Please wait...

Solution
Q.1 Correct
Q.1 In-correct
Q.1 Unattempt
Let f be a function such that f (xy) =
f(x)
y
 for all positive real numbers x , y. If f (20) = 15 , then f (50) =
©
Let f be a function such that f (xy) =
f(x)
y
 for all positive real numbers x , y. If f (20) = 15 , then f (50) =
©
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt
If f : A → B is a function defined by f (x) =
x2−x
x2+2x
 then, which one of the following is true?
©
If f : A → B is a function defined by f (x) =
x2−x
x2+2x
 then, which one of the following is true?
©
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt
The statement n5−5n3 + 4n is divisible by 120 is true for
©
The statement n5−5n3 + 4n is divisible by 120 is true for
©
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt
Let A = [
75
48
] , B = [
43
75
] and C = [
−53
7−4
]
If Tr(S) denotes the trace of a square matrix S then
∞
Σ
k=0
1
3k
 Tr {A(BC)k} =
©
Let A = [
75
48
] , B = [
43
75
] and C = [
−53
7−4
]
If Tr(S) denotes the trace of a square matrix S then
∞
Σ
k=0
1
3k
 Tr {A(BC)k} =
©
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt
If the inverse of the matrix A = [
345
2−18
5−27
] is B then BT
©
If the inverse of the matrix A = [
345
2−18
5−27
] is B then BT
©
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt
If x = α , y = β , z = γ is the solution of the systeym of equations x + y + z = 4 , 2x - y + 3z = 9 , 3x + y + 2z = 8 , then 4α + 2β + 3γ =
©
If x = α , y = β , z = γ is the solution of the systeym of equations x + y + z = 4 , 2x - y + 3z = 9 , 3x + y + 2z = 8 , then 4α + 2β + 3γ =
©
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt
(
2
i+√3
)100+(
2
i−√3
)100 =
©
(
2
i+√3
)100+(
2
i−√3
)100 =
©
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt
If z is a complex number such that |z−
6
z
| = 5 , then the maximum value of |z| is
©
If z is a complex number such that |z−
6
z
| = 5 , then the maximum value of |z| is
©
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt
If a = 3 + 4i , Z1 and Z2 are two complex numbers such that |Z1| = 3 and |Z2−α| = 2 , then the maximum value of |Z1−Z2| is
©
If a = 3 + 4i , Z1 and Z2 are two complex numbers such that |Z1| = 3 and |Z2−α| = 2 , then the maximum value of |Z1−Z2| is
©
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt
If α is the real root and β, γ are the complex roots of the equation x3+3x2 + 3x + 28 = 0 then 2α + 3β + 3γ =
©
If α is the real root and β, γ are the complex roots of the equation x3+3x2 + 3x + 28 = 0 then 2α + 3β + 3γ =
©
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt
Given that α , β , γ , δ are in a geometric progression. If a , β are the roots of x2 - x + p = 0 and γ , δ are the roots of x2 - 4x + q = 0 , where p and q are integers, then the ordered pair (p , q) =
©
Given that α , β , γ , δ are in a geometric progression. If a , β are the roots of x2 - x + p = 0 and γ , δ are the roots of x2 - 4x + q = 0 , where p and q are integers, then the ordered pair (p , q) =
©
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt
If A, B, C are the sets of all values of x, for which x2 - 5x - 14 is positive, −6x2 + 2x - 3 is negative and 4x - 5x2 + 2 is positive and 4x - 5x2 + 2 is positive respectively, then A ∩ B ∩ C =
©
If A, B, C are the sets of all values of x, for which x2 - 5x - 14 is positive, −6x2 + 2x - 3 is negative and 4x - 5x2 + 2 is positive and 4x - 5x2 + 2 is positive respectively, then A ∩ B ∩ C =
©
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt
The complete solution set of the inequation √x2−3x+2 > (3 - x) is
©
The complete solution set of the inequation √x2−3x+2 > (3 - x) is
©
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt
The greatest real root of the equation 6x4−35x3+62x2 - 35x + 6 = 0 is
©
The greatest real root of the equation 6x4−35x3+62x2 - 35x + 6 = 0 is
©
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt
I : The number of all ten digited numbers that can be formed with all the distinct digits and which are divisible by 4 is 15 x 8!.
II : The number of positive integers that can be formed by using the digits 0 , 1 , 2 , 3 , 4 , 5 without any repetition is 1630.
©
I : The number of all ten digited numbers that can be formed with all the distinct digits and which are divisible by 4 is 15 x 8!.
II : The number of positive integers that can be formed by using the digits 0 , 1 , 2 , 3 , 4 , 5 without any repetition is 1630.
©
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt
A man has 5 male and 4 female relatives. His wife has 4 male and 5 female relatives. The number of ways in which they can invite 5 male and 5 female relatives so that 5 of them are man’s relatives and remaining 5 are his wife’s relatives
©
A man has 5 male and 4 female relatives. His wife has 4 male and 5 female relatives. The number of ways in which they can invite 5 male and 5 female relatives so that 5 of them are man’s relatives and remaining 5 are his wife’s relatives
©
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt
If the coefficients of rth , (r + 1) th and (r + 2) th terms in the expansion of (1+x)14 are in an arithmetic progression , then r =
©
If the coefficients of rth , (r + 1) th and (r + 2) th terms in the expansion of (1+x)14 are in an arithmetic progression , then r =
©
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt
If x =
5
2!3
+
5.7
3!32
 +
5.7.9
4!33
 + ... , then x2 + 4x =
©
If x =
5
2!3
+
5.7
3!32
 +
5.7.9
4!33
 + ... , then x2 + 4x =
©
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt
The coefficient of x3 in the expansion of
x
(x+1)(x−2)2
 is
©
The coefficient of x3 in the expansion of
x
(x+1)(x−2)2
 is
©
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt
If the periods of the functions sin (ax + b) and tan (cx + d) are respectively
4
7
 and
2
5
 , then sin (|a| + |c|) + cos (|a| - |c|) =
©
If the periods of the functions sin (ax + b) and tan (cx + d) are respectively
4
7
 and
2
5
 , then sin (|a| + |c|) + cos (|a| - |c|) =
©
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt
The smallest positive value of x (in degrees) for which
tan (x + 100°) = tan (x + 50°) . tan x - tan (x - 50°) is
©
The smallest positive value of x (in degrees) for which
tan (x + 100°) = tan (x + 50°) . tan x - tan (x - 50°) is
©
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt
For α = 0 , if cos (θ + α) , cos θ and cos (θ - α) are in harmonic progression, then sec2 θ , cos2
α
2
 =
©
For α = 0 , if cos (θ + α) , cos θ and cos (θ - α) are in harmonic progression, then sec2 θ , cos2
α
2
 =
©
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt
If cos 2θ + α sin θ = 2α - 7 has a solution , then
©
If cos 2θ + α sin θ = 2α - 7 has a solution , then
