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Solution
Q.1 Correct
Q.1 In-correct
Q.1 Unattempt
If nCr denotes the number of combinations of n distinct things taken r at a time, then the domain of the function g(x)=(16x)C(2x1) is
If nCr denotes the number of combinations of n distinct things taken r at a time, then the domain of the function g(x)=(16x)C(2x1) is
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt
Let X={[
ab
cd
]
a
,b
,c
,d
}
. If f:X is defined by f(A)=det(A)AX, then f is
Let X={[
ab
cd
]
a
,b
,c
,d
}
. If f:X is defined by f(A)=det(A)AX, then f is
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt
If f(x) is a function such that f(x+y)=f(x)+f(y) and f(1)=7 then
n
r=1
f(r)
=
If f(x) is a function such that f(x+y)=f(x)+f(y) and f(1)=7 then
n
r=1
f(r)
=
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt
If A is a square matrix of order 3 , then |Adj(AdjA2)|=
If A is a square matrix of order 3 , then |Adj(AdjA2)|=
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt
If A and B are two square matrices of the same order and (AB+BA)T+(ABBA)T=2BA then
If A and B are two square matrices of the same order and (AB+BA)T+(ABBA)T=2BA then
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt
If adj[
102
112
021
]
=[
5m2
110
22n
]
, then m+n=
If adj[
102
112
021
]
=[
5m2
110
22n
]
, then m+n=
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt
If A=[
03
00
]
and f(x)=x+x2+x3+.....+x2023, then f(A)+I=
If A=[
03
00
]
and f(x)=x+x2+x3+.....+x2023, then f(A)+I=
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt
If i=1 then
n=0
(
i
3
)
n
=
If i=1 then
n=0
(
i
3
)
n
=
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt
If i=1 then Arg[
(1+i)2025
(1i)2022
]
=
If i=1 then Arg[
(1+i)2025
(1i)2022
]
=
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt
The locus of z such that |
zi
z+i
|
=2
, where z=x+iy, is
The locus of z such that |
zi
z+i
|
=2
, where z=x+iy, is
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt
If xn=cos
π
2n
+isin
π
2n
, then n=1xn=
If xn=cos
π
2n
+isin
π
2n
, then n=1xn=
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt
If the roots of the equation z2i=0 are α and β, then |ArgβArgα|=
If the roots of the equation z2i=0 are α and β, then |ArgβArgα|=
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt
If x2+2px2p+8>0 for all real values of x, then the set of all possible values of p is
If x2+2px2p+8>0 for all real values of x, then the set of all possible values of p is
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt
If (α,β) is the range of
x+3
(x1)(x+2)
, then the sum of the intercepts of the line αx+βy+1=0 on the coordinate axes is
If (α,β) is the range of
x+3
(x1)(x+2)
, then the sum of the intercepts of the line αx+βy+1=0 on the coordinate axes is
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt
The quadratic equation whose roots are sin218 and cos236 is
The quadratic equation whose roots are sin218 and cos236 is
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt
The roots of the equation x4+x34x2+x+1=0 are diminished by h so that the transformed equation does not contain x2 term. If the values of such hare α and β, then 12(αβ)2=
The roots of the equation x4+x34x2+x+1=0 are diminished by h so that the transformed equation does not contain x2 term. If the values of such hare α and β, then 12(αβ)2=
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt
α,β,γ are the roots of the equation x3+2x2x2=0 then α6+β6+γ6=
α,β,γ are the roots of the equation x3+2x2x2=0 then α6+β6+γ6=
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt
The number of diagonals of a polygon is 35 . If A, B are two distinct vertices of this polygon, then the number of all those triangles formed by joining three vertices of the polygon having AB as one of its sides is
The number of diagonals of a polygon is 35 . If A, B are two distinct vertices of this polygon, then the number of all those triangles formed by joining three vertices of the polygon having AB as one of its sides is
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt
There are 10 points in a plane, of which no three points are collinear except 4 . Then, the number of distinct triangles that can be formed by joining any three points of these ten points, such that at least one of the vertices of every triangle formed is from the given 4 collinear points is
There are 10 points in a plane, of which no three points are collinear except 4 . Then, the number of distinct triangles that can be formed by joining any three points of these ten points, such that at least one of the vertices of every triangle formed is from the given 4 collinear points is
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt
A student is asked to answer 10 out of 13 questions in an examination such that he must answer atleast four questions from the first five questions. Then the total number of possible choices available to him is
A student is asked to answer 10 out of 13 questions in an examination such that he must answer atleast four questions from the first five questions. Then the total number of possible choices available to him is
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt
If (c,c) is the set of all values of x for which the expansion of (75x)23 is valid, then 5c+7=
If (c,c) is the set of all values of x for which the expansion of (75x)23 is valid, then 5c+7=
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt
If n is a positive integer and f(n) is the coefficient of xn in the expansion of (1+x)(1x)n, then f(2023)=
If n is a positive integer and f(n) is the coefficient of xn in the expansion of (1+x)(1x)n, then f(2023)=
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt
If y=
3
4
+
3.5
4.8
+
3.5.7
4.8.12
+...
