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Solution
Q.1 Correct
Q.1 In-correct
Q.1 Unattempt
The set of all real values of x for which f(x)=log2(2x−2)+√1−x is also real is
The set of all real values of x for which f(x)=log2(2x−2)+√1−x is also real is
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt
Let f(x)=1−x,g(x)=‌
1
1−x
,h(x)=‌
1
x
 be three functions, for x≠0, 1. If a function F(x) satisfies f(F(h(x)))=g(x), then
Let f(x)=1−x,g(x)=‌
1
1−x
,h(x)=‌
1
x
 be three functions, for x≠0, 1. If a function F(x) satisfies f(F(h(x)))=g(x), then
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt
If [
02a
b04
−3c0
] is a skew-symmetric matrix, then [
ab
ba
][
bc
cb
]=
If [
02a
b04
−3c0
] is a skew-symmetric matrix, then [
ab
ba
][
bc
cb
]=
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt
If [
−12b
a56
3c7
] is a symmetric matrix, then |
abc
bca
cab
|=
If [
−12b
a56
3c7
] is a symmetric matrix, then |
abc
bca
cab
|=
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt
If the matrix A=[
122
212
221
] satisfies the matrix equation A2−4A−5I=0, then A−1=
If the matrix A=[
122
212
221
] satisfies the matrix equation A2−4A−5I=0, then A−1=
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt
Consider the simultaneous linear equations AX=B and AY=Q. If A is an invertible matrix and B is the unique solution of AY=Q, then the solution of AX=B is
Consider the simultaneous linear equations AX=B and AY=Q. If A is an invertible matrix and B is the unique solution of AY=Q, then the solution of AX=B is
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt
If (2x−y+1)+i(x−2y−1)=2−3i, then the multiplicative inverse of (x−iy) is
If (2x−y+1)+i(x−2y−1)=2−3i, then the multiplicative inverse of (x−iy) is
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt
If α,β are the roots of the equation x2−2√3x+4=0 then α6+β6=
If α,β are the roots of the equation x2−2√3x+4=0 then α6+β6=
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt
If cis α is the common value of (−1)1∕4 and (−i)1∕2 then tan‌α=
If cis α is the common value of (−1)1∕4 and (−i)1∕2 then tan‌α=
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt
When b=17, it is found that the roots of the equation x2+bx+c=0 are −2 and −15. If α,β are the roots of the same equation when b=13 then |α−β|=
When b=17, it is found that the roots of the equation x2+bx+c=0 are −2 and −15. If α,β are the roots of the same equation when b=13 then |α−β|=
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt
Let x be a real number , Match the following