©
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt
If x = a is a solution of the equation sin−1
x
2
+sin−1
2x
3
 = sin−1 x , then the roots of the equation x2 - ax - 1 = 0 are
©
If x = a is a solution of the equation sin−1
x
2
+sin−1
2x
3
 = sin−1 x , then the roots of the equation x2 - ax - 1 = 0 are
©
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt
The set of all real values of* for which
f (x) = loge √
1+x
1−x
 + loge(
1+√1−x2
x
) + Cot h−1 x + loge(
1+√1+x2
x
) + Sin h−1 x is defines is
©
The set of all real values of* for which
f (x) = loge √
1+x
1−x
 + loge(
1+√1−x2
x
) + Cot h−1 x + loge(
1+√1+x2
x
) + Sin h−1 x is defines is
©
Q.26 Correct
Q.26 In-correct
Q.26 Unattempt
In a triangle ABC, if the angle A = 60°, then
1
a+b
+
1
a+c
 =
©
In a triangle ABC, if the angle A = 60°, then
1
a+b
+
1
a+c
 =
©
Q.27 Correct
Q.27 In-correct
Q.27 Unattempt
In a Δ ABC , 8R3 Σ sin3 A cos (B - C) =
©
In a Δ ABC , 8R3 Σ sin3 A cos (B - C) =
©
Q.28 Correct
Q.28 In-correct
Q.28 Unattempt
In a Δ ABC. if a : b : c = 4 : 5 : 6 then the ratio of the radius radius of the incircle is
©
In a Δ ABC. if a : b : c = 4 : 5 : 6 then the ratio of the radius radius of the incircle is
©
Q.29 Correct
Q.29 In-correct
Q.29 Unattempt
→
a
,
→
b
,
→
c
 care three mutually perpendicular unit vectors in the right handed system. If the points P, Q, R with position vectors 2
→
a
+5
→
b
−4
→
c
 ,
→
a
+4
→
b
−3
→
c
 and k
→
a
+7
→
b
−6
→
c
 respectively lie on a line. then, the ratio in which the point P divides QR is
©
→
a
,
→
b
,
→
c
 care three mutually perpendicular unit vectors in the right handed system. If the points P, Q, R with position vectors 2
→
a
+5
→
b
−4
→
c
 ,
→
a
+4
→
b
−3
→
c
 and k
→
a
+7
→
b
−6
→
c
 respectively lie on a line. then, the ratio in which the point P divides QR is
©
Q.30 Correct
Q.30 In-correct
Q.30 Unattempt
Let π be the plane passing through the points
^
i
 ,
^
j
 ,
^
i
+
^
j
+
^
k
 and L be the line passing through the point
^
i
+2
^
j
+3
^
k
 and parallel to the vector
^
i
−
^
j
+
^
k
. If P (α , β , g) is the point of intersection of the plane π and line L, then , √(α2+β2)γ2 =
©
Let π be the plane passing through the points
^
i
 ,
^
j
 ,
^
i
+
^
j
+
^
k
 and L be the line passing through the point
^
i
+2
^
j
+3
^
k
 and parallel to the vector
^
i
−
^
j
+
^
k
. If P (α , β , g) is the point of intersection of the plane π and line L, then , √(α2+β2)γ2 =
©
Q.31 Correct
Q.31 In-correct
Q.31 Unattempt
If
→
a
 =
^
i
−
^
j
−
^
k
 ,
→
b
 = 2
^
i
−3
^
j
+
^
k
 and
→
p1
 ,
→
p2
 are the orthogonal projection vectors of
→
a
 on
→
b
 and
→
b
 on
→
a
 respectively, then )
→
p1
+
→
p2
) . (
→
p1
−
→
p2
) =
©
If
→
a
 =
^
i
−
^
j
−
^
k
 ,
→
b
 = 2
^
i
−3
^
j
+
^
k
 and
→
p1
 ,
→
p2
 are the orthogonal projection vectors of
→
a
 on
→
b
 and
→
b
 on
→
a
 respectively, then )
→
p1
+
→
p2
) . (
→
p1
−
→
p2
) =
©
Q.32 Correct
Q.32 In-correct
Q.32 Unattempt
Let
→
a
,
→
b
,
→
c
 be three non-coplanar vectors and
→
a
′ =
→
b
×
→
c
[
→
a
→
b
→
c
]
 ,
→
b
′ =
→
c
×
→
a
[
→
a
→
b
→
c
]
 ,
→
c
′ =
→
a
×
→
b
[
→
a
→
b
→
c
]
. The length of the altitude of the parallelopiped formed by
→
a
′,
→
b
′,
→
c
′ as coterminus edges, with respect to the base having
→
a
′ and
→
c
′ as its adjacent sides is
©
Let
→
a
,
→
b
,
→
c
 be three non-coplanar vectors and
→
a
′ =
→
b
×
→
c
[
→
a
→
b
→
c
]
 ,
→
b
′ =
→
c
×
→
a
[
→
a
→
b
→
c
]
 ,
→
c
′ =
→
a
×
→
b
[
→
a
→
b
→
c
]
. The length of the altitude of the parallelopiped formed by
→
a
′,
→
b
′,
→
c
′ as coterminus edges, with respect to the base having
→
a
′ and
→
c
′ as its adjacent sides is
©
Q.33 Correct
Q.33 In-correct
Q.33 Unattempt
Let
→
a
,
→
b
,
→
c
 be three non-coplanar vectors. Let Si (i = 1 , 2 , 3 , 4 , 5 , 6) denote the six scalar triple products formed by all possible permutations of
→
a
,
→
b
,
→
c
. If i , j , k , l are randomly chosen distinct numbers from 1 to 6 and if x =
Si
Sj
+
Sk
Sl
 , y =
Si
Sj
−
Sk
Sl
 then x2+y2 =
©
Let
→
a
,
→
b
,
→
c
 be three non-coplanar vectors. Let Si (i = 1 , 2 , 3 , 4 , 5 , 6) denote the six scalar triple products formed by all possible permutations of
→
a
,
→
b
,
→
c
. If i , j , k , l are randomly chosen distinct numbers from 1 to 6 and if x =
Si
Sj
+
Sk
Sl
 , y =
Si
Sj
−
Sk
Sl
 then x2+y2 =
©
Q.34 Correct
Q.34 In-correct
Q.34 Unattempt
If
→
a
=
^
i
−2
^
j
+
^
k
,
→
b
=
^
i
+3
^
j
−2
^
k
,
→
c
= 2
^
i
+
^
j
−
^
k
and
→
d
=
^
i
+
^
j
+
^
k
then the volume (in cubic units) of the tetrahedron having (
→
a
×
→
b
)×
→
c
,
→
b
,
→
d
as its coterminous edges is
©
If
→
a
=
^
i
−2
^
j
+
^
k
,
→
b
=
^
i
+3
^
j
−2
^
k
,
→
c
= 2
^
i
+
^
j
−
^
k
and
→
d
=
^
i
+
^
j
+
^
k
then the volume (in cubic units) of the tetrahedron having (
→
a
×
→
b
)×
→
c
,
→
b
,
→
d
as its coterminous edges is
©
Q.35 Correct
Q.35 In-correct
Q.35 Unattempt
The mean deviation of the data 3, 5, 11, 13, 17, 19, 23, 29 about its arithmetic mean is
©
The mean deviation of the data 3, 5, 11, 13, 17, 19, 23, 29 about its arithmetic mean is
©
Q.36 Correct
Q.36 In-correct
Q.36 Unattempt
If the weights of 10 persons (in kgs) are observed as : 45, 49, 55, 50, 41, 44, 60, 58, 53, 55 then, the variance of their weights is
©
If the weights of 10 persons (in kgs) are observed as : 45, 49, 55, 50, 41, 44, 60, 58, 53, 55 then, the variance of their weights is
©
Q.37 Correct
Q.37 In-correct
Q.37 Unattempt
If two dice are rolled at a time, then the probability of getting an odd number on the first die or a total of 7 on both dice is
©
If two dice are rolled at a time, then the probability of getting an odd number on the first die or a total of 7 on both dice is
©
Q.38 Correct
Q.38 In-correct
Q.38 Unattempt
If A and B are two events of a random experiment such that P (
→
A
) = 0.3 , P (
→
B
) = 0.4 and P (A ∩
→
B
) = 0.5 , then P (A ∪ B) + P (B | A ∪
→
B
) =
©
If A and B are two events of a random experiment such that P (
→
A
) = 0.3 , P (
→
B
) = 0.4 and P (A ∩
→
B
) = 0.5 , then P (A ∪ B) + P (B | A ∪
→
B
) =
©
Q.39 Correct
Q.39 In-correct
Q.39 Unattempt
A speaks truth in 4 out of 5 times. A die is tossed. If A reports that there is 4 on the die, then the probability that there was 4 on the die. is
©
A speaks truth in 4 out of 5 times. A die is tossed. If A reports that there is 4 on the die, then the probability that there was 4 on the die. is
©
Q.40 Correct
Q.40 In-correct
Q.40 Unattempt
Let S = {1 , 2 , 3 , ... , 50} and Ak be the set of multiples of k in S for k ∊ N. If is a number chosen from Ak , then match the items of List - I with the items of List - II.
List - I List - II
A) P (x3 < 30) I)
1
2
B) P (15 x4 ≤ 36) II)
2
3
C) P (x7 > 35) III)
2
7
D) P (x11 > 11)IV)
1
4
V)
3
4
IV)
9
16