to , then
If y=
3
4
+
3.5
4.8
+
3.5.7
4.8.12
+...
to , then
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt
If
3x+2
(x+1)(2x2+3)
=
A
x+1
+
Bx+C
2x2+3
, then AB+C=
If
3x+2
(x+1)(2x2+3)
=
A
x+1
+
Bx+C
2x2+3
, then AB+C=
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt
The period of the function f(x)=elog(sinx)+(tanx)3cosec(3x5) is
The period of the function f(x)=elog(sinx)+(tanx)3cosec(3x5) is
Q.26 Correct
Q.26 In-correct
Q.26 Unattempt
If cosθ=
3
5
and π<θ<
3π
2
, then tan
θ
2
+sin
θ
2
+2cos
θ
2
=
If cosθ=
3
5
and π<θ<
3π
2
, then tan
θ
2
+sin
θ
2
+2cos
θ
2
=
Q.27 Correct
Q.27 In-correct
Q.27 Unattempt
If sin2θ and cos2θ are solutions of x2+axc=0, then
If sin2θ and cos2θ are solutions of x2+axc=0, then
Q.28 Correct
Q.28 In-correct
Q.28 Unattempt
If x=log(y+y2+1) then y=
If x=log(y+y2+1) then y=
Q.29 Correct
Q.29 In-correct
Q.29 Unattempt
In ABC, if a:b:c=4:5:6, then the ratio of the circumradius to its inradius is
In ABC, if a:b:c=4:5:6, then the ratio of the circumradius to its inradius is
Q.30 Correct
Q.30 In-correct
Q.30 Unattempt
The perimeter of a ABC is 6 times the arithmetic mean of the values of the sine of its angles. If its side BC is of unit length, then A=
The perimeter of a ABC is 6 times the arithmetic mean of the values of the sine of its angles. If its side BC is of unit length, then A=
Q.31 Correct
Q.31 In-correct
Q.31 Unattempt
If |a|=4,|b|=5,|ab|=3 and θ is the angle between the vectors a and b, then cot2θ=
If |a|=4,|b|=5,|ab|=3 and θ is the angle between the vectors a and b, then cot2θ=
Q.32 Correct
Q.32 In-correct
Q.32 Unattempt
If A(1,2,3),B(3,7,2),C(6,7,7) and D(1,0,1) are points in a plane, then the vector equation of the line passing through the centroids of ABD and ACD is
If A(1,2,3),B(3,7,2),C(6,7,7) and D(1,0,1) are points in a plane, then the vector equation of the line passing through the centroids of ABD and ACD is
Q.33 Correct
Q.33 In-correct
Q.33 Unattempt
If a+b+c=0,|a|=3,|b|=5,|c|=7, then the angle between a and b is
If a+b+c=0,|a|=3,|b|=5,|c|=7, then the angle between a and b is
Q.34 Correct
Q.34 In-correct
Q.34 Unattempt
If 2ij+3k,12ij3k,i+2j4k and λi+2jk are the position vectors of four coplanar points, then λ=
If 2ij+3k,12ij3k,i+2j4k and λi+2jk are the position vectors of four coplanar points, then λ=
Q.35 Correct
Q.35 In-correct
Q.35 Unattempt
Let a=i+2j2k and b=2ij2k be two vectors. If the orthogonal projection vector of a on b is x and orthogonal projection vector of b on a is y then |xy|=
Let a=i+2j2k and b=2ij2k be two vectors. If the orthogonal projection vector of a on b is x and orthogonal projection vector of b on a is y then |xy|=
Q.36 Correct
Q.36 In-correct
Q.36 Unattempt
The variance of 50 observations is 7 . Suppose that each observation in this data is multiplied by 6 and then 5 is subtracted from it. Then the variance of that new data is
The variance of 50 observations is 7 . Suppose that each observation in this data is multiplied by 6 and then 5 is subtracted from it. Then the variance of that new data is
Q.37 Correct
Q.37 In-correct
Q.37 Unattempt
A bag contains four balls. Two balls are drawn randomly and found them to be white. The probability that all the balls in the bag are white is