The correct math is :
Let x be a real number , Match the following

The correct math is :
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt
If α,β,γ are the roots of the equation 5x3−2x−4=0, then α3+β3+γ3=
If α,β,γ are the roots of the equation 5x3−2x−4=0, then α3+β3+γ3=
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt
If the roots of x5−ax4+bx3−cx2+dx−1=0 are all positive such that their arithmetic mean and geometric mean are equal, then a+b+c+d=
If the roots of x5−ax4+bx3−cx2+dx−1=0 are all positive such that their arithmetic mean and geometric mean are equal, then a+b+c+d=
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt
The equation of lowest degree with rational coefficients having roots √3+√2i and √3−√2 is
The equation of lowest degree with rational coefficients having roots √3+√2i and √3−√2 is
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt
The number of non-real roots of the equation x10−3x8+5x6−5x4+3x2−1=0 is
The number of non-real roots of the equation x10−3x8+5x6−5x4+3x2−1=0 is
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt
Let ℕ be the set of positive integers. The number of distinct triplets (x,y,z) satisfying x,y,z∈ℕ,x<y<z and x+y+z=12 is
Let ℕ be the set of positive integers. The number of distinct triplets (x,y,z) satisfying x,y,z∈ℕ,x<y<z and x+y+z=12 is
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt
A question paper has 3 parts and each part contains 4 questions. The number of different ways in which a candidate can answer 8 questions choosing at least two from each part is
A question paper has 3 parts and each part contains 4 questions. The number of different ways in which a candidate can answer 8 questions choosing at least two from each part is
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt
If k is the coefficient of x5 in the expansion of (2x2−‌
1
3x3
)5 then ‌
3k
2
=
If k is the coefficient of x5 in the expansion of (2x2−‌
1
3x3
)5 then ‌
3k
2
=
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt
If ‌
42−13x
x2+x−6
=‌
A
lx+m
+‌
B
px+q
 where lm>0 and pq<0 then ‌
Alp
Bmq
=
If ‌
42−13x
x2+x−6
=‌
A
lx+m
+‌
B
px+q
 where lm>0 and pq<0 then ‌
Alp
Bmq
=
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt
If ‌
3x+5
(x+1)(2x2+3)
=‌
A
x+1
+‌
Bx+C
2x2+3
 and f(x)=Ax3+Bx2+7x+C, then 5C−f′(−2)=
If ‌
3x+5
(x+1)(2x2+3)
=‌
A
x+1
+‌
Bx+C
2x2+3
 and f(x)=Ax3+Bx2+7x+C, then 5C−f′(−2)=
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt
If f(x)=|
−sin‌x2‌sin‌2‌x4cos2x
cos‌x4sin2x2‌sin‌2‌x
0−cos‌xsin‌x
| then f(‌
5π
4
)+f′(‌
5π
4
)=
If f(x)=|
−sin‌x2‌sin‌2‌x4cos2x
cos‌x4sin2x2‌sin‌2‌x
0−cos‌xsin‌x
| then f(‌
5π
4
)+f′(‌
5π
4
)=
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt
If |sin‌α−cos‌α|=‌
3
4
, then |sec‌2‌α−tan‌2‌α|=
If |sin‌α−cos‌α|=‌
3
4
, then |sec‌2‌α−tan‌2‌α|=
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt
If ‌
1
sin‌45∘‌sin‌46∘
+‌
1
sin‌46∘‌sin‌47∘
+... upto 45 terms =‌
1
sin‌x∘
, then sin(‌
π
2
x)=
If ‌
1
sin‌45∘‌sin‌46∘
+‌
1
sin‌46∘‌sin‌47∘
+... upto 45 terms =‌
1
sin‌x∘
, then sin(‌
π
2
x)=
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt
If the minimum value of cos(sinh(log‌x)+cosh(log‌x)) is k, then cosh(k+1)=
If the minimum value of cos(sinh(log‌x)+cosh(log‌x)) is k, then cosh(k+1)=
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt
If sinh‌x=‌
−1
2
 then tanh‌2‌x=
If sinh‌x=‌
−1
2
 then tanh‌2‌x=
Q.26 Correct
Q.26 In-correct
Q.26 Unattempt
If the sides of a triangle ABC whose perimeter is 42 are in arithmetic progression, its circum-radius is ‌
65
8
 and B<A<C then sin‌A=
If the sides of a triangle ABC whose perimeter is 42 are in arithmetic progression, its circum-radius is ‌
65
8
 and B<A<C then sin‌A=
Q.27 Correct
Q.27 In-correct
Q.27 Unattempt
In a triangle ABC, if a=7,c=11,cos‌A=‌
17
22
,cos‌C=‌
1
14
 then b‌tan‌
B
2
‌tan‌
C−A
2
=
In a triangle ABC, if a=7,c=11,cos‌A=‌
17
22
,cos‌C=‌
1
14
 then b‌tan‌
B
2
‌tan‌
C−A
2
=
Q.28 Correct
Q.28 In-correct
Q.28 Unattempt
In any triangle ABC,r2‌cot‌
A
2
‌cot‌
B
2
‌cot‌
C
2
=
In any triangle ABC,r2‌cot‌
A
2
‌cot‌
B
2
‌cot‌
C
2
=
Q.29 Correct
Q.29 In-correct
Q.29 Unattempt
Let the vectors AB=2i+2j+k and AC=2i+4j+4k be two sides of a triangle ABC. If G is the centroid of △ABC, then ‌
27
7
|AG|2+5=
Let the vectors AB=2i+2j+k and AC=2i+4j+4k be two sides of a triangle ABC. If G is the centroid of △ABC, then ‌
27
7
|AG|2+5=
Q.30 Correct
Q.30 In-correct
Q.30 Unattempt
If (α,β,γ) is a triad of real numbers satisfying
i−2j+5k=α(i+j+k)+β(i+2j+3k)+γ(2i−j+k), then α2−β2+γ2=
If (α,β,γ) is a triad of real numbers satisfying
i−2j+5k=α(i+j+k)+β(i+2j+3k)+γ(2i−j+k), then α2−β2+γ2=
Q.31 Correct
Q.31 In-correct
Q.31 Unattempt
Let L be a line passing through a point A and parallel to the vector 2i+j−2k. Let −7i−5j+11k be the position vector of a point P on L such that |AP|=12. Then the position vector of A can be
Let L be a line passing through a point A and parallel to the vector 2i+j−2k. Let −7i−5j+11k be the position vector of a point P on L such that |AP|=12. Then the position vector of A can be
Q.32 Correct
Q.32 In-correct
Q.32 Unattempt
If θ is the angle between the vectors 2i−j+2k and ai+4j+bk and cos‌θ=‌
2
3
 then 2(a+b+3)=
If θ is the angle between the vectors 2i−j+2k and ai+4j+bk and cos‌θ=‌
2
3
 then 2(a+b+3)=
Q.33 Correct
Q.33 In-correct
Q.33 Unattempt
A bisector of the angle between the normals of the planes 4x+3y=5 and x+2y+2z=4 is along the vector
A bisector of the angle between the normals of the planes 4x+3y=5 and x+2y+2z=4 is along the vector
Q.34 Correct
Q.34 In-correct
Q.34 Unattempt
Let the volume of the tetrahedron with vertices i−j−2k,−2i+j−2k,−i−2j+k, 2i+2j+ak be ‌
20
3
. Then the integral value of a is
Let the volume of the tetrahedron with vertices i−j−2k,−2i+j−2k,−i−2j+k, 2i+2j+ak be ‌
20
3
. Then the integral value of a is
Q.35 Correct
Q.35 In-correct
Q.35 Unattempt
The mean deviation from the mean for the observations 1,3,5,7,11,13,17,19,23 is
The mean deviation from the mean for the observations 1,3,5,7,11,13,17,19,23 is
Q.36 Correct
Q.36 In-correct
Q.36 Unattempt
When two dice are thrown, the probability of getting an ordered pair (x,y) such that x2+y2≤25 where x,y are numbers that show up on the two dice, is
When two dice are thrown, the probability of getting an ordered pair (x,y) such that x2+y2≤25 where x,y are numbers that show up on the two dice, is
Q.37 Correct
Q.37 In-correct
Q.37 Unattempt
If two cards are drawn simultaneously from a well shuffled pack of 52 cards, then the probability of getting a card having a prime number and a card having a number which is a multiple of 5 is