The correct match is
©
Let S = {1 , 2 , 3 , ... , 50} and Ak be the set of multiples of k in S for k ∊ N. If is a number chosen from Ak , then match the items of List - I with the items of List - II.
List - I List - II
A) P (x3 < 30) I)
1
2
B) P (15 x4 ≤ 36) II)
2
3
C) P (x7 > 35) III)
2
7
D) P (x11 > 11)IV)
1
4
V)
3
4
IV)
9
16

The correct match is
©
Q.41 Correct
Q.41 In-correct
Q.41 Unattempt
If X is a Poisson variate such that P(X = 2) = 9 P(X = 4) + 90 P(X = 6), then the ordered pair (Mean (X), Variance (X)) =
©
If X is a Poisson variate such that P(X = 2) = 9 P(X = 4) + 90 P(X = 6), then the ordered pair (Mean (X), Variance (X)) =
©
Q.42 Correct
Q.42 In-correct
Q.42 Unattempt
If the points A (0,
4
3
) , B (- 1 , 0) and C (1 , 0) are such that the distance from a point P to the line BC is equal to the geometric mean of the distances fr om P to the lines AB and AC\ then the point P lies on the curve
©
If the points A (0,
4
3
) , B (- 1 , 0) and C (1 , 0) are such that the distance from a point P to the line BC is equal to the geometric mean of the distances fr om P to the lines AB and AC\ then the point P lies on the curve
©
Q.43 Correct
Q.43 In-correct
Q.43 Unattempt
Let P be the point (4, 1) and Q be its image in the line y = x. If Q is translated through a distance 2 units along the negative Y-axis to reach the point R. then the co-ordinates of Rare
©
Let P be the point (4, 1) and Q be its image in the line y = x. If Q is translated through a distance 2 units along the negative Y-axis to reach the point R. then the co-ordinates of Rare
©
Q.44 Correct
Q.44 In-correct
Q.44 Unattempt
The normal form of the line x + y + 1 = 0 is
©
The normal form of the line x + y + 1 = 0 is
©
Q.45 Correct
Q.45 In-correct
Q.45 Unattempt
The vertices of a triangle OBC are O (0 , 0), B ( - 3, - 1) and C (- 1 , - 3). If the line joining the point D on OC and E on OB is parallel to BC and the perpendicular distance of O from DE is
1
2
, then the equation of DE is
©
The vertices of a triangle OBC are O (0 , 0), B ( - 3, - 1) and C (- 1 , - 3). If the line joining the point D on OC and E on OB is parallel to BC and the perpendicular distance of O from DE is
1
2
, then the equation of DE is
©
Q.46 Correct
Q.46 In-correct
Q.46 Unattempt
A variable line passing through the fixed point (α, β) intersects the co- ordinate axes at A and B. If O is the origin, then the locus of the centroid of the triangle OAB is
©
A variable line passing through the fixed point (α, β) intersects the co- ordinate axes at A and B. If O is the origin, then the locus of the centroid of the triangle OAB is
©
Q.47 Correct
Q.47 In-correct
Q.47 Unattempt
If A is the orthocentre of the triangle formed by 2x2−y2 = 0 , x + y - 1 = 0 and B is the centroid of die triangle formed by 2x2 - 5xy + 2y2 = 0 , 7x - 2y - 12 = 0 , then the distance between A and B is
©
If A is the orthocentre of the triangle formed by 2x2−y2 = 0 , x + y - 1 = 0 and B is the centroid of die triangle formed by 2x2 - 5xy + 2y2 = 0 , 7x - 2y - 12 = 0 , then the distance between A and B is
©
Q.48 Correct
Q.48 In-correct
Q.48 Unattempt
The distance between the pair of lines represented by x2+2√2 xy + 2y2 + 4x + 4√2 y + 1 = 0 , is x2+2√2 xy + 2y2 + 4x + 4√2 y + 1 = 0
©
The distance between the pair of lines represented by x2+2√2 xy + 2y2 + 4x + 4√2 y + 1 = 0 , is x2+2√2 xy + 2y2 + 4x + 4√2 y + 1 = 0
©
Q.49 Correct
Q.49 In-correct
Q.49 Unattempt
The number of integers a. for which a chord of the circle x2+y2 = 75 is bisected at (8 , α) and that the slope of the chord i an integer , is
©
The number of integers a. for which a chord of the circle x2+y2 = 75 is bisected at (8 , α) and that the slope of the chord i an integer , is
©
Q.50 Correct
Q.50 In-correct
Q.50 Unattempt
If the line x - 6y - 12 = 0 meets the circle S = x2+y2 - 4x + 8y + 6 = 0 at A and B, then the point of intersection of the tangents at A and B to S = 0 is
©
If the line x - 6y - 12 = 0 meets the circle S = x2+y2 - 4x + 8y + 6 = 0 at A and B, then the point of intersection of the tangents at A and B to S = 0 is
©
Q.51 Correct
Q.51 In-correct
Q.51 Unattempt
A circle of radius 5 units passes through A (- 5 , 0) and B (5 , 0). If P (5 cos α , 5 sin α), Q (5 cos β , 5 sin β) are two points on this circle such that α - β =
π
2
 , then the locus of the point of intersection of the lines AP and BQ is
©
A circle of radius 5 units passes through A (- 5 , 0) and B (5 , 0). If P (5 cos α , 5 sin α), Q (5 cos β , 5 sin β) are two points on this circle such that α - β =
π
2
 , then the locus of the point of intersection of the lines AP and BQ is
©
Q.52 Correct
Q.52 In-correct
Q.52 Unattempt
Two circles which cut each other orthogonally, pass through the points (a , 0) and (- a , 0). If both of them touch the line y = mx + c , then c2 =
©
Two circles which cut each other orthogonally, pass through the points (a , 0) and (- a , 0). If both of them touch the line y = mx + c , then c2 =
©
Q.53 Correct
Q.53 In-correct
Q.53 Unattempt
For the system of circles given by (x2+y22gx) + λ (x2+y2+2fy+k) = 0 , where g ≠ 0 , f ≠ 0 and is a parameter, if the line joining the point circles of the system subtends a right angle at the origin , then
k
f2
 =
©
For the system of circles given by (x2+y22gx) + λ (x2+y2+2fy+k) = 0 , where g ≠ 0 , f ≠ 0 and is a parameter, if the line joining the point circles of the system subtends a right angle at the origin , then
k
f2
 =
©
Q.54 Correct
Q.54 In-correct
Q.54 Unattempt
For the parabola y2 + 2x + 2y - 3 = 0 match the items in List - I with those from List - II.
List - I List - II
A) Vertex I) 2x - 5 = 0
B) Focus II) (
3
2
,−1)
C) Equation of the Directrix III) x - 2 = 0
D) Equation of the AxisIV) y + 1 = 0
V) (2 , - 1)
VI) (2,
3
2
)

The correct match is
©
For the parabola y2 + 2x + 2y - 3 = 0 match the items in List - I with those from List - II.
List - I List - II
A) Vertex I) 2x - 5 = 0
B) Focus II) (
3
2
,−1)
C) Equation of the Directrix III) x - 2 = 0
D) Equation of the AxisIV) y + 1 = 0
V) (2 , - 1)
VI) (2,
3
2
)