A bag contains four balls. Two balls are drawn randomly and found them to be white. The probability that all the balls in the bag are white is
Q.38 Correct
Q.38 In-correct
Q.38 Unattempt
If the coefficients a and b of a quadratic expression x2+ax+b are choosen from the sets A={3,4,5} and B={1,2,3,4} respectively, then the probability that the equation x2+ax+b=0 has real roots is
If the coefficients a and b of a quadratic expression x2+ax+b are choosen from the sets A={3,4,5} and B={1,2,3,4} respectively, then the probability that the equation x2+ax+b=0 has real roots is
Q.39 Correct
Q.39 In-correct
Q.39 Unattempt
A random variable X has the following probability distribution

A random variable X has the following probability distribution

Q.40 Correct
Q.40 In-correct
Q.40 Unattempt
5 persons entered a lift cabin in the cellar of a 7-floor building apart from cellar. If each of them independently and with equal probability can leave the cabin at any floor out of the 7 floors beginning with the first, then the probability of all the 5 persons leaving the cabin at different floors is
5 persons entered a lift cabin in the cellar of a 7-floor building apart from cellar. If each of them independently and with equal probability can leave the cabin at any floor out of the 7 floors beginning with the first, then the probability of all the 5 persons leaving the cabin at different floors is
Q.41 Correct
Q.41 In-correct
Q.41 Unattempt
If a point P moves so that the distance from (0,2) to P is
1
2
times the distance of P from (1,0), then the locus of the point P is
If a point P moves so that the distance from (0,2) to P is
1
2
times the distance of P from (1,0), then the locus of the point P is
Q.42 Correct
Q.42 In-correct
Q.42 Unattempt
Let d be the distance between the parallel lines 3x2y+5=0 and 3x2y+5+213=0. Let L13x2y+k1=0(k1>0) and L23x2y+k2=0(k2>0) be two lines that are at the distance of
4d
13
and
3d
13
from the line 3x2y+5=0. Then the combined equation of the lines L1=0 and L2=0 is
Let d be the distance between the parallel lines 3x2y+5=0 and 3x2y+5+213=0. Let L13x2y+k1=0(k1>0) and L23x2y+k2=0(k2>0) be two lines that are at the distance of
4d
13
and
3d
13
from the line 3x2y+5=0. Then the combined equation of the lines L1=0 and L2=0 is
Q.43 Correct
Q.43 In-correct
Q.43 Unattempt
If (h,k) is the image of the point (3,4) with respect to the line 2x3y5=0 and (l,m) is the foot of the perpendicular from (h,k) on to the line 3x+2y+12=0, then lh+mk+1=
If (h,k) is the image of the point (3,4) with respect to the line 2x3y5=0 and (l,m) is the foot of the perpendicular from (h,k) on to the line 3x+2y+12=0, then lh+mk+1=
Q.44 Correct
Q.44 In-correct
Q.44 Unattempt
A straight line parallel to the line y=3x passes through Q(2,3) and cuts the line 2x+4y27=0 at P. Then the length of the line segment PQ is
A straight line parallel to the line y=3x passes through Q(2,3) and cuts the line 2x+4y27=0 at P. Then the length of the line segment PQ is
Q.45 Correct
Q.45 In-correct
Q.45 Unattempt
If a line ax+2y=k forms a triangle of area 3 sq. units with the coordinate axis and is perpendicular to the line 2x3y+7=0, then the product of all the possible values of k is
If a line ax+2y=k forms a triangle of area 3 sq. units with the coordinate axis and is perpendicular to the line 2x3y+7=0, then the product of all the possible values of k is