If two cards are drawn simultaneously from a well shuffled pack of 52 cards, then the probability of getting a card having a prime number and a card having a number which is a multiple of 5 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)=‌
2
3
,P(B)=‌
4
15
 and P(A∩B)=‌
1
5
, then
√195[P(B∣(A∪B))+P(A∪B)]=
If A and B are two events of a random experiment such that P(A)=‌
2
3
,P(B)=‌
4
15
 and P(A∩B)=‌
1
5
, then
√195[P(B∣(A∪B))+P(A∪B)]=
Q.39 Correct
Q.39 In-correct
Q.39 Unattempt
A random variable X has the range {0,1,2,...}. If P(X=r)=k(1+r)3−r, for r=0,1,2,... where k>0 is a real number, then P(X=0)+P(X=1)+P(X=2)=
A random variable X has the range {0,1,2,...}. If P(X=r)=k(1+r)3−r, for r=0,1,2,... where k>0 is a real number, then P(X=0)+P(X=1)+P(X=2)=
Q.40 Correct
Q.40 In-correct
Q.40 Unattempt
In an experiment a person gets success α times out of β trails. If the experiment consists of n trials, then the probability that he fails at least (n−1) times is
In an experiment a person gets success α times out of β trails. If the experiment consists of n trials, then the probability that he fails at least (n−1) times is
Q.41 Correct
Q.41 In-correct
Q.41 Unattempt
If the distance from a variable point P to a fixed point A(a,0) is equal to the perpendicular distance from P to the line x+y=0 then the equation of the locus of P is
If the distance from a variable point P to a fixed point A(a,0) is equal to the perpendicular distance from P to the line x+y=0 then the equation of the locus of P is
Q.42 Correct
Q.42 In-correct
Q.42 Unattempt
The point to which the origin is to be shifted by translation of axes so that the transformed equation of y2+4y+8x−2=0 will not contain y term and constant term is
The point to which the origin is to be shifted by translation of axes so that the transformed equation of y2+4y+8x−2=0 will not contain y term and constant term is
Q.43 Correct
Q.43 In-correct
Q.43 Unattempt
If the line 2x−y−4=0 divides the line segment joining the points (2,−1) and (1,−4) at the point (a,b) in the ratio m:n then 4(a−b(‌
m
n
)2)=
If the line 2x−y−4=0 divides the line segment joining the points (2,−1) and (1,−4) at the point (a,b) in the ratio m:n then 4(a−b(‌
m
n
)2)=
Q.44 Correct
Q.44 In-correct
Q.44 Unattempt
The distance between the points of concurrency of the two families of straight lines given by x+(5λ+1)y+1−3λ=0 and (5µ+2)x−3y+3+6µ=0 is
The distance between the points of concurrency of the two families of straight lines given by x+(5λ+1)y+1−3λ=0 and (5µ+2)x−3y+3+6µ=0 is
Q.45 Correct
Q.45 In-correct
Q.45 Unattempt
Let the line L drawn perpendicular to the lines 2x−3y+4=0 and 6x−9y+7=0 meet them at A and B respectively. If P(1,1) is a point on L, then the ratio in which P divides AB is
Let the line L drawn perpendicular to the lines 2x−3y+4=0 and 6x−9y+7=0 meet them at A and B respectively. If P(1,1) is a point on L, then the ratio in which P divides AB is
Q.46 Correct
Q.46 In-correct
Q.46 Unattempt
The orthocentre of the triangle formed by the points (1,3),(−3,5) and (5,−1) is
The orthocentre of the triangle formed by the points (1,3),(−3,5) and (5,−1) is
Q.47 Correct
Q.47 In-correct
Q.47 Unattempt
If αx2+2γxy+βy2=0 is the equation of pair of lines passing through the origin and perpendicular to the pair of lines bhx2+abxy+ahy2=0(a≠0,b≠0), then ‌
αβ
γ2
=
If αx2+2γxy+βy2=0 is the equation of pair of lines passing through the origin and perpendicular to the pair of lines bhx2+abxy+ahy2=0(a≠0,b≠0), then ‌
αβ
γ2
=
Q.48 Correct
Q.48 In-correct
Q.48 Unattempt
‌
x2
a
+‌
xy
h
+‌
y2
b
=0(a≠0,h≠0,b≠0) represents two coincident lines if
‌
x2
a
+‌
xy
h
+‌
y2
b
=0(a≠0,h≠0,b≠0) represents two coincident lines if
Q.49 Correct
Q.49 In-correct
Q.49 Unattempt
If the lines joining the origin to the points of intersection of the line x+y=k and the curve x2+y2−2x−4y+2=0 are at right angles then the sum of all the possible values of k is
If the lines joining the origin to the points of intersection of the line x+y=k and the curve x2+y2−2x−4y+2=0 are at right angles then the sum of all the possible values of k is
Q.50 Correct
Q.50 In-correct
Q.50 Unattempt
The equation of the incircle of the triangle formed by the lines x=0,y=0 and 3x+4y−24=0 is
The equation of the incircle of the triangle formed by the lines x=0,y=0 and 3x+4y−24=0 is
Q.51 Correct
Q.51 In-correct
Q.51 Unattempt
If two tangents are drawn from the point P(‌
π
4
) on the circle x2+y2=4 to the circle x2+y2=1 then the slopes of the tangents are
If two tangents are drawn from the point P(‌
π
4
) on the circle x2+y2=4 to the circle x2+y2=1 then the slopes of the tangents are
Q.52 Correct
Q.52 In-correct
Q.52 Unattempt
If 5x+6y−34=0 and 2x+y+c=0 are conjugate lines with respect to the circle x2+y2−8x−10y+25=0 then the point on the line 2x+y+c=0 is
If 5x+6y−34=0 and 2x+y+c=0 are conjugate lines with respect to the circle x2+y2−8x−10y+25=0 then the point on the line 2x+y+c=0 is
Q.53 Correct
Q.53 In-correct
Q.53 Unattempt
If C1 and C2 are the centres of similitude with respect to the circles x2+y2+6x+8y+24=0 and x2+y2−6x−8y+9=0 then C1C2=
If C1 and C2 are the centres of similitude with respect to the circles x2+y2+6x+8y+24=0 and x2+y2−6x−8y+9=0 then C1C2=
Q.54 Correct
Q.54 In-correct
Q.54 Unattempt
Let x+y=0 be the radical axis of the circles S≡x2+y2+2gx+2fy+c=0 and S1≡x2+y2−6x−4y+4=0 and the radius of the circle S=0 be 1 . The g+f=
Let x+y=0 be the radical axis of the circles S≡x2+y2+2gx+2fy+c=0 and S1≡x2+y2−6x−4y+4=0 and the radius of the circle S=0 be 1 . The g+f=
Q.55 Correct
Q.55 In-correct
Q.55 Unattempt
The radius of the circle which cuts all the three circles x2+y2−4x−4y+3=0, x2+y2+4x−4y+3=0 and x2+y2+4x+4y+3=0 orthogonally is
The radius of the circle which cuts all the three circles x2+y2−4x−4y+3=0, x2+y2+4x−4y+3=0 and x2+y2+4x+4y+3=0 orthogonally is
Q.56 Correct
Q.56 In-correct
Q.56 Unattempt
Statement I : 4x2+y2−4xy−30x−50y+40=0 is the equation of parabola having (2,3) as its focus and x+2y+5=0 as its directrix.
Statement II : The equation of the directrix of the parabola x2−4x+16y+52=0 is y+1=0.
Which of the above statements is (are) true?
Statement I : 4x2+y2−4xy−30x−50y+40=0 is the equation of parabola having (2,3) as its focus and x+2y+5=0 as its directrix.
Statement II : The equation of the directrix of the parabola x2−4x+16y+52=0 is y+1=0.
Which of the above statements is (are) true?
Q.57 Correct
Q.57 In-correct
Q.57 Unattempt
The cartesian equation of the parabola x=−2+2t2,y=2+4t is
The cartesian equation of the parabola x=−2+2t2,y=2+4t is
Q.58 Correct
Q.58 In-correct
Q.58 Unattempt
If ax2+by2=15 is the equation of the ellipse for which distance between its foci is 2 and distance between its directrices is 5 , then a+b=
If ax2+by2=15 is the equation of the ellipse for which distance between its foci is 2 and distance between its directrices is 5 , then a+b=