The correct match is
©
Q.55 Correct
Q.55 In-correct
Q.55 Unattempt
The area (in sq.units) of the triangle formed by the normal to the parabola y2 = 16x whose slope is
1
2
 with the co-ordinates axes is
©
The area (in sq.units) of the triangle formed by the normal to the parabola y2 = 16x whose slope is
1
2
 with the co-ordinates axes is
©
Q.56 Correct
Q.56 In-correct
Q.56 Unattempt
If the major axis of an ellipse lies on the Y-axis, its minor axis lies on the X-axis and the length of its latus rectum is equal to
2
3
 of its minor axis, then the eccentricity of that ellipse is
©
If the major axis of an ellipse lies on the Y-axis, its minor axis lies on the X-axis and the length of its latus rectum is equal to
2
3
 of its minor axis, then the eccentricity of that ellipse is
©
Q.57 Correct
Q.57 In-correct
Q.57 Unattempt
If y = x + c is a normal to the ellipse
x2
25
+
y2
9
 = 1 , then c2 =
©
If y = x + c is a normal to the ellipse
x2
25
+
y2
9
 = 1 , then c2 =
©
Q.58 Correct
Q.58 In-correct
Q.58 Unattempt
The area (in sq. units) of the quadrilateral formed by the four common tangents drawn to the two hyperbolas
x2
a2
−
y2
b2
 = 1 and
y2
a2
−
x2
b2
 = 1 (a > b) is
©
The area (in sq. units) of the quadrilateral formed by the four common tangents drawn to the two hyperbolas
x2
a2
−
y2
b2
 = 1 and
y2
a2
−
x2
b2
 = 1 (a > b) is
©
Q.59 Correct
Q.59 In-correct
Q.59 Unattempt
The direction cosines of the line which is perpendicular to the lines with direction cosines proportional to (1, -2 , -2) and (0, 2 , 1) are
©
The direction cosines of the line which is perpendicular to the lines with direction cosines proportional to (1, -2 , -2) and (0, 2 , 1) are
©
Q.60 Correct
Q.60 In-correct
Q.60 Unattempt
The number of lines passing through (0, 0, 0) and making an angle of 45° with each of the three co-ordinate axes is
©
The number of lines passing through (0, 0, 0) and making an angle of 45° with each of the three co-ordinate axes is
©
Q.61 Correct
Q.61 In-correct
Q.61 Unattempt
The equation of the plane which passes through the point (2, 5, -8) and perpendicular to each of the planes 2x - 3y + 4z + 1 = 0 and 4x + y - 2z + 6 = 0 is
©
The equation of the plane which passes through the point (2, 5, -8) and perpendicular to each of the planes 2x - 3y + 4z + 1 = 0 and 4x + y - 2z + 6 = 0 is
©
Q.62 Correct
Q.62 In-correct
Q.62 Unattempt
lim
x→
π
6
sin(x−
π
6
)
√3
2
−cosx
 =
©
lim
x→
π
6
sin(x−
π
6
)
√3
2
−cosx
 =
©
Q.63 Correct
Q.63 In-correct
Q.63 Unattempt
The positive integer n for which
lim
x→0
(cosx−1)(cosx−ex)
xn
 exists and is finite , is
©
The positive integer n for which
lim
x→0
(cosx−1)(cosx−ex)
xn
 exists and is finite , is
©
Q.64 Correct
Q.64 In-correct
Q.64 Unattempt
If f (x) =
x
∫
−1
 |t| dt , x ≥ - 1 , then
©
If f (x) =
x
∫
−1
 |t| dt , x ≥ - 1 , then
©
Q.65 Correct
Q.65 In-correct
Q.65 Unattempt
If x = sinh−1 [log (1 + √y)], then
dy
dx
 =
©
If x = sinh−1 [log (1 + √y)], then
dy
dx
 =
©
Q.66 Correct
Q.66 In-correct
Q.66 Unattempt
If f (x) =
(7x+1)sinx
exlogx
 and f' (x) = f (x) g (x) , then g' (x) =
©
If f (x) =
(7x+1)sinx
exlogx
 and f' (x) = f (x) g (x) , then g' (x) =
©
Q.67 Correct
Q.67 In-correct
Q.67 Unattempt
If f (x) =
1
9
|
xosx10
12cosx1
012cosx
| , then
d2f
dx2
 =
©
If f (x) =
1
9
|
xosx10
12cosx1
012cosx
| , then
d2f
dx2
 =
©
Q.68 Correct
Q.68 In-correct
Q.68 Unattempt
The angle between the curves y2 = 8 (x + 4) and y2 = 24 (4 - x) is
©
The angle between the curves y2 = 8 (x + 4) and y2 = 24 (4 - x) is
©
Q.69 Correct
Q.69 In-correct
Q.69 Unattempt
The function f (x) = x
1
x
 for x > 0 , is
©
The function f (x) = x
1
x
 for x > 0 , is
©
Q.70 Correct
Q.70 In-correct
Q.70 Unattempt
Let f : [0,
1
2
] → R be given by f (x) = x (x - 1) (x - 2). The value 'c', when Lagrange's mean - value theorem is applied for f (x) , is
©
Let f : [0,
1
2
] → R be given by f (x) = x (x - 1) (x - 2). The value 'c', when Lagrange's mean - value theorem is applied for f (x) , is
©
Q.71 Correct
Q.71 In-correct
Q.71 Unattempt
If a tangent to the ellipse
x2
a2
+
y2
b2
 = 1 (a > b > 0) having slope
1
3
 is a normal to the circle x2+y2 + 2x + 2y + 1 = 0 , then the maximum value of ab is
©
If a tangent to the ellipse
x2
a2
+
y2
b2
 = 1 (a > b > 0) having slope
1
3
 is a normal to the circle x2+y2 + 2x + 2y + 1 = 0 , then the maximum value of ab is
©
Q.72 Correct
Q.72 In-correct
Q.72 Unattempt
∫
sin8x−cos8x
1−2sin2x+2sin4x
 dx =
©
∫
sin8x−cos8x
1−2sin2x+2sin4x
 dx =
©
Q.73 Correct
Q.73 In-correct
Q.73 Unattempt
∫
2x12+5x9
(1+x3+x5)
 dx =
©
∫
2x12+5x9
(1+x3+x5)
 dx =
©
Q.74 Correct
Q.74 In-correct
Q.74 Unattempt
∫
x2+cos2x
(1+x2)sin2x
 dx =
©
∫
x2+cos2x
(1+x2)sin2x
 dx =
©
Q.75 Correct
Q.75 In-correct
Q.75 Unattempt
If In = ∫ sinn x dx for n = 1 , 2 , 3 , ... , then 8 I8 + 7 (I7−I8) - 6 I5 =
©
If In = ∫ sinn x dx for n = 1 , 2 , 3 , ... , then 8 I8 + 7 (I7−I8) - 6 I5 =
©
Q.76 Correct
Q.76 In-correct
Q.76 Unattempt
lim
n→∞
1+32+243+...+n5
n6
 =
©
lim
n→∞
1+32+243+...+n5
n6
 =
©
Q.77 Correct
Q.77 In-correct
Q.77 Unattempt
Let a > 1 and b > 1. If f (t) is a periodic function of period T and
∞
∫
0
a−bt f (t) dt = k
T
∫
0
a−bt f 9t) dt , then k =
©
Let a > 1 and b > 1. If f (t) is a periodic function of period T and
∞
∫
0
a−bt f (t) dt = k
T
∫
0
a−bt f 9t) dt , then k =
©
Q.78 Correct
Q.78 In-correct
Q.78 Unattempt
The area (in sq.units) enclosed by the curves = sin x + cos x and y = |cos x - sin x| over the interval [0,
π
2
] is
©
The area (in sq.units) enclosed by the curves = sin x + cos x and y = |cos x - sin x| over the interval [0,
π
2
] is
©
Q.79 Correct
Q.79 In-correct
Q.79 Unattempt
The degree and order respectively of the differential equation of the family of the curves represented by y = √x(x+√c) are
(Here c is a parameter)

©
The degree and order respectively of the differential equation of the family of the curves represented by y = √x(x+√c) are
(Here c is a parameter)

©
Q.80 Correct
Q.80 In-correct
Q.80 Unattempt
The solution of the differential equation
x+y−1
x+y−2
dy
dx
 =
x+y+1
x+y+2
 , given that y = 1 when x = 1 , is
©
The solution of the differential equation
x+y−1
x+y−2
dy
dx
 =
x+y+1
x+y+2
 , given that y = 1 when x = 1 , is
©
Q.81 Correct
Q.81 In-correct
Q.81 Unattempt
If 'A' represents density, 'B' represents velocity, ‘C' represents specific heat capacity and 'D' represents wavelength, then the quantity having the dimensions of product of A, B, C and D is
©
If 'A' represents density, 'B' represents velocity, ‘C' represents specific heat capacity and 'D' represents wavelength, then the quantity having the dimensions of product of A, B, C and D is
©
Q.82 Correct
Q.82 In-correct
Q.82 Unattempt
A ball dropped from a building of height 12 m falls oil a slab of 1 m height from the ground and makes a perfect elastic collision. Later the ball falls on a wooden table of height 0.5 m. makes inelastic collision and falls on the ground. If the coefficient of restitution between the ball and the table is 0.5. then the velocity of the ball while touching the ground is about
(Acceleration due to gravity = 10 ms−2)
©
A ball dropped from a building of height 12 m falls oil a slab of 1 m height from the ground and makes a perfect elastic collision. Later the ball falls on a wooden table of height 0.5 m. makes inelastic collision and falls on the ground. If the coefficient of restitution between the ball and the table is 0.5. then the velocity of the ball while touching the ground is about
(Acceleration due to gravity = 10 ms−2)
©
Q.83 Correct
Q.83 In-correct
Q.83 Unattempt
Two food packets are thrown with same velocity in the same direction with different angles of projection simultaneously. The angle of projection of one packet is 15°. At the same moment one boy starts running from rest from the point of projection with an acceleration of 10 ms−2 to catch them. If he caught one packet at a distance of 20 m and other packet in
1
2
 s later the first packet, then the angle of projection of the second packet is
(Acceleration due to gravity = 10 ms−2)
©
Two food packets are thrown with same velocity in the same direction with different angles of projection simultaneously. The angle of projection of one packet is 15°. At the same moment one boy starts running from rest from the point of projection with an acceleration of 10 ms−2 to catch them. If he caught one packet at a distance of 20 m and other packet in
1
2
 s later the first packet, then the angle of projection of the second packet is
(Acceleration due to gravity = 10 ms−2)
©
Q.84 Correct
Q.84 In-correct
Q.84 Unattempt