Q.46 Correct
Q.46 In-correct
Q.46 Unattempt
The orthocenter of the triangle whose sides are given by x+y+10=0, xy2=0 and 2x+y7=0 is
The orthocenter of the triangle whose sides are given by x+y+10=0, xy2=0 and 2x+y7=0 is
Q.47 Correct
Q.47 In-correct
Q.47 Unattempt
For l, the equation (2l3)x2+2lxyy2=0 represents a pair of distinct lines
For l, the equation (2l3)x2+2lxyy2=0 represents a pair of distinct lines
Q.48 Correct
Q.48 In-correct
Q.48 Unattempt
If the parametric equations of the circle passing through the points (3,4),(3,2) and (1,4) is x=a+rcosθ,y=b+rsinθ then bara=
If the parametric equations of the circle passing through the points (3,4),(3,2) and (1,4) is x=a+rcosθ,y=b+rsinθ then bara=
Q.49 Correct
Q.49 In-correct
Q.49 Unattempt
If the parametric equations of the circle passing through the points (3,4),(3,2) and (1,4) is x=a+rcosθ,y=b+rsinθ then bara=
If the parametric equations of the circle passing through the points (3,4),(3,2) and (1,4) is x=a+rcosθ,y=b+rsinθ then bara=
Q.50 Correct
Q.50 In-correct
Q.50 Unattempt
If the angle between the pair of tangents drawn to the circle x2+y22x+4y+3=0 from the point (6,5) is θ, then cotθ=
If the angle between the pair of tangents drawn to the circle x2+y22x+4y+3=0 from the point (6,5) is θ, then cotθ=
Q.51 Correct
Q.51 In-correct
Q.51 Unattempt
If the angle between the circles x2+y24x6y+k=0 and x2+y2+8x4y+11=0 is
π
2
, then the value of k is
If the angle between the circles x2+y24x6y+k=0 and x2+y2+8x4y+11=0 is
π
2
, then the value of k is
Q.52 Correct
Q.52 In-correct
Q.52 Unattempt
The radius of a circle touching all the four circles (x±λ)2+(y±λ)2=λ2 is (x±λ)2+(y±λ)2=λ2 అనే నాలుగు వృత్తాలను స్పృశించే ఒక వృత్తము యొక్క వ్యాసార్ళం
The radius of a circle touching all the four circles (x±λ)2+(y±λ)2=λ2 is (x±λ)2+(y±λ)2=λ2 అనే నాలుగు వృత్తాలను స్పృశించే ఒక వృత్తము యొక్క వ్యాసార్ళం
Q.53 Correct
Q.53 In-correct
Q.53 Unattempt
If the radical centre of the given three circles x2+y2=1,x2+y22x3=0 and x2+y22y3=0 is C(α,β) and r is the sum of the radii of the given circles, then the circle with C(α,β) as centre and r as radius is
If the radical centre of the given three circles x2+y2=1,x2+y22x3=0 and x2+y22y3=0 is C(α,β) and r is the sum of the radii of the given circles, then the circle with C(α,β) as centre and r as radius is
Q.54 Correct
Q.54 In-correct
Q.54 Unattempt
If x2y+k=0 is a tangent to the parabola y24x4y+8=0, then the value of k is
If x2y+k=0 is a tangent to the parabola y24x4y+8=0, then the value of k is
Q.55 Correct
Q.55 In-correct
Q.55 Unattempt
If the points of intersection of the parabolas y2=5x and x2=5y lie on the line L, then the area of the triangle formed by the directrix of one parabola, latus rectum of another parabola and the line L is
If the points of intersection of the parabolas y2=5x and x2=5y lie on the line L, then the area of the triangle formed by the directrix of one parabola, latus rectum of another parabola and the line L is
Q.56 Correct
Q.56 In-correct
Q.56 Unattempt
If the line xcosα+ysinα=23 is a tangent to the ellipse
x2
16
+
y2
8
=1
and α is an acute angle then α=
If the line xcosα+ysinα=23 is a tangent to the ellipse
x2
16
+
y2
8
=1
and α is an acute angle then α=
Q.57 Correct
Q.57 In-correct
Q.57 Unattempt