Q.59 Correct
Q.59 In-correct
Q.59 Unattempt
Assertion( A ) : The image of ‌
x2
25
+‌
y2
16
=1 in the line x+y=10 is ‌
(x−10)2
16
+‌
(y−10)2
25
=1.
Reason(R) : The image of a curve ' C ' in a line L is the locus of the image of every point of C with respect to the line L.
The correct option among the following is:
Assertion( A ) : The image of ‌
x2
25
+‌
y2
16
=1 in the line x+y=10 is ‌
(x−10)2
16
+‌
(y−10)2
25
=1.
Reason(R) : The image of a curve ' C ' in a line L is the locus of the image of every point of C with respect to the line L.
The correct option among the following is:
Q.60 Correct
Q.60 In-correct
Q.60 Unattempt
If the latus rectum of a hyperbola subtends an angle of 120∘ at its centre, then its eccentricity is
If the latus rectum of a hyperbola subtends an angle of 120∘ at its centre, then its eccentricity is
Q.61 Correct
Q.61 In-correct
Q.61 Unattempt
Let P(‌
π
4
),Q(‌
5π
4
),R(‌
3π
4
),T(‌
7π
4
) be the points on the hyperbola x2−4y2−4=0 in the parametric form. Then the area of the quadrilateral PQRT is (in square units)
Let P(‌
π
4
),Q(‌
5π
4
),R(‌
3π
4
),T(‌
7π
4
) be the points on the hyperbola x2−4y2−4=0 in the parametric form. Then the area of the quadrilateral PQRT is (in square units)
Q.62 Correct
Q.62 In-correct
Q.62 Unattempt
If A(1,2,3),B(2,−3,1),C(3,2,−1) are three vertices of a tetrahedron ABCD and G(‌
5
2
,‌
3
2
,‌
9
4
) is its centroid then the point which divides GD in the ratio 1:2 is
If A(1,2,3),B(2,−3,1),C(3,2,−1) are three vertices of a tetrahedron ABCD and G(‌
5
2
,‌
3
2
,‌
9
4
) is its centroid then the point which divides GD in the ratio 1:2 is
Q.63 Correct
Q.63 In-correct
Q.63 Unattempt
Let D be the foot of the perpendicular drawn from the point A(2,0,3) to the line joining the points B(0,4,1) and C(−2,0,4). Then the ratio in which D divides BC is
Let D be the foot of the perpendicular drawn from the point A(2,0,3) to the line joining the points B(0,4,1) and C(−2,0,4). Then the ratio in which D divides BC is
Q.64 Correct
Q.64 In-correct
Q.64 Unattempt
Let 6x−3y+2z−6=0 be the given plane. If a,b,c are the intercepts made by the plane on X, Y, Z - axes respectively; l,m,n are the direction cosines of a normal drawn to the plane and p is the perpendicular distance from the origin to the plane, then |al+bm+cn|=
Let 6x−3y+2z−6=0 be the given plane. If a,b,c are the intercepts made by the plane on X, Y, Z - axes respectively; l,m,n are the direction cosines of a normal drawn to the plane and p is the perpendicular distance from the origin to the plane, then |al+bm+cn|=
Q.65 Correct
Q.65 In-correct
Q.65 Unattempt
lim
x→0
‌
tan2(πsec4x)
π2x4
=
lim
x→0
‌
tan2(πsec4x)
π2x4
=
Q.66 Correct
Q.66 In-correct
Q.66 Unattempt
lim
x→0
(‌
4!
x8
(1−cos‌
x2
3
−cos‌
x2
4
+cos‌
x2
3
‌cos‌
x2
4
))=
lim
x→0
(‌
4!
x8
(1−cos‌
x2
3
−cos‌
x2
4
+cos‌
x2
3
‌cos‌
x2
4
))=
Q.67 Correct
Q.67 In-correct
Q.67 Unattempt
Let f(x)=sin‌x,g(x)=cos‌x,h(x)=x2 then
lim
x→1
‌
f(g(h(x)))−f(g(h(1)))
x−1
=
Let f(x)=sin‌x,g(x)=cos‌x,h(x)=x2 then
lim
x→1
‌
f(g(h(x)))−f(g(h(1)))
x−1
=
Q.68 Correct
Q.68 In-correct
Q.68 Unattempt
If x‌cos(k+y)=cos‌y then ‌
dy
dx
 at y=‌
π
2
 is
If x‌cos(k+y)=cos‌y then ‌
dy
dx
 at y=‌
π
2
 is
Q.69 Correct
Q.69 In-correct
Q.69 Unattempt
If x=a(cos‌θ+θ‌sin‌θ),y=f(θ),f(2π)=0,‌
dy
dx
=‌
tan‌θ
θ
,θ≠0 and θ≠(2n+1)‌
π
2
, then f(‌
π
3
)=
If x=a(cos‌θ+θ‌sin‌θ),y=f(θ),f(2π)=0,‌
dy
dx
=‌
tan‌θ
θ
,θ≠0 and θ≠(2n+1)‌
π
2
, then f(‌
π
3
)=
Q.70 Correct
Q.70 In-correct
Q.70 Unattempt
The equation of the normal to the curve 4x2+9y2=36 at the point P(‌
7π
4
)
The equation of the normal to the curve 4x2+9y2=36 at the point P(‌
7π
4
)
Q.71 Correct
Q.71 In-correct
Q.71 Unattempt
If θ is the acute angle between the curves x2+y2=4 and y2=3x then tan‌θ=
If θ is the acute angle between the curves x2+y2=4 and y2=3x then tan‌θ=
Q.72 Correct
Q.72 In-correct
Q.72 Unattempt
Let √3 be the radius and ‌
π
3
 be the semivertical angle of the given cone. Then the height of the right circular cylinder of maximum volume that can be inscribed in the given cone is
Let √3 be the radius and ‌
π
3
 be the semivertical angle of the given cone. Then the height of the right circular cylinder of maximum volume that can be inscribed in the given cone is
Q.73 Correct
Q.73 In-correct
Q.73 Unattempt
Given that ‌
d
dx
(Tan−1x)=‌
1
1+x2
 and ‌
d
dx
(Sinh−1x)=‌
1
√1+x2
. Then ∫‌
3x6−2x4+x2−2
x2+1
dx=
Given that ‌
d
dx
(Tan−1x)=‌
1
1+x2
 and ‌
d
dx
(Sinh−1x)=‌
1
√1+x2
. Then ∫‌
3x6−2x4+x2−2
x2+1
dx=
Q.74 Correct
Q.74 In-correct
Q.74 Unattempt
∫‌
sin‌x⋅sec2x−tan‌x⋅sin‌x+cos‌x
(1−cos‌2‌x)
dx=
∫‌
sin‌x⋅sec2x−tan‌x⋅sin‌x+cos‌x
(1−cos‌2‌x)
dx=
Q.75 Correct
Q.75 In-correct
Q.75 Unattempt
If f(x)=∫‌
16x7+5x10
(x3+2+3x8)2
dx(x≥0) and f(0)=1, then the value of f(−1) is
If f(x)=∫‌
16x7+5x10
(x3+2+3x8)2
dx(x≥0) and f(0)=1, then the value of f(−1) is
Q.76 Correct
Q.76 In-correct
Q.76 Unattempt
It is given that ‌
d
dt
(t‌log‌t−t)=log‌t then exp(
1
∫
0
2x‌log(1+x2)‌d‌x)=
It is given that ‌
d
dt
(t‌log‌t−t)=log‌t then exp(
1
∫
0
2x‌log(1+x2)‌d‌x)=
Q.77 Correct
Q.77 In-correct
Q.77 Unattempt
2a
∫
0
f(x)dx=
2a
∫
0
f(x)dx=
Q.78 Correct
Q.78 In-correct
Q.78 Unattempt
The equation of any member of the family of all the ellipses whose axes are along the coordinate axes satisfies the differential equation
The equation of any member of the family of all the ellipses whose axes are along the coordinate axes satisfies the differential equation
Q.79 Correct
Q.79 In-correct
Q.79 Unattempt
The degree of the differential equation (‌
d2y
dx2
)‌
4
3
+x(‌
dy
dx
)2−y‌cos(‌
dy
dx
)=0 is
The degree of the differential equation (‌
d2y
dx2
)‌
4
3
+x(‌
dy
dx
)2−y‌cos(‌
dy
dx
)=0 is
Q.80 Correct
Q.80 In-correct
Q.80 Unattempt
The general solution of the differential equation ‌
dy
dx
=‌
2x−3y+5
6x−9y+7
 is
The general solution of the differential equation ‌
dy
dx
=‌
2x−3y+5
6x−9y+7
 is
Q.81 Correct
Q.81 In-correct
Q.81 Unattempt
Two charged particles of mass 1gm each are placed 1m apart. If each of these possesses 1 femto coulomb of charge, then the dominant force of interaction between them is
Two charged particles of mass 1gm each are placed 1m apart. If each of these possesses 1 femto coulomb of charge, then the dominant force of interaction between them is
Q.82 Correct
Q.82 In-correct
Q.82 Unattempt
A physical quantity S is related to four observables a,b,c,d as S=‌
√ab
c3d4
. If the percentage errors of measurement in a, b, c, d are 2%,1%,1% and 1% respectively, then percentage error in the quantity S is
A physical quantity S is related to four observables a,b,c,d as S=‌
√ab
c3d4
. If the percentage errors of measurement in a, b, c, d are 2%,1%,1% and 1% respectively, then percentage error in the quantity S is