A body is projected up a smooth inclined plane of length 20 √2 m from point A as shown in the figure. The top (B) of the inclined plane is connected to a well of diameter 40 m. If the body just manages to cross the well then the velocity of projection is
(Acceleration due to gravity = 10 ms−2)

A body is projected up a smooth inclined plane of length 20 √2 m from point A as shown in the figure. The top (B) of the inclined plane is connected to a well of diameter 40 m. If the body just manages to cross the well then the velocity of projection is
(Acceleration due to gravity = 10 ms−2)
Q.85 Correct
Q.85 In-correct
Q.85 Unattempt
A body is acted on by a force given by F = (15 + 3t2) N. The impulse received by the body during the first 2 seconds is
©
A body is acted on by a force given by F = (15 + 3t2) N. The impulse received by the body during the first 2 seconds is
©
Q.86 Correct
Q.86 In-correct
Q.86 Unattempt
A body starts sliding down from the top of an inclined plane inclined at an angle 0 with horizontal. The first one third of the incline is smooth, the next one third has coefficient of friction
µ
2
 and the last one third has coefficient of friction |i. If the body comes to rest at the bottom of the plane then the value of µ is
©
A body starts sliding down from the top of an inclined plane inclined at an angle 0 with horizontal. The first one third of the incline is smooth, the next one third has coefficient of friction
µ
2
 and the last one third has coefficient of friction |i. If the body comes to rest at the bottom of the plane then the value of µ is
©
Q.87 Correct
Q.87 In-correct
Q.87 Unattempt
A motor pumps a liquid of density ρ through a pipe of cross sectional area A. If the liquid moves with a speed v in this pipe, then the rate of kinetic energy imparted to the liquid is proportional to
©
A motor pumps a liquid of density ρ through a pipe of cross sectional area A. If the liquid moves with a speed v in this pipe, then the rate of kinetic energy imparted to the liquid is proportional to
©
Q.88 Correct
Q.88 In-correct
Q.88 Unattempt

Two particles 1 and 2 are allowed to descend on two frictionless chords OP and OQ as shown in figure. The ratio of the speeds of the particles 1 and 2 respectively when they reach the circumference is

Two particles 1 and 2 are allowed to descend on two frictionless chords OP and OQ as shown in figure. The ratio of the speeds of the particles 1 and 2 respectively when they reach the circumference is
Q.89 Correct
Q.89 In-correct
Q.89 Unattempt

A uniform rod of mass 'm' and length 'l' is pivoted smoothly at ‘O' as shown in figure. If a horizontal force ‘F' acts at the bottom of the rod and 'ω' is the angular velocity of the rod which is a function of angle of rotation ‘0\ then the maximum angular displacement of the rod is
(Acceleration due to gravity = g)

A uniform rod of mass 'm' and length 'l' is pivoted smoothly at ‘O' as shown in figure. If a horizontal force ‘F' acts at the bottom of the rod and 'ω' is the angular velocity of the rod which is a function of angle of rotation ‘0\ then the maximum angular displacement of the rod is
(Acceleration due to gravity = g)
Q.90 Correct
Q.90 In-correct
Q.90 Unattempt
An electric motor of power 75 W rotates a flywheel of moment of inertia 0.36 kg m2 at a constant rate of 100 rad s−1. If the power is switched off the time taken for the wheel to come to rest is
©
An electric motor of power 75 W rotates a flywheel of moment of inertia 0.36 kg m2 at a constant rate of 100 rad s−1. If the power is switched off the time taken for the wheel to come to rest is
©
Q.91 Correct
Q.91 In-correct
Q.91 Unattempt
A particle is executing simple harmonic motion along a straight line PQ. At three points A, B and C on the line PQ. lying on one side of the mean position, the velocities of the particle are 8 ms−1, 7 ms−1 and 4 ms−1 respectively. If AB = BC = 1 m. the velocity of the particle at mean position is
©
A particle is executing simple harmonic motion along a straight line PQ. At three points A, B and C on the line PQ. lying on one side of the mean position, the velocities of the particle are 8 ms−1, 7 ms−1 and 4 ms−1 respectively. If AB = BC = 1 m. the velocity of the particle at mean position is
©
Q.92 Correct
Q.92 In-correct
Q.92 Unattempt
The gravitational potential difference between the surface of a planet and a point 20 m above it is 16 J kg−1. The workdone in moving a 4 kg body by 8 m on a slope of 60° from the horizontal is
©
The gravitational potential difference between the surface of a planet and a point 20 m above it is 16 J kg−1. The workdone in moving a 4 kg body by 8 m on a slope of 60° from the horizontal is
©
Q.93 Correct
Q.93 In-correct
Q.93 Unattempt
The area of cross-section of steel wire is 0.1 cm2 and Youns's modulus of steel is 2 × 1011 N m−2 . The force required to stretch by 0.1% of its length is
©
The area of cross-section of steel wire is 0.1 cm2 and Youns's modulus of steel is 2 × 1011 N m−2 . The force required to stretch by 0.1% of its length is
©
Q.94 Correct
Q.94 In-correct
Q.94 Unattempt
A sphere of radius R has a concentric spherical cavity of radius r. The relative density of the material of the sphere is o. It just floats when placed in tank hill of water. The value of
R
r
 is
©
A sphere of radius R has a concentric spherical cavity of radius r. The relative density of the material of the sphere is o. It just floats when placed in tank hill of water. The value of
R
r
 is
©
Q.95 Correct
Q.95 In-correct
Q.95 Unattempt

Figure shows a system of two concentric spheres of radii r1 and r2 at temperatures T1 and T2 respectively. The radial rate of flow of heat in a substance tilled between the two concentric spheres is proportional to

Figure shows a system of two concentric spheres of radii r1 and r2 at temperatures T1 and T2 respectively. The radial rate of flow of heat in a substance tilled between the two concentric spheres is proportional to
 
Q.96 Correct
Q.96 In-correct
Q.96 Unattempt
A composite bar of uniform cross section is made of 25 cm of Copper. 10 cm of Nickel and 15 cm of Aluminium with perfect thermal contacts. Tire free copper end of the rod is at 100 °C and the free Aluminium end is at 0 °C. If KCu = 2 KAl and KAl = 3 KNi, then the temperatures of Cu-Ni and Ni-Al junctions are respectively
(Assume no loss of heat occurs from the sides of the rod. K- thermal conductivity)
©
A composite bar of uniform cross section is made of 25 cm of Copper. 10 cm of Nickel and 15 cm of Aluminium with perfect thermal contacts. Tire free copper end of the rod is at 100 °C and the free Aluminium end is at 0 °C. If KCu = 2 KAl and KAl = 3 KNi, then the temperatures of Cu-Ni and Ni-Al junctions are respectively
(Assume no loss of heat occurs from the sides of the rod. K- thermal conductivity)
©
Q.97 Correct
Q.97 In-correct
Q.97 Unattempt
The specific heat capacities of three liquids A. B and C are in the ratio 1:2:3 and the masses of the liquids are in the ratio 1:1:1. The temperatures of the liquids A. B and C are 15 °C. 30 °C and 45 °C respectively. Then match the resultant temperature of the mixture given in list-II with the corresponding mixture given in list - I.
List - I List - II
A) Mixture of liquids A and B I) 25 °C
B) Mixture of liquids B and C II) 35 °C
C) Mixture of liquids C and A III) 37.5 °C
D) Mixture of liquids A- B and CIV) 39 °C

The correct answer is
©
The specific heat capacities of three liquids A. B and C are in the ratio 1:2:3 and the masses of the liquids are in the ratio 1:1:1. The temperatures of the liquids A. B and C are 15 °C. 30 °C and 45 °C respectively. Then match the resultant temperature of the mixture given in list-II with the corresponding mixture given in list - I.
List - I List - II
A) Mixture of liquids A and B I) 25 °C
B) Mixture of liquids B and C II) 35 °C
C) Mixture of liquids C and A III) 37.5 °C
D) Mixture of liquids A- B and CIV) 39 °C

