aq) + e− → M+ (aq)
M+ (aq) + e− → M (s)
©
The electrode potentials for
M2+ (aq) + e− → M+ (aq)
M+ (aq) + e− → M (s)
©
Q.144 Correct
Q.144 In-correct
Q.144 Unattempt
The half life periods of a first order reaction at 300 K and 400 K are 50 s and 10s respectively.
The activation energy of the reaction in kJ mol−1 is (log 5 = 0.70)
©
The half life periods of a first order reaction at 300 K and 400 K are 50 s and 10s respectively.
The activation energy of the reaction in kJ mol−1 is (log 5 = 0.70)
©
Q.145 Correct
Q.145 In-correct
Q.145 Unattempt
Which one of the following statements is collect for adsorption of solutes on solids in solutions?
©
Which one of the following statements is collect for adsorption of solutes on solids in solutions?
©
Q.146 Correct
Q.146 In-correct
Q.146 Unattempt
Identify the metal which is not common to German Silver and Brass.
©
Identify the metal which is not common to German Silver and Brass.
©
Q.147 Correct
Q.147 In-correct
Q.147 Unattempt
Which of the following reactions are correct with respect to the formation of products?
I) 2NaOH + SO2 → Na2SO4+H2
II) 2XeF4+3O2F2
143K
→
 2XeO3+7F2
III) PCl5+4H2O → H3PO4+5HCl
IV) 2NaNO2+2HCl → 2NaCl + NO + NO2+H2O
©
Which of the following reactions are correct with respect to the formation of products?
I) 2NaOH + SO2 → Na2SO4+H2
II) 2XeF4+3O2F2
143K
→
 2XeO3+7F2
III) PCl5+4H2O → H3PO4+5HCl
IV) 2NaNO2+2HCl → 2NaCl + NO + NO2+H2O
©
Q.148 Correct
Q.148 In-correct
Q.148 Unattempt
Chlorine oxidises sulphmdioxide in the presence of water to give an oxyacid A. Chlorine also oxidises iodine in the presence of water to give an oxyacid B. The oxidation states of S and I in A and B are respectively
©
Chlorine oxidises sulphmdioxide in the presence of water to give an oxyacid A. Chlorine also oxidises iodine in the presence of water to give an oxyacid B. The oxidation states of S and I in A and B are respectively
©
Q.149 Correct
Q.149 In-correct
Q.149 Unattempt
White phosphorous is heated with concentrated NaOH in CO2, atmosphere to form a gas A and compound B. When A is bubbled into aqueous CuSO4 solution copper phosphide and C are formed. B and C are respectively
©
White phosphorous is heated with concentrated NaOH in CO2, atmosphere to form a gas A and compound B. When A is bubbled into aqueous CuSO4 solution copper phosphide and C are formed. B and C are respectively
©
Q.150 Correct
Q.150 In-correct
Q.150 Unattempt
Which of the following set of elements do not possess f-electrons?
©
Which of the following set of elements do not possess f-electrons?
©
Q.151 Correct
Q.151 In-correct
Q.151 Unattempt
The Δ0 of a coordination complex of a metal ion (3d1) is 1000 kJ mol−1. If the energy of t2g orbitals is -400 kJ mol−1, the energy (in kJ mol−1) of eg orbitals is
©
The Δ0 of a coordination complex of a metal ion (3d1) is 1000 kJ mol−1. If the energy of t2g orbitals is -400 kJ mol−1, the energy (in kJ mol−1) of eg orbitals is
©
Q.152 Correct
Q.152 In-correct
Q.152 Unattempt
How many of the following polymers given, come under the category of condensation polymers?
Bakelite. Teflon. Nylon 6, Dacron, Polvisoprene, Melamine, Neoprene
©
How many of the following polymers given, come under the category of condensation polymers?
Bakelite. Teflon. Nylon 6, Dacron, Polvisoprene, Melamine, Neoprene
©
Q.153 Correct
Q.153 In-correct
Q.153 Unattempt
Identify the correct set from the following.
©
Identify the correct set from the following.
©
Q.154 Correct
Q.154 In-correct
Q.154 Unattempt
Which one of the following contains - As = As - in its structure?
©
Which one of the following contains - As = As - in its structure?
©
Q.155 Correct
Q.155 In-correct
Q.155 Unattempt

What are X and Y in the following reaction sequence?

 
What are X and Y in the following reaction sequence?
 
Q.156 Correct
Q.156 In-correct
Q.156 Unattempt
Which of the following sets is in the correct order regarding the property mentioned against them?
Sets Property
I) NCCH2COOH > FCH2COOH > H3CCH2COOH acidity
II) CH3CH2CHO > PhCOCH3 > PhCHO reactivity
III) H3COCH2CH3 < H3CCH2CHO < H3CCH2CH2OH boiling points
 
©
Which of the following sets is in the correct order regarding the property mentioned against them?
Sets Property
I) NCCH2COOH > FCH2COOH > H3CCH2COOH acidity
II) CH3CH2CHO > PhCOCH3 > PhCHO reactivity
III) H3COCH2CH3 < H3CCH2CHO < H3CCH2CH2OH boiling points
 
©
Q.157 Correct
Q.157 In-correct
Q.157 Unattempt
Identify the products (X. Y) and reaction mechanism (Z) of the following reaction?
 

 
Identify the products (X. Y) and reaction mechanism (Z) of the following reaction?
 
Q.158 Correct
Q.158 In-correct
Q.158 Unattempt
What are the products formed when an aldehyde (RCHO) is reacted with Tollens reagent?
©
What are the products formed when an aldehyde (RCHO) is reacted with Tollens reagent?
©
Q.159 Correct
Q.159 In-correct
Q.159 Unattempt

The following species are involved in the formation of an ester from a carboxylic acid in the presence of acid. The correct sequence of formation of these species is

The following species are involved in the formation of an ester from a carboxylic acid in the presence of acid. The correct sequence of formation of these species is
 
Q.160 Correct
Q.160 In-correct
Q.160 Unattempt
Identify the reagents (X. Y. Z) used in the conversion of 3-methylaniline to 3-nitrotoluene
©
Identify the reagents (X. Y. Z) used in the conversion of 3-methylaniline to 3-nitrotoluene
©
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