Q.83 Correct
Q.83 In-correct
Q.83 Unattempt
A particle moves along a straight line such that its displacement ' x ' varies with time ' t ' as x=αt3+βt2+γ, where α,β,γ are constants. V1 is the average velocity of the particle during its journey between t=1s and t=3s. V2 is the instantaneous velocity of the particle at t=3s. The ratio ‌
V1
V2
 is
A particle moves along a straight line such that its displacement ' x ' varies with time ' t ' as x=αt3+βt2+γ, where α,β,γ are constants. V1 is the average velocity of the particle during its journey between t=1s and t=3s. V2 is the instantaneous velocity of the particle at t=3s. The ratio ‌
V1
V2
 is
Q.84 Correct
Q.84 In-correct
Q.84 Unattempt
A man walking along a straight line with a velocity 6km∕h encounters rain falling vertically down with a velocity 6√3km∕h. At what angle the man should hold his umbrella so that he can protect himself from rain
A man walking along a straight line with a velocity 6km∕h encounters rain falling vertically down with a velocity 6√3km∕h. At what angle the man should hold his umbrella so that he can protect himself from rain
Q.85 Correct
Q.85 In-correct
Q.85 Unattempt
An aircraft is flying at a height of ' H ' above the ground and at a speed of ' V '. The maximum angle subtended at a ground observation point by the aircraft after time T is
An aircraft is flying at a height of ' H ' above the ground and at a speed of ' V '. The maximum angle subtended at a ground observation point by the aircraft after time T is
Q.86 Correct
Q.86 In-correct
Q.86 Unattempt
A merry - go - round rotating at a constant angular speed completes 9 rotations in 18 seconds. What is its angular speed?
A merry - go - round rotating at a constant angular speed completes 9 rotations in 18 seconds. What is its angular speed?
Q.87 Correct
Q.87 In-correct
Q.87 Unattempt
A motor car moving with velocity 7m∕s stops in 10m distance when brakes are applied. What is the relation between the resistance force (R) and the weight (W) of the car? (Take value of g=9.8m∕s2 )
A motor car moving with velocity 7m∕s stops in 10m distance when brakes are applied. What is the relation between the resistance force (R) and the weight (W) of the car? (Take value of g=9.8m∕s2 )
Q.88 Correct
Q.88 In-correct
Q.88 Unattempt
A ball of mass 1kg moves in a straight line with velocity v=cxα, where c=1 (SI unit) and α is a constant. If the work done by the net force during its displacement from x=0 to x=4m is 128J, then the α is
A ball of mass 1kg moves in a straight line with velocity v=cxα, where c=1 (SI unit) and α is a constant. If the work done by the net force during its displacement from x=0 to x=4m is 128J, then the α is
Q.89 Correct
Q.89 In-correct
Q.89 Unattempt
Assertion(A): In an elastic collision of two billiard balls, both kinetic energy and linear momentum remain conserved.
Reason (R): During the collision of the balls, as the collision is elastic there is no exchange of energy. Therefore, both energy and momentum are conserved.
The correct option among the following is
Assertion(A): In an elastic collision of two billiard balls, both kinetic energy and linear momentum remain conserved.
Reason (R): During the collision of the balls, as the collision is elastic there is no exchange of energy. Therefore, both energy and momentum are conserved.
The correct option among the following is
Q.90 Correct
Q.90 In-correct
Q.90 Unattempt
A wheel of radius with 0.5m and a moment of inertia of 10kg⋅m2 is rotating freely at an angular speed of 70rev∕min. The wheel can be stopped in 5.0s by pressing a wet cloth against the rim and exerting a radially inward force of 88N. The coefficient of kinetic friction between the wheel and wet cloth is
A wheel of radius with 0.5m and a moment of inertia of 10kg⋅m2 is rotating freely at an angular speed of 70rev∕min. The wheel can be stopped in 5.0s by pressing a wet cloth against the rim and exerting a radially inward force of 88N. The coefficient of kinetic friction between the wheel and wet cloth is
Q.91 Correct
Q.91 In-correct
Q.91 Unattempt
A simple pendulum of length 1m and having a bob of mass 100g is suspended in a car, moving on a circular track of radius 100m with uniform speed 10m∕s. If the pendulum makes small oscillation in a radial direction about its equilibrium position, then its time period can be given by T=2π∕α1∕4. The value of α is
[ Take g=10m∕s2]
A simple pendulum of length 1m and having a bob of mass 100g is suspended in a car, moving on a circular track of radius 100m with uniform speed 10m∕s. If the pendulum makes small oscillation in a radial direction about its equilibrium position, then its time period can be given by T=2π∕α1∕4. The value of α is
[ Take g=10m∕s2]
Q.92 Correct
Q.92 In-correct
Q.92 Unattempt
A uniform sphere A with radius R exerts a force F on a small particle B situated at a distance 2R from the centre of the sphere. A spherical portion of diameter R is cut from the sphere A as shown in the figure. If F′ is the new gravitational force between the remaining part of the sphere A and the particle B then the correct relation between F and F′
A uniform sphere A with radius R exerts a force F on a small particle B situated at a distance 2R from the centre of the sphere. A spherical portion of diameter R is cut from the sphere A as shown in the figure. If F′ is the new gravitational force between the remaining part of the sphere A and the particle B then the correct relation between F and F′
Q.93 Correct
Q.93 In-correct
Q.93 Unattempt
An object of mass 15kg is attached to the end of a metal wire of unstretched length 1.0m. The object is then whirled in a vertical circle with an angular velocity of 4rad∕s at the bottom of the circle. If the cross sectional area of the wire is 0.05cm2 and Young's modulus of metal is 2×1011N∕m2, then the elongation of the wire when the mass is at the lowest point of its path
(Take g=10m∕s2 )
An object of mass 15kg is attached to the end of a metal wire of unstretched length 1.0m. The object is then whirled in a vertical circle with an angular velocity of 4rad∕s at the bottom of the circle. If the cross sectional area of the wire is 0.05cm2 and Young's modulus of metal is 2×1011N∕m2, then the elongation of the wire when the mass is at the lowest point of its path
(Take g=10m∕s2 )
Q.94 Correct
Q.94 In-correct
Q.94 Unattempt
In the figure, the chamber A contains a gas, movable chamber B is placed on the top of the gas and it contains n metal balls. The weight of chamber B is supported by the gas. Chamber C has vacuum. Let the gas be in equilibrium at pressure P. Let P′ be the pressure if one of the balls is taken away. Find (P−P′)∕P.