The correct answer is
©
Q.98 Correct
Q.98 In-correct
Q.98 Unattempt
A gas (γ = 1.5) undergoes a cycle of adiabatic, isobaric and isochoric processes in an order. If the volume of the gas is doubled in the adiabatic process then the efficiency of the cycle is approximately
©
A gas (γ = 1.5) undergoes a cycle of adiabatic, isobaric and isochoric processes in an order. If the volume of the gas is doubled in the adiabatic process then the efficiency of the cycle is approximately
©
Q.99 Correct
Q.99 In-correct
Q.99 Unattempt
The y-components of velocities of the molecules of a gas are - 7 , - 6 , - 5 , - 4 , - 3 , - 2 , - 1 , 0 , + 1 , + 2 , + 3 , + 4 , + 5 , + 6 , + 7 ms−1 then the rms velocity is
©
The y-components of velocities of the molecules of a gas are - 7 , - 6 , - 5 , - 4 , - 3 , - 2 , - 1 , 0 , + 1 , + 2 , + 3 , + 4 , + 5 , + 6 , + 7 ms−1 then the rms velocity is
©
Q.100 Correct
Q.100 In-correct
Q.100 Unattempt
A metal wire of length 80 cm area of cross-section 3 mm2 and material density 3000 kg m−3 is joined to another metal wire of length 60 cm. area of cross-section 1 mm2 and material density 9000 kg m−3 . The free ends of the two wires are stretched between two rigid supports and a tension of 40 N is produced in the wires. The minimum frequency of the timing fork which can produce stationary waves with the joint of the wires as a node is
©
A metal wire of length 80 cm area of cross-section 3 mm2 and material density 3000 kg m−3 is joined to another metal wire of length 60 cm. area of cross-section 1 mm2 and material density 9000 kg m−3 . The free ends of the two wires are stretched between two rigid supports and a tension of 40 N is produced in the wires. The minimum frequency of the timing fork which can produce stationary waves with the joint of the wires as a node is
©
Q.101 Correct
Q.101 In-correct
Q.101 Unattempt
A source producing sound of frequency 720 Hz is falling freely from the top of a tower of height 20 in. The frequency of sound heard by an observer on the top of the tower when the source just reaches the ground is
(Acceleration due to gravity =10 ms−2 and speed of sound in air = 340 ms−1)
©
A source producing sound of frequency 720 Hz is falling freely from the top of a tower of height 20 in. The frequency of sound heard by an observer on the top of the tower when the source just reaches the ground is
(Acceleration due to gravity =10 ms−2 and speed of sound in air = 340 ms−1)
©
Q.102 Correct
Q.102 In-correct
Q.102 Unattempt
In a spherical glass marble of radius 6 cm. a small air bubble is formed at 1 cm fr om the centre of the marble. The apparent position of the air bubble from the nearest point on the surface of the marble is about
(Refractive index of glass is 1.5)
©
In a spherical glass marble of radius 6 cm. a small air bubble is formed at 1 cm fr om the centre of the marble. The apparent position of the air bubble from the nearest point on the surface of the marble is about
(Refractive index of glass is 1.5)
©
Q.103 Correct
Q.103 In-correct
Q.103 Unattempt
In Young's double slit experiment, the two slits are separated by 0.5 cm and the screen is at 0.5 m from the slits. If 20000 bright hinges are counted per meter on the screen, then the wavelength of light used is
©
In Young's double slit experiment, the two slits are separated by 0.5 cm and the screen is at 0.5 m from the slits. If 20000 bright hinges are counted per meter on the screen, then the wavelength of light used is
©
Q.104 Correct
Q.104 In-correct
Q.104 Unattempt
A dipole has two charges +1 µC and -1 µC and each of mass 1 kg. The separation between the charges is 1 m. An electric field 20 × 103 Vm−1 is applied on the dipole. If the dipole is deflected through 2° horn equilibrium position, then the time taken by it to come to equilibrium position again is
©
A dipole has two charges +1 µC and -1 µC and each of mass 1 kg. The separation between the charges is 1 m. An electric field 20 × 103 Vm−1 is applied on the dipole. If the dipole is deflected through 2° horn equilibrium position, then the time taken by it to come to equilibrium position again is
©
Q.105 Correct
Q.105 In-correct
Q.105 Unattempt

In the following four cases, charged particles are at equal distances from the origin. Arrange them in the descending order of magnitude of the net electric field at the origin.

In the following four cases, charged particles are at equal distances from the origin. Arrange them in the descending order of magnitude of the net electric field at the origin.
Q.106 Correct
Q.106 In-correct
Q.106 Unattempt
A capacitance of 2 µF is required in an electrical circuit across a potential of 1.0 kV. A large number of 1 µF capacitors are available which can withstand a potential difference of not more than 300 V. The minimum number of capacitors required to achieve this is
©
A capacitance of 2 µF is required in an electrical circuit across a potential of 1.0 kV. A large number of 1 µF capacitors are available which can withstand a potential difference of not more than 300 V. The minimum number of capacitors required to achieve this is
©
Q.107 Correct
Q.107 In-correct
Q.107 Unattempt
A charge '5 C ‘ is placed at the centre of shell of radius r = 3 m and having charge '5 C ‘. The potential at a point
r
2
 distance horn the centre of the shell will be
©
A charge '5 C ‘ is placed at the centre of shell of radius r = 3 m and having charge '5 C ‘. The potential at a point
r
2
 distance horn the centre of the shell will be
©
Q.108 Correct
Q.108 In-correct
Q.108 Unattempt
Electrical energy costs 25 paisa per kilowatt hour. Assuming that no energy is wasted, the cost of heating 4.6 kg of water from 25 °C to the boiling point is
©
Electrical energy costs 25 paisa per kilowatt hour. Assuming that no energy is wasted, the cost of heating 4.6 kg of water from 25 °C to the boiling point is
©
Q.109 Correct
Q.109 In-correct
Q.109 Unattempt
A 500 W heater is designed to operate at 200 V potential difference. If it is connected across 160 V line, the heat it will produce in 20 minute is
©
A 500 W heater is designed to operate at 200 V potential difference. If it is connected across 160 V line, the heat it will produce in 20 minute is
©
Q.110 Correct
Q.110 In-correct
Q.110 Unattempt
A wire of length 44 cm carrying a current of 2 A is bent and the two ends are joined. This shape is placed in a uniform magnetic field of 50 mT. If the magnetic field is in north-south direction, then the maximum torque acting on the shape is
©
A wire of length 44 cm carrying a current of 2 A is bent and the two ends are joined. This shape is placed in a uniform magnetic field of 50 mT. If the magnetic field is in north-south direction, then the maximum torque acting on the shape is
©
Q.111 Correct
Q.111 In-correct
Q.111 Unattempt
A Toroid has a non-ferromagnetic core of inner radius 20.5 cm and outer radius 21.5 cm. around which 4200 turns of a wire are wound. If the current in the wire is 10 A. the magnetic field inside the core of the toroid is
(µ0 = 4π × 10~7Hm−1)
©
A Toroid has a non-ferromagnetic core of inner radius 20.5 cm and outer radius 21.5 cm. around which 4200 turns of a wire are wound. If the current in the wire is 10 A. the magnetic field inside the core of the toroid is
(µ0 = 4π × 10~7Hm−1)
©
Q.112 Correct
Q.112 In-correct
Q.112 Unattempt
Two short bar magnets A and B are arranged coaxially. The distance between their centres is 30 cm. A compass needle placed on their axis at a distance of 6 cm from B shows no deflection. The ratio of the magnetic moments of A and B is
©
Two short bar magnets A and B are arranged coaxially. The distance between their centres is 30 cm. A compass needle placed on their axis at a distance of 6 cm from B shows no deflection. The ratio of the magnetic moments of A and B is
©
Q.113 Correct
Q.113 In-correct
Q.113 Unattempt
A circular coil of area 0.1 m2 having 200 turns is placed in a magnetic field of 40 T. The plane of the coil makes 30° with the field. If the field is removed for 0.1s then the induced emf in the coil is
©
A circular coil of area 0.1 m2 having 200 turns is placed in a magnetic field of 40 T. The plane of the coil makes 30° with the field. If the field is removed for 0.1s then the induced emf in the coil is
©
Q.114 Correct
Q.114 In-correct
Q.114 Unattempt
A coil has an inductance 0.7 H and it is joined in series with a resistance of 220 Ω. When ac of 220 V. 50 Hz is applied to it. then wattless component in the circuit is
©
A coil has an inductance 0.7 H and it is joined in series with a resistance of 220 Ω. When ac of 220 V. 50 Hz is applied to it. then wattless component in the circuit is
©
Q.115 Correct
Q.115 In-correct
Q.115 Unattempt
A plane electromagnetic wave propagating in a non-magnetic dielectric medium is given by E = E0[4×10−7x−50t] where 'x' is in metre and 't' is in second. If the relative permeability of the medium , µr = 1 then the dielectric constant of the medium is
©
A plane electromagnetic wave propagating in a non-magnetic dielectric medium is given by E = E0[4×10−7x−50t] where 'x' is in metre and 't' is in second. If the relative permeability of the medium , µr = 1 then the dielectric constant of the medium is
©
Q.116 Correct
Q.116 In-correct
Q.116 Unattempt
All electrons ejected from a metal surface by the incident light of wavelength 200 mil can be stopped before travelling 1 in in the direction of uniform electric field of 4 NC−1. The work function of the metal surface is
©
All electrons ejected from a metal surface by the incident light of wavelength 200 mil can be stopped before travelling 1 in in the direction of uniform electric field of 4 NC−1. The work function of the metal surface is
©
Q.117 Correct
Q.117 In-correct
Q.117 Unattempt
A hydrogen atom emits a photon of wavelength
36
35R
 when it is jumped from its nth excited state to ground state. Then the quantum number w is
(R is Rydberg constant)