If x+3y=3 is the tangent to the ellipse 2x2+3y2=k at a point P then the equation of the normal to this ellipse at P is
If x+3y=3 is the tangent to the ellipse 2x2+3y2=k at a point P then the equation of the normal to this ellipse at P is
Q.58 Correct
Q.58 In-correct
Q.58 Unattempt
If the angle between the asymptotes of a hyperbola is 30 then its eccentricity is
If the angle between the asymptotes of a hyperbola is 30 then its eccentricity is
Q.59 Correct
Q.59 In-correct
Q.59 Unattempt
In a triangle ABC, if the mid points of sides AB,BC,CA are (3,0,0),(0,4,0),(0,0,5) respectively, then AB2+BC2+CA2=
In a triangle ABC, if the mid points of sides AB,BC,CA are (3,0,0),(0,4,0),(0,0,5) respectively, then AB2+BC2+CA2=
Q.60 Correct
Q.60 In-correct
Q.60 Unattempt
If l,m,n and a, b, c are direction cosines of two lines then
If l,m,n and a, b, c are direction cosines of two lines then
Q.61 Correct
Q.61 In-correct
Q.61 Unattempt
If (2,1,3) is the foot of the perpendicular drawn from the origin to a plane, then the equation of that plane is
If (2,1,3) is the foot of the perpendicular drawn from the origin to a plane, then the equation of that plane is
Q.62 Correct
Q.62 In-correct
Q.62 Unattempt
lim
n
1
n3
n
k=1
(k2x)
=
lim
n
1
n3
n
k=1
(k2x)
=
Q.63 Correct
Q.63 In-correct
Q.63 Unattempt
The quadratic equation whose roots are l=
lim
θ0
(
3sinθ4sin3θ
θ
)
and m=
lim
θ0
(
2tanθ
θ(1tan2θ)
)
is
The quadratic equation whose roots are l=
lim
θ0
(
3sinθ4sin3θ
θ
)
and m=
lim
θ0
(
2tanθ
θ(1tan2θ)
)
is
Q.64 Correct
Q.64 In-correct
Q.64 Unattempt
On differentiation if we get f(x,y)dyg(x,y)dx=0 from 2x23xy+y2+x+2y8=0 then
g(2,2)
f(1,1)
=
On differentiation if we get f(x,y)dyg(x,y)dx=0 from 2x23xy+y2+x+2y8=0 then
g(2,2)
f(1,1)
=
Q.65 Correct
Q.65 In-correct
Q.65 Unattempt
If f(x)=ex,h(x)=(fof)(x), then
h(x)
h(x)
=
If f(x)=ex,h(x)=(fof)(x), then
h(x)
h(x)
=
Q.66 Correct
Q.66 In-correct
Q.66 Unattempt
If siny=sin3t and x=sint, then
dy
dx
=
If siny=sin3t and x=sint, then
dy
dx
=
Q.67 Correct
Q.67 In-correct
Q.67 Unattempt
If a line having slope 2 is a tangent to the curve y=x46x3+13x212x+5 at points P(x1,y1) and Q(x2,y2),x1,x,N then x1x2y1y2=
If a line having slope 2 is a tangent to the curve y=x46x3+13x212x+5 at points P(x1,y1) and Q(x2,y2),x1,x,N then x1x2y1y2=
Q.68 Correct
Q.68 In-correct
Q.68 Unattempt
Let m be the slope of the normal L drawn at (1,2) to the curve x=t27t+7, y=t24t10 and ax+by+c=0 be the equation of the normal L. If G.C.D. of (a,b,c) is 1 , then m(a+b+c)=
Let m be the slope of the normal L drawn at (1,2) to the curve x=t27t+7, y=t24t10 and ax+by+c=0 be the equation of the normal L. If G.C.D. of (a,b,c) is 1 , then m(a+b+c)=
Q.69 Correct
Q.69 In-correct
Q.69 Unattempt
If the function f(x)=xex,x attains its maximum value β at x=α then (α,β)=
If the function f(x)=xex,x attains its maximum value β at x=α then (α,β)=
Q.70 Correct
Q.70 In-correct
Q.70 Unattempt
If
x49Tan1(x50)
(1+x100)
d
x
=k(Tan1(x50))2+c
, then k=
If
x49Tan1(x50)
(1+x100)
d
x
=k(Tan1(x50))2+c
, then k=
Q.71 Correct
Q.71 In-correct
Q.71 Unattempt
If (logx)3x5dx=
x6
A
[B(logx)3+C(logx)2+D(logx)1]
+k
and A,B,C,D are integers, then A(B+C+D)=
If (logx)3x5dx=
x6
A
[B(logx)3+C(logx)2+D(logx)1]
+k
and A,B,C,D are integers, then A(B+C+D)=
Q.72 Correct
Q.72 In-correct
Q.72 Unattempt