In the figure, the chamber A contains a gas, movable chamber B is placed on the top of the gas and it contains n metal balls. The weight of chamber B is supported by the gas. Chamber C has vacuum. Let the gas be in equilibrium at pressure P. Let P′ be the pressure if one of the balls is taken away. Find (P−P′)∕P.

Q.95 Correct
Q.95 In-correct
Q.95 Unattempt
A liquid flows steadily through a cylindrical pipe having a radius 2R at a point A and radius R at point B farther along the flow direction. If the velocity at point B is 4v, what will be the velocity at point A ?
A liquid flows steadily through a cylindrical pipe having a radius 2R at a point A and radius R at point B farther along the flow direction. If the velocity at point B is 4v, what will be the velocity at point A ?
Q.96 Correct
Q.96 In-correct
Q.96 Unattempt
A piece of metal has a weight of 49gm in air and 39gm in a liquid of density 1.2×103kg∕m3kept at 32‌∘C. When the temperature of the liquid is raised to 42‌∘C the metal piece has a weight of 40gm. If the density of the liquid at 42∘C is 1.0×103kg∕m3, then the coefficient of linear expansion of the metal is
A piece of metal has a weight of 49gm in air and 39gm in a liquid of density 1.2×103kg∕m3kept at 32‌∘C. When the temperature of the liquid is raised to 42‌∘C the metal piece has a weight of 40gm. If the density of the liquid at 42∘C is 1.0×103kg∕m3, then the coefficient of linear expansion of the metal is
Q.97 Correct
Q.97 In-correct
Q.97 Unattempt
A metal cooking pot has a base area of 0.2m2 and thickness 2.0cm. It boils water at a rate of 3.0kg∕min when placed on a hot plate. The temperature of the part of the hot plate in contact with the pot is approximately
[Thermal conductivity of metal is 120Js−1m−1K−1, heat of vaporisation of water is 2×106J∕kg]
A metal cooking pot has a base area of 0.2m2 and thickness 2.0cm. It boils water at a rate of 3.0kg∕min when placed on a hot plate. The temperature of the part of the hot plate in contact with the pot is approximately
[Thermal conductivity of metal is 120Js−1m−1K−1, heat of vaporisation of water is 2×106J∕kg]
Q.98 Correct
Q.98 In-correct
Q.98 Unattempt
A quantity of monoatomic gas undergoes a process in which pressure is changed linearly with volume. The pressure and volume are changed from initial value (Po,Vo) to final value (3Po,3Vo). The heat absorbed by the gas during the process is
A quantity of monoatomic gas undergoes a process in which pressure is changed linearly with volume. The pressure and volume are changed from initial value (Po,Vo) to final value (3Po,3Vo). The heat absorbed by the gas during the process is
Q.99 Correct
Q.99 In-correct
Q.99 Unattempt
An ideal gas having initial pressure P, volume V and temperature T is allowed to expand adiabatically until its volume becomes 4V, while its temperature falls to ‌
T
2
. If the work done by the gas during the expansion is αPV, the value of α is
An ideal gas having initial pressure P, volume V and temperature T is allowed to expand adiabatically until its volume becomes 4V, while its temperature falls to ‌
T
2
. If the work done by the gas during the expansion is αPV, the value of α is
Q.100 Correct
Q.100 In-correct
Q.100 Unattempt
At what temperature, an oxygen molecule has the same r.m.s velocity as the hydrogen molecule has at 20K ?
At what temperature, an oxygen molecule has the same r.m.s velocity as the hydrogen molecule has at 20K ?
Q.101 Correct
Q.101 In-correct
Q.101 Unattempt
Two strings A and B produce beat of frequency ∆f1>0. The tension in string A is slightly increased and the beat frequency is found to be ∆f2>0. If the original frequency of A is f0 and ∆f2<∆f1, then the frequency of B is
Two strings A and B produce beat of frequency ∆f1>0. The tension in string A is slightly increased and the beat frequency is found to be ∆f2>0. If the original frequency of A is f0 and ∆f2<∆f1, then the frequency of B is
Q.102 Correct
Q.102 In-correct
Q.102 Unattempt
A light ray travels from a medium with refractive index n1 to another medium of refractive index n2. If n1=2 and n2=√3, then find the critical angle.
A light ray travels from a medium with refractive index n1 to another medium of refractive index n2. If n1=2 and n2=√3, then find the critical angle.
Q.103 Correct
Q.103 In-correct
Q.103 Unattempt
In Young's double slit experiment for what order does the wavelength of red light (λ=780nm) coincide with (m+1)‌th ‌ order of blue light (λ=520nm)
In Young's double slit experiment for what order does the wavelength of red light (λ=780nm) coincide with (m+1)‌th ‌ order of blue light (λ=520nm)
Q.104 Correct
Q.104 In-correct
Q.104 Unattempt
Three charges are arranged on the vertices of a right angle triangle as shown in the figure. The magnitude of dipole moment of the combination in the unit of C−cm is
Three charges are arranged on the vertices of a right angle triangle as shown in the figure. The magnitude of dipole moment of the combination in the unit of C−cm is
Q.105 Correct
Q.105 In-correct
Q.105 Unattempt
A parallel - plate capacitor of plate area 10cm2 and plate separation 3mm is charged to a potential difference 12V and then the battery is disconnected. A slab of dielectric constant 3 is then inserted between the plates. The work done on the system in the process of inserting the slab is αε0. The value of α is
(Take ε0 as the permittivity of free space)
A parallel - plate capacitor of plate area 10cm2 and plate separation 3mm is charged to a potential difference 12V and then the battery is disconnected. A slab of dielectric constant 3 is then inserted between the plates. The work done on the system in the process of inserting the slab is αε0. The value of α is
(Take ε0 as the permittivity of free space)
Q.106 Correct
Q.106 In-correct
Q.106 Unattempt
A metal has 9×1028 conduction electrons per m3 and its resistivity is 1×10−8Ωm. If the drift speed of an electron in the metal is 1.6×106m∕s then its mean free path is ( mass of electron =9×10−31kg and charge of electron =1.6×10−19C )
A metal has 9×1028 conduction electrons per m3 and its resistivity is 1×10−8Ωm. If the drift speed of an electron in the metal is 1.6×106m∕s then its mean free path is ( mass of electron =9×10−31kg and charge of electron =1.6×10−19C )
Q.107 Correct
Q.107 In-correct
Q.107 Unattempt
The resistivity of a metal is 1×10−8Ωm. If it contains 9×1028 electrons per m3 then the relaxation time of electrons inside the metal is nearly ( electron mass =9×10−31kg)
The resistivity of a metal is 1×10−8Ωm. If it contains 9×1028 electrons per m3 then the relaxation time of electrons inside the metal is nearly ( electron mass =9×10−31kg)
Q.108 Correct
Q.108 In-correct
Q.108 Unattempt
A particle of mass m and charge q travelling with a velocity v along the x - axis enters a uniform electric field
→
E
 directed along the y - axis. What will be the trajectory of the particle?
A particle of mass m and charge q travelling with a velocity v along the x - axis enters a uniform electric field
→
E
 directed along the y - axis. What will be the trajectory of the particle?
Q.109 Correct
Q.109 In-correct
Q.109 Unattempt
A long solenoid with 10.0 turn ∕cm and a radius of 8cm carries a current of 7mA. A current carrying straight conductor is located along the central axis of the solenoid. If the direction of resulting magnetic field is 60∘ to axial direction at a point 5cm from the axis of the solenoid along the radial direction, then the current in the conductor is [Take √2=1.4,√3=1.7]
A long solenoid with 10.0 turn ∕cm and a radius of 8cm carries a current of 7mA. A current carrying straight conductor is located along the central axis of the solenoid. If the direction of resulting magnetic field is 60∘ to axial direction at a point 5cm from the axis of the solenoid along the radial direction, then the current in the conductor is [Take √2=1.4,√3=1.7]
Q.110 Correct
Q.110 In-correct
Q.110 Unattempt
A thin magnetic needle is placed in a magnetic field of 200G with its axis at 30∘ to the direction of the field. Find the magnetic moment of the needle if it experiences a torque of 0.012Nm in this field.
A thin magnetic needle is placed in a magnetic field of 200G with its axis at 30∘ to the direction of the field. Find the magnetic moment of the needle if it experiences a torque of 0.012Nm in this field.
Q.111 Correct
Q.111 In-correct
Q.111 Unattempt
A wire loop of area 0.2m2 has a resistance of 20Ω. A magnetic field pointing normal to the loop has a magnitude of 0.25T and is reduced to zero at a uniform rate in 10−4sec. What is induced emf and resulting current?
A wire loop of area 0.2m2 has a resistance of 20Ω. A magnetic field pointing normal to the loop has a magnitude of 0.25T and is reduced to zero at a uniform rate in 10−4sec. What is induced emf and resulting current?
Q.112 Correct
Q.112 In-correct
Q.112 Unattempt
A resistor of resistance of 100Ω is connected to an AC source ε=10‌sin(250πs−1)‌t. The energy dissipated as heat during t=0 to t=1ms is approximately.
A resistor of resistance of 100Ω is connected to an AC source ε=10‌sin(250πs−1)‌t. The energy dissipated as heat during t=0 to t=1ms is approximately.
Q.113 Correct
Q.113 In-correct
Q.113 Unattempt
About 20% of the power of a 100W bulb is converted to visible radiation. Assuming that the radiation is emitted isotropically and neglecting reflection, the average intensity of visible radiation at a distance of 5m is ‌
α
25π
W∕m2. The value of α is
About 20% of the power of a 100W bulb is converted to visible radiation. Assuming that the radiation is emitted isotropically and neglecting reflection, the average intensity of visible radiation at a distance of 5m is ‌
α
25π
W∕m2. The value of α is
Q.114 Correct
Q.114 In-correct
Q.114 Unattempt
Light strikes a metal surface causing photoelectric emission. The wavelength of incident light is 248nm. If the stopping potential for the ejected electrons is 2.8eV, then the work function of the metal is
(Take hc =1240eV.nm)
Light strikes a metal surface causing photoelectric emission. The wavelength of incident light is 248nm. If the stopping potential for the ejected electrons is 2.8eV, then the work function of the metal is
(Take hc =1240eV.nm)
Q.115 Correct
Q.115 In-correct
Q.115 Unattempt
The de-Broglie wavelength associated with an electron, accelerated through a potential difference of 121 volts is about:
[Take Plank's constant =h=6.6×10−34J⋅s, mass of electron 9×10−31kg ]
The de-Broglie wavelength associated with an electron, accelerated through a potential difference of 121 volts is about:
[Take Plank's constant =h=6.6×10−34J⋅s, mass of electron 9×10−31kg ]
Q.116 Correct
Q.116 In-correct
Q.116 Unattempt
The difference in the wavelength between the maximum and minimum of Balmer series [Use RH=1×107m−1 ]
The difference in the wavelength between the maximum and minimum of Balmer series [Use RH=1×107m−1 ]
Q.117 Correct
Q.117 In-correct
Q.117 Unattempt
The radius and mass number of nucleus ' 1 ' is R1 and A1 respectively. The radius and mass number of nucleus ' 2 ' is R2 and A2 respectively. If A2 is larger than A1 by 2%, then R2 is larger than R1 by
The radius and mass number of nucleus ' 1 ' is R1 and A1 respectively. The radius and mass number of nucleus ' 2 ' is R2 and A2 respectively. If A2 is larger than A1 by 2%, then R2 is larger than R1 by
Q.118 Correct
Q.118 In-correct
Q.118 Unattempt
Current I through a given p−n junction when a voltage V is applied across it is given to be I=I0(e‌
V
2VT
−1) where I0 and VT are constants. If rd(I) is the dynamic resistance of the junction, then rd(1000I0)=αrd(10I0), where α is approximately equal to
Current I through a given p−n junction when a voltage V is applied across it is given to be I=I0(e‌
V
2VT
−1) where I0 and VT are constants. If rd(I) is the dynamic resistance of the junction, then rd(1000I0)=αrd(10I0), where α is approximately equal to
Q.119 Correct
Q.119 In-correct
Q.119 Unattempt
For an n-p-n transistor structure which of the following statements is NOT true?
For an n-p-n transistor structure which of the following statements is NOT true?
Q.120 Correct
Q.120 In-correct
Q.120 Unattempt
The range of frequency bands used for standard AM broadcast is
The range of frequency bands used for standard AM broadcast is
Q.121 Correct
Q.121 In-correct
Q.121 Unattempt
If the uncertainty in velocity is ‌
1
2m
√‌
h
π
, then the ratio of uncertainty in position and momentum is
If the uncertainty in velocity is ‌
1
2m
√‌
h
π
, then the ratio of uncertainty in position and momentum is
Q.122 Correct
Q.122 In-correct
Q.122 Unattempt
The valency shell electronic configuration of Cr and Cu atoms, respectively, are
The valency shell electronic configuration of Cr and Cu atoms, respectively, are
Q.123 Correct
Q.123 In-correct
Q.123 Unattempt
Identify all the correct statements for Lanthanide contraction.
a) The covalent properties of the Lanthanide metal hydroxides increases from La to Lu.
b) The chemical reactivity decreases from La to Lu.
c) La(OH)3 is more basic than Lu(OH)3.
d) Zr and Hf have about the same radius.
e) Separation of Lanthanides from one another is easy,
Identify all the correct statements for Lanthanide contraction.
a) The covalent properties of the Lanthanide metal hydroxides increases from La to Lu.
b) The chemical reactivity decreases from La to Lu.
c) La(OH)3 is more basic than Lu(OH)3.
d) Zr and Hf have about the same radius.
e) Separation of Lanthanides from one another is easy,
Q.124 Correct
Q.124 In-correct
Q.124 Unattempt
The correct order of the electron gain enthalpy of the given elements is
The correct order of the electron gain enthalpy of the given elements is
Q.125 Correct
Q.125 In-correct
Q.125 Unattempt
The correct pair of species with (A) the highest bond order and (B) diamagnetic character is
The correct pair of species with (A) the highest bond order and (B) diamagnetic character is
Q.126 Correct
Q.126 In-correct
Q.126 Unattempt
The incomplete Lewis representation of CO32− is given below. The formal charge on atoms marked as a, b, and c, respectively, are
The incomplete Lewis representation of CO32− is given below. The formal charge on atoms marked as a, b, and c, respectively, are
Q.127 Correct
Q.127 In-correct
Q.127 Unattempt
A plot of the compressibility factor (z) vs P is shown below for H2,He,N2,CO2 and SO2. Identify the plot for CO2 gas.