©
A hydrogen atom emits a photon of wavelength
36
35R
 when it is jumped from its nth excited state to ground state. Then the quantum number w is
(R is Rydberg constant)

©
Q.118 Correct
Q.118 In-correct
Q.118 Unattempt
Assertion (A): Fragments produced in the fission of
‌
92
U235 are radioactive
Reason (R) : The fragments in the fission of
235
‌
U have a proton to neutron ratio of 2. 5
©
Assertion (A): Fragments produced in the fission of
‌
92
U235 are radioactive
Reason (R) : The fragments in the fission of
235
‌
U have a proton to neutron ratio of 2. 5
©
Q.119 Correct
Q.119 In-correct
Q.119 Unattempt

In the circuit given, the current through Zener diode is

In the circuit given, the current through Zener diode is
Q.120 Correct
Q.120 In-correct
Q.120 Unattempt
Coaxial cable, a widely used wire medium for transmission of signals offers a bandwidth of approximately
©
Coaxial cable, a widely used wire medium for transmission of signals offers a bandwidth of approximately
©
Q.121 Correct
Q.121 In-correct
Q.121 Unattempt
The spectral line observed at 434 mu in the Balmer series of the hydrogen spectrum corresponds to a transition of an electron from the w orbit. What is the value of w?
(Rydberg constant RH = 109.677 cm−1)
©
The spectral line observed at 434 mu in the Balmer series of the hydrogen spectrum corresponds to a transition of an electron from the w orbit. What is the value of w?
(Rydberg constant RH = 109.677 cm−1)
©
Q.122 Correct
Q.122 In-correct
Q.122 Unattempt
The energy of 2s orbitals of H, He and Li follow the order

©
The energy of 2s orbitals of H, He and Li follow the order

©
Q.123 Correct
Q.123 In-correct
Q.123 Unattempt
X and Y are two elements which form oxides of the type XO3 and Y2O5 with lighest oxygen content. Identify the group numbers to which X and Y belongs
©
X and Y are two elements which form oxides of the type XO3 and Y2O5 with lighest oxygen content. Identify the group numbers to which X and Y belongs
©
Q.124 Correct
Q.124 In-correct
Q.124 Unattempt
Match the following.
List - I List - II
A) [CrF6]3− I) sp3d2, square planar
B) XeF4 II) sp3d , square planar
C) PCl5 III) sp3d2 , square pyramid
D) BrF5IV) sp3d , trigonal bipyramidal
V) sp3d2 , octahedral

The correct answer is
©
Match the following.
List - I List - II
A) [CrF6]3− I) sp3d2, square planar
B) XeF4 II) sp3d , square planar
C) PCl5 III) sp3d2 , square pyramid
D) BrF5IV) sp3d , trigonal bipyramidal
V) sp3d2 , octahedral

The correct answer is
©
Q.125 Correct
Q.125 In-correct
Q.125 Unattempt
Identify the pair of species having same hybridisation for central atom but possess different geometry
©
Identify the pair of species having same hybridisation for central atom but possess different geometry
©
Q.126 Correct
Q.126 In-correct
Q.126 Unattempt
At T(K). a hypothetical gas consisting of 100 molecules has the following distribution of velocities. (N = Number of molecules: V = velocity in cm s−1).
N V
2 4 × 103
2 4 × 108
10 3 × 104
20 5.5 × 105
25 4 × 105
35 6.8 × 106
6 2 × 107

Tlie most probable velocity (in cm s−1) for tliis gas is
©
At T(K). a hypothetical gas consisting of 100 molecules has the following distribution of velocities. (N = Number of molecules: V = velocity in cm s−1).
N V
2 4 × 103
2 4 × 108
10 3 × 104
20 5.5 × 105
25 4 × 105
35 6.8 × 106
6 2 × 107

Tlie most probable velocity (in cm s−1) for tliis gas is
©
Q.127 Correct
Q.127 In-correct
Q.127 Unattempt
4.90 a of impure potassium chlorate on heating shows a weight loss of 0.384 g. What percent of the impure potassium chlorate has decomposed?
©
4.90 a of impure potassium chlorate on heating shows a weight loss of 0.384 g. What percent of the impure potassium chlorate has decomposed?
©
Q.128 Correct
Q.128 In-correct
Q.128 Unattempt
The standard molar enthalpy of vaporisation of benzene ΔvapH° at 353 K is 30.8 kJ mol−1. If the benzene vapours behave as an ideal gas. the change in internal energy of vaporisation of 78 g of benzene at 353 K in kJ mol−1 is (1 L - atm = 101.32 J)
©
The standard molar enthalpy of vaporisation of benzene ΔvapH° at 353 K is 30.8 kJ mol−1. If the benzene vapours behave as an ideal gas. the change in internal energy of vaporisation of 78 g of benzene at 353 K in kJ mol−1 is (1 L - atm = 101.32 J)
©
Q.129 Correct
Q.129 In-correct
Q.129 Unattempt
The equilibrium partial pressures of CO(g) , CO2(g) in the equilibrium reaction CO2(g) + C(s) ⇌ 2CO2(g) at 1000K are 0.66 and 0.15 bar respectively. The equilibrium constant Kc approximately is
©
The equilibrium partial pressures of CO(g) , CO2(g) in the equilibrium reaction CO2(g) + C(s) ⇌ 2CO2(g) at 1000K are 0.66 and 0.15 bar respectively. The equilibrium constant Kc approximately is
©
Q.130 Correct
Q.130 In-correct
Q.130 Unattempt
20 mL of 0.2 M sodium hydroxide solution is added to 40 mL of 0.2 M acetic acid solution. What is the pH of the solution? (pKa of CH3COOH = 4.8)
©
20 mL of 0.2 M sodium hydroxide solution is added to 40 mL of 0.2 M acetic acid solution. What is the pH of the solution? (pKa of CH3COOH = 4.8)
©
Q.131 Correct
Q.131 In-correct
Q.131 Unattempt
111 acidic medium, aqueous potassium permanganate with hydrogen peroxide gives
©
111 acidic medium, aqueous potassium permanganate with hydrogen peroxide gives
©
Q.132 Correct
Q.132 In-correct
Q.132 Unattempt
Winch of the following metal ions form the stable super oxide?

©
Winch of the following metal ions form the stable super oxide?

©
Q.133 Correct
Q.133 In-correct
Q.133 Unattempt
The product/s formed when borax dissolves in water is/are:

©
The product/s formed when borax dissolves in water is/are:

©
Q.134 Correct
Q.134 In-correct
Q.134 Unattempt
Identify the correct statement.

©
Identify the correct statement.

©
Q.135 Correct
Q.135 In-correct
Q.135 Unattempt
The concentration of fluoride ions in drinking water upto 1 ppm make the enamel on teeth much harder by converting X into fluorapatite. What is X?
©
The concentration of fluoride ions in drinking water upto 1 ppm make the enamel on teeth much harder by converting X into fluorapatite. What is X?
©
Q.136 Correct
Q.136 In-correct
Q.136 Unattempt
Nitrogen, sulphur and phosphorus present in organic compounds are detected by the formation of which of the following coloured substances respectively.
©
Nitrogen, sulphur and phosphorus present in organic compounds are detected by the formation of which of the following coloured substances respectively.
©
Q.137 Correct
Q.137 In-correct
Q.137 Unattempt
The number of electrophiles and nucleophiles present in the species given below are respectively.
BF3,CO2,Me3N , SO3,CH3CO+,HS− , NO2+,FeCl3,H2O
©
The number of electrophiles and nucleophiles present in the species given below are respectively.
BF3,CO2,Me3N , SO3,CH3CO+,HS− , NO2+,FeCl3,H2O
©
Q.138 Correct
Q.138 In-correct
Q.138 Unattempt

What is D in the following reaction sequence?