dx
(x2+1)(x2+4)
=
dx
(x2+1)(x2+4)
=
Q.73 Correct
Q.73 In-correct
Q.73 Unattempt
dx
(x1)
3
4
(x+2)
5
4
=
dx
(x1)
3
4
(x+2)
5
4
=
Q.74 Correct
Q.74 In-correct
Q.74 Unattempt
1
1
x
|x
|dx=
1
1
x
|x
|dx=
Q.75 Correct
Q.75 In-correct
Q.75 Unattempt
π
2
π
2
sin2xcos2x(sinx+cosx)dx
=
π
2
π
2
sin2xcos2x(sinx+cosx)dx
=
Q.76 Correct
Q.76 In-correct
Q.76 Unattempt
The area (in square units) of the region bounded by the curve y=|sin2x| and the X-axis in [0,2π] is
The area (in square units) of the region bounded by the curve y=|sin2x| and the X-axis in [0,2π] is
Q.77 Correct
Q.77 In-correct
Q.77 Unattempt
If
3
0
(3x24x+2)dx
=k
, then an integer root of 3x24x+2=
3k
5
is
If
3
0
(3x24x+2)dx
=k
, then an integer root of 3x24x+2=
3k
5
is
Q.78 Correct
Q.78 In-correct
Q.78 Unattempt
If the order and degree of the differential equation corresponding to the family of curves y2=4a(x+a) ( a is parameter) are m and n respectively, then m+n2=
If the order and degree of the differential equation corresponding to the family of curves y2=4a(x+a) ( a is parameter) are m and n respectively, then m+n2=
Q.79 Correct
Q.79 In-correct
Q.79 Unattempt
If the solution of the differential equation
dy
dx
=
2x+3y
3x2y
is y=xtan(f(x))+c then f(x)=
If the solution of the differential equation
dy
dx
=
2x+3y
3x2y
is y=xtan(f(x))+c then f(x)=
Q.80 Correct
Q.80 In-correct
Q.80 Unattempt
The general solution of the differential equation (x2+2)dy+2xydx=ex(x2+2)dx is
The general solution of the differential equation (x2+2)dy+2xydx=ex(x2+2)dx is
Q.81 Correct
Q.81 In-correct
Q.81 Unattempt
The ratio of the relative strengths of strong and weak nuclear forces is
The ratio of the relative strengths of strong and weak nuclear forces is
Q.82 Correct
Q.82 In-correct
Q.82 Unattempt
The number of significant figures in the measurement of a length 0.079000m is
The number of significant figures in the measurement of a length 0.079000m is
Q.83 Correct
Q.83 In-correct
Q.83 Unattempt
The acceleration of a vertically projected body at its highest reaching position is
The acceleration of a vertically projected body at its highest reaching position is
Q.84 Correct
Q.84 In-correct
Q.84 Unattempt
A player can throw a ball to a maximum horizontal distance of 80m. If he throws the ball vertically with the same velocity, then the maximum height reached by the ball is
A player can throw a ball to a maximum horizontal distance of 80m. If he throws the ball vertically with the same velocity, then the maximum height reached by the ball is
Q.85 Correct
Q.85 In-correct
Q.85 Unattempt
If a man of mass 50kg is in a lift moving down with an acceleration equal to acceleration due to gravity, then the apparent weight of the man is
If a man of mass 50kg is in a lift moving down with an acceleration equal to acceleration due to gravity, then the apparent weight of the man is
Q.86 Correct
Q.86 In-correct
Q.86 Unattempt
An engine is dragging a mass of 5000kg with a velocity of 5ms1 along a smooth inclined plane of inclination 1 in 50 . Then the power of the engine is
An engine is dragging a mass of 5000kg with a velocity of 5ms1 along a smooth inclined plane of inclination 1 in 50 . Then the power of the engine is
Q.87 Correct
Q.87 In-correct
Q.87 Unattempt