A plot of the compressibility factor (z) vs P is shown below for H2,He,N2,CO2 and SO2. Identify the plot for CO2 gas.

Q.128 Correct
Q.128 In-correct
Q.128 Unattempt
The average molecular weight of the air which has 21% of O2 and 79% of N2, is
The average molecular weight of the air which has 21% of O2 and 79% of N2, is
Q.129 Correct
Q.129 In-correct
Q.129 Unattempt
The number of significant figures in 2.0400 is
The number of significant figures in 2.0400 is
Q.130 Correct
Q.130 In-correct
Q.130 Unattempt
Identify the values of a,b,c,d and e for the following unbalanced reaction
aKNO3+5C12H22O11⟶bN2+cCO2+dH2O+eK2CO3
Identify the values of a,b,c,d and e for the following unbalanced reaction
aKNO3+5C12H22O11⟶bN2+cCO2+dH2O+eK2CO3
Q.131 Correct
Q.131 In-correct
Q.131 Unattempt
Given H2(g)+‌
1
2
O2(g)→H2O(l);∆H=−285kJ
N2O5(g)+H2O(l)→2HNO3(l);∆H=−76.6kJ
N2(g)+3O2(g)+H2(g)→2HNO3(l);∆H=−348.2kJ
Calculatethe ∆H of 2N2(g)+5O2(g)→2N2O5(g).
Given H2(g)+‌
1
2
O2(g)→H2O(l);∆H=−285kJ
N2O5(g)+H2O(l)→2HNO3(l);∆H=−76.6kJ
N2(g)+3O2(g)+H2(g)→2HNO3(l);∆H=−348.2kJ
Calculatethe ∆H of 2N2(g)+5O2(g)→2N2O5(g).
Q.132 Correct
Q.132 In-correct
Q.132 Unattempt
In which of the following reactions at equilibria, the position of the equilibrium shifts towards the products, if the total pressure is increased?
(i) X2(g)+3Y2(g)⇌2XY3(g)
(ii) ‌‌X2(g)+Y2(g)⇌2XY(g)
(iii) X2(g)+Z2(g)⇌2XZ(g)
(iv) ‌‌X2(g)+Y4(g)⇌2XY2(g)
In which of the following reactions at equilibria, the position of the equilibrium shifts towards the products, if the total pressure is increased?
(i) X2(g)+3Y2(g)⇌2XY3(g)
(ii) ‌‌X2(g)+Y2(g)⇌2XY(g)
(iii) X2(g)+Z2(g)⇌2XZ(g)
(iv) ‌‌X2(g)+Y4(g)⇌2XY2(g)
Q.133 Correct
Q.133 In-correct
Q.133 Unattempt
Phosphorous and phosphoric acids are, respectively, acids.
Phosphorous and phosphoric acids are, respectively, acids.
Q.134 Correct
Q.134 In-correct
Q.134 Unattempt
The freezing point of heavy water at 1atm pressure is
The freezing point of heavy water at 1atm pressure is
Q.135 Correct
Q.135 In-correct
Q.135 Unattempt
Which of the following salts can accommodate more number of H2O molecules per molecule in their halide hydrates?
Which of the following salts can accommodate more number of H2O molecules per molecule in their halide hydrates?
Q.136 Correct
Q.136 In-correct
Q.136 Unattempt
The correct order of Lewis acidic character of boron trihaldes is
The correct order of Lewis acidic character of boron trihaldes is
Q.137 Correct
Q.137 In-correct
Q.137 Unattempt
The acidic oxide from the following is
The acidic oxide from the following is
Q.138 Correct
Q.138 In-correct
Q.138 Unattempt
The correct order of rate of acid mediated dehydration reaction of the following compounds is