What is D in the following reaction sequence?
 
 
©
Q.139 Correct
Q.139 In-correct
Q.139 Unattempt
In which of the following reactions alkane is not formed?
©
In which of the following reactions alkane is not formed?
©
Q.140 Correct
Q.140 In-correct
Q.140 Unattempt
An element forms a body centered cubic (bcc) lattice with edge length of 300 pm. If the density of the element is 7.2 g cm−3 , the number of atoms present in 324 g of it approximately is
©
An element forms a body centered cubic (bcc) lattice with edge length of 300 pm. If the density of the element is 7.2 g cm−3 , the number of atoms present in 324 g of it approximately is
©
Q.141 Correct
Q.141 In-correct
Q.141 Unattempt
An ideal solution of hexane and heptane at 30 °C has a vapour pressure of 95 bar with hexane mole fraction 0.305. In vapour phase hexane mole fraction is 0.555. The vapour pressures of pure hexane and heptane at 30 °C respectively in bar are
©
An ideal solution of hexane and heptane at 30 °C has a vapour pressure of 95 bar with hexane mole fraction 0.305. In vapour phase hexane mole fraction is 0.555. The vapour pressures of pure hexane and heptane at 30 °C respectively in bar are
©
Q.142 Correct
Q.142 In-correct
Q.142 Unattempt

The vapour pressure of a solution (b) as a friction of temperature (a) is plotted as a graph for two solutions of same molar concentration along with water as shown below. A. B and C are respectively.

The vapour pressure of a solution (b) as a friction of temperature (a) is plotted as a graph for two solutions of same molar concentration along with water as shown below. A. B and C are respectively.
Q.143 Correct
Q.143 In-correct
Q.143 Unattempt
If E°cell is 1.05 V. the emf of the cell for the following cell reaction
Ni (s) + 2 Ag+ (0.004 M) → Ni2+ (0.16 M) + 2 Ag (s) at 298 K in V is
©
If E°cell is 1.05 V. the emf of the cell for the following cell reaction
Ni (s) + 2 Ag+ (0.004 M) → Ni2+ (0.16 M) + 2 Ag (s) at 298 K in V is
©
Q.144 Correct
Q.144 In-correct
Q.144 Unattempt
Which one of the following is not the correct statement with respect to order of a reaction?
©
Which one of the following is not the correct statement with respect to order of a reaction?
©
Q.145 Correct
Q.145 In-correct
Q.145 Unattempt
300 mL of gold sol is mixed with 30 mL of 10% NaCl solution. The mass of Haemoglobin in mg required to protect the gold sol from coagulation is (gold number of Haemoglobin is 0.03)
©
300 mL of gold sol is mixed with 30 mL of 10% NaCl solution. The mass of Haemoglobin in mg required to protect the gold sol from coagulation is (gold number of Haemoglobin is 0.03)
©
Q.146 Correct
Q.146 In-correct
Q.146 Unattempt
In froth-floatation process what is the depressant used in the separation of sulphide ores of Zinc and Lead?
©
In froth-floatation process what is the depressant used in the separation of sulphide ores of Zinc and Lead?
©
Q.147 Correct
Q.147 In-correct
Q.147 Unattempt
In which of the following oxyacids of phosphorous, one P = O, two P - H and one P - OH bonds are present.
©
In which of the following oxyacids of phosphorous, one P = O, two P - H and one P - OH bonds are present.
©
Q.148 Correct
Q.148 In-correct
Q.148 Unattempt
Identify the reaction in which SO2 is not formed?
©
Identify the reaction in which SO2 is not formed?
©
Q.149 Correct
Q.149 In-correct
Q.149 Unattempt
In which of the following reactions oxygen gas is not formed?
©
In which of the following reactions oxygen gas is not formed?
©
Q.150 Correct
Q.150 In-correct
Q.150 Unattempt
The magnetic moment of which of the following complexes is maximum?
©
The magnetic moment of which of the following complexes is maximum?
©
Q.151 Correct
Q.151 In-correct
Q.151 Unattempt
A metal ion (Mn+) forms octahedral [ML6]n+] and tetrahedral [ML4]n+] complexes with same ligand at different experimental conditions. The Δ0 of [ML6]n− is 3 eV. What is the energy in eV of eg orbital of [ML6]n+ complex?
©
A metal ion (Mn+) forms octahedral [ML6]n+] and tetrahedral [ML4]n+] complexes with same ligand at different experimental conditions. The Δ0 of [ML6]n− is 3 eV. What is the energy in eV of eg orbital of [ML6]n+ complex?
©
Q.152 Correct
Q.152 In-correct
Q.152 Unattempt
The catalyst triethyl aluminium and titanium tetrachloride finds use in the formation of the polymer
©
The catalyst triethyl aluminium and titanium tetrachloride finds use in the formation of the polymer
©
Q.153 Correct
Q.153 In-correct
Q.153 Unattempt
Match the following.
List - I List - II
A) Ascorbic acid I) Rickets
B) Vitamin D II) Muscular weakness
C) Vitamin B1 III) Convulsions
D) Vitamin EIV) Amla
V) Beri Beri

The correct answer is
©
Match the following.
List - I List - II
A) Ascorbic acid I) Rickets
B) Vitamin D II) Muscular weakness
C) Vitamin B1 III) Convulsions
D) Vitamin EIV) Amla
V) Beri Beri

The correct answer is
©
Q.154 Correct
Q.154 In-correct
Q.154 Unattempt
Identify the correct pairs from the following.
I) Sodium benzoate Antioxidant
II) Sodium stearate Soap
Iii) Sodium lauryl sulphate Antiseptic
IV) AlitameArtificial sweetner


©
Identify the correct pairs from the following.
I) Sodium benzoate Antioxidant
II) Sodium stearate Soap
Iii) Sodium lauryl sulphate Antiseptic
IV) AlitameArtificial sweetner


©
Q.155 Correct
Q.155 In-correct
Q.155 Unattempt
The number of monochloroderivatives possible, when 2, 2- Dimethylpropane reacts with Chlorine in the presence of UV-light is
©
The number of monochloroderivatives possible, when 2, 2- Dimethylpropane reacts with Chlorine in the presence of UV-light is
©
Q.156 Correct
Q.156 In-correct
Q.156 Unattempt
Iii the following sequence of reactions identify the functional groups present in the resulting compound Y.
C6H5N2Cl
H2O
→
283K
 X
i)‌C‌H‌C‌l3∕aq.NaOH
→
ii)‌H3‌O+
 Y
©
Iii the following sequence of reactions identify the functional groups present in the resulting compound Y.
C6H5N2Cl
H2O
→
283K
 X
i)‌C‌H‌C‌l3∕aq.NaOH
→
ii)‌H3‌O+
 Y
©
Q.157 Correct
Q.157 In-correct
Q.157 Unattempt
The coll ect set of reagents (X. Y. Z) required to convert benzene to m - nitrobenzoic acid are
©
The coll ect set of reagents (X. Y. Z) required to convert benzene to m - nitrobenzoic acid are
©
Q.158 Correct
Q.158 In-correct
Q.158 Unattempt
The reduction products of an aldehyde, ketone and carboxylic acid in the presence of lithium aluminium hydride are respectively X, Y and Z. What are X, Y and Z?
©
The reduction products of an aldehyde, ketone and carboxylic acid in the presence of lithium aluminium hydride are respectively X, Y and Z. What are X, Y and Z?
©
Q.159 Correct
Q.159 In-correct
Q.159 Unattempt
A carbonyl compound 'A' (C8H8O) does not give iodoform test and on oxidation gave 'B'. On heating B with ammonia at higher temperature forms 'C'. What are ‘A’ and ‘C ’?
©
A carbonyl compound 'A' (C8H8O) does not give iodoform test and on oxidation gave 'B'. On heating B with ammonia at higher temperature forms 'C'. What are ‘A’ and ‘C ’?
©
Q.160 Correct
Q.160 In-correct
Q.160 Unattempt

What is Y in the following reaction sequence

What is Y in the following reaction sequence
Get latest Exam Updates
& Study Material Alerts!
No, Thanks
Click on Allow to receive notifications
×
Open Now