A ball falls freely from a height h on a rigid horizontal plane. If the coefficient of restitution is e, then the total distance travelled by the ball before hitting the plane second time is
A ball falls freely from a height h on a rigid horizontal plane. If the coefficient of restitution is e, then the total distance travelled by the ball before hitting the plane second time is
Q.88 Correct
Q.88 In-correct
Q.88 Unattempt
The velocity of a particle having magnitude of 10ms1 in the direction of 60 with positive X-axis is
The velocity of a particle having magnitude of 10ms1 in the direction of 60 with positive X-axis is
Q.89 Correct
Q.89 In-correct
Q.89 Unattempt
The ratio of the radii of two solid spheres of same mass is 2:3. The ratio of the moments of inertia of the spheres about their diameters is
The ratio of the radii of two solid spheres of same mass is 2:3. The ratio of the moments of inertia of the spheres about their diameters is
Q.90 Correct
Q.90 In-correct
Q.90 Unattempt
The displacement of a particle executing simple harmonic motion is given by x=2cos(t) where t is the time in seconds then the time period of the particle is
The displacement of a particle executing simple harmonic motion is given by x=2cos(t) where t is the time in seconds then the time period of the particle is
Q.91 Correct
Q.91 In-correct
Q.91 Unattempt
A man weighing 75kg is standing in a lift. The weight of the man standing on a weighing machine kept in the lift when the lift is moving downwards freely under gravity is
A man weighing 75kg is standing in a lift. The weight of the man standing on a weighing machine kept in the lift when the lift is moving downwards freely under gravity is
Q.92 Correct
Q.92 In-correct
Q.92 Unattempt
The dimensions of four wires of the same material are given below. The increase in length is maximum in the wire of
The dimensions of four wires of the same material are given below. The increase in length is maximum in the wire of
Q.93 Correct
Q.93 In-correct
Q.93 Unattempt
A cylindrical vessel, open at the top, contains 15 litres of water. Water drains out through a small opening at the bottom. 5 litre of water comes out in time t1, the next 5 litre in further time t2, and the last 5 litre in further time t3, Then
A cylindrical vessel, open at the top, contains 15 litres of water. Water drains out through a small opening at the bottom. 5 litre of water comes out in time t1, the next 5 litre in further time t2, and the last 5 litre in further time t3, Then
Q.94 Correct
Q.94 In-correct
Q.94 Unattempt
A cylinder of mass m and material density ρ hanging from a string is lowered into a vessel of cross-sectional area A containing a liquid of density σ(<ρ) until it is fully immersed. The increase in pressure at the bottom of the vessel is
A cylinder of mass m and material density ρ hanging from a string is lowered into a vessel of cross-sectional area A containing a liquid of density σ(<ρ) until it is fully immersed. The increase in pressure at the bottom of the vessel is
Q.95 Correct
Q.95 In-correct
Q.95 Unattempt
The Fahrenheit and Kelvin scales of temperature will have the same reading at a temperature of
The Fahrenheit and Kelvin scales of temperature will have the same reading at a temperature of
Q.96 Correct
Q.96 In-correct
Q.96 Unattempt
If the ratio of