The correct order of rate of acid mediated dehydration reaction of the following compounds is

Q.139 Correct
Q.139 In-correct
Q.139 Unattempt
The major products P and Q in the following reactions, respectively, are

The major products P and Q in the following reactions, respectively, are

Q.140 Correct
Q.140 In-correct
Q.140 Unattempt
The major product formed in the following reaction sequence is

The major product formed in the following reaction sequence is

Q.141 Correct
Q.141 In-correct
Q.141 Unattempt
The number of nearest neighbours in a BCC unit cell is
The number of nearest neighbours in a BCC unit cell is
Q.142 Correct
Q.142 In-correct
Q.142 Unattempt
The Henry's law constant for the solubility of N2 gas in water at 298K is 1×10+5atm. The mole fraction of air is 0.8. The number of moles of N2 from air dissolved in 10 moles of water at 298K and 5atm pressure is
The Henry's law constant for the solubility of N2 gas in water at 298K is 1×10+5atm. The mole fraction of air is 0.8. The number of moles of N2 from air dissolved in 10 moles of water at 298K and 5atm pressure is
Q.143 Correct
Q.143 In-correct
Q.143 Unattempt
What is the effect of external pressure on the osmotic pressure (OP) of a solution?
What is the effect of external pressure on the osmotic pressure (OP) of a solution?
Q.144 Correct
Q.144 In-correct
Q.144 Unattempt
Given E∘Mn7+∕Mn2+=1.51V,EMn4+∕Mn2+∘=1.23V
Calculate the EMn7+∕Mn4+
Given E∘Mn7+∕Mn2+=1.51V,EMn4+∕Mn2+∘=1.23V
Calculate the EMn7+∕Mn4+
Q.145 Correct
Q.145 In-correct
Q.145 Unattempt
The reaction 2A→2B+C has a rate constant of 1.2×10−2s−1. Which of the following is correct?
The reaction 2A→2B+C has a rate constant of 1.2×10−2s−1. Which of the following is correct?
Q.146 Correct
Q.146 In-correct
Q.146 Unattempt
Which of the following does not show Tyndall effect?
Which of the following does not show Tyndall effect?
Q.147 Correct
Q.147 In-correct
Q.147 Unattempt
A nitrogen oxide that forms "in situ" when dilute FeSO4 is treated with aqueous solution of nitrate ion and then careful addition of conc. H2SO4 along the sides of test tube, is
A nitrogen oxide that forms "in situ" when dilute FeSO4 is treated with aqueous solution of nitrate ion and then careful addition of conc. H2SO4 along the sides of test tube, is
Q.148 Correct
Q.148 In-correct
Q.148 Unattempt
On treating SO2 with aqueous solution of KMnO4, the manganese ion reduces to
On treating SO2 with aqueous solution of KMnO4, the manganese ion reduces to
Q.149 Correct
Q.149 In-correct
Q.149 Unattempt
Match the following

The correct match is :
Match the following

The correct match is :
Q.150 Correct
Q.150 In-correct
Q.150 Unattempt
The correct decreasing order of the following 'Xe' compounds to act as both fluorinating and oxidizing agent is
i) XeF6
ii) XeF4
iii) XeF2
The correct decreasing order of the following 'Xe' compounds to act as both fluorinating and oxidizing agent is
i) XeF6
ii) XeF4
iii) XeF2
Q.151 Correct
Q.151 In-correct
Q.151 Unattempt
The correct order of ionic radii of trivalent ions Y3+,La3+,Eu3+, and Lu3+ is
(Y=39,La=57,Eu=63,Lu=71)
The correct order of ionic radii of trivalent ions Y3+,La3+,Eu3+, and Lu3+ is
(Y=39,La=57,Eu=63,Lu=71)
Q.152 Correct
Q.152 In-correct
Q.152 Unattempt
When permanganate ion is heated at 513K, led to the formation of two manganese based products. The physical properties of the product in which manganese with the higher oxidation state than the other are
When permanganate ion is heated at 513K, led to the formation of two manganese based products. The physical properties of the product in which manganese with the higher oxidation state than the other are
Q.153 Correct
Q.153 In-correct
Q.153 Unattempt
Assertion (A) : Both Glucose and Fructose have the same D-configuration.
Reason (R) : Both Glucose and Fructose are dextrorotatory.
The correct option among the following is
Assertion (A) : Both Glucose and Fructose have the same D-configuration.
Reason (R) : Both Glucose and Fructose are dextrorotatory.
The correct option among the following is
Q.154 Correct
Q.154 In-correct
Q.154 Unattempt
The major product of the following reactions is

The major product of the following reactions is

Q.155 Correct
Q.155 In-correct
Q.155 Unattempt
Benzene on reaction with acetyl chloride in the presence of anhydrous AlCl3 gave the product P. The product P on reaction with methylmagnesium bromide followed by treatment with water furnished the product Q. The molecular formula of Q is
Benzene on reaction with acetyl chloride in the presence of anhydrous AlCl3 gave the product P. The product P on reaction with methylmagnesium bromide followed by treatment with water furnished the product Q. The molecular formula of Q is
Q.156 Correct
Q.156 In-correct
Q.156 Unattempt
Sodium tertiary butoxide on reaction with methyl bromide produced the product P. Sodium methoxide upon reaction with tertiary butyl bromide generated the product Q. The products P and Q are
Sodium tertiary butoxide on reaction with methyl bromide produced the product P. Sodium methoxide upon reaction with tertiary butyl bromide generated the product Q. The products P and Q are
Q.157 Correct
Q.157 In-correct
Q.157 Unattempt
Match the following

Match the following

Q.158 Correct
Q.158 In-correct
Q.158 Unattempt
In the following compounds, the ones that give positive iodoform test are
(I) CH3CH2COCH2CH3
(II)CH3CH(OH)CH3
(III)

(IV)CH3CH2COCH3
(V)PhCOPh
(VI)
In the following compounds, the ones that give positive iodoform test are
(I) CH3CH2COCH2CH3
(II)CH3CH(OH)CH3
(III)

(IV)CH3CH2COCH3
(V)PhCOPh
(VI)
Q.159 Correct
Q.159 In-correct
Q.159 Unattempt
Which of the following set of compounds react with NaHCO3 ?
Which of the following set of compounds react with NaHCO3 ?
Q.160 Correct
Q.160 In-correct
Q.160 Unattempt
Among the following set of reactions, the most suitable method for preparing secondary amine is
Among the following set of reactions, the most suitable method for preparing secondary amine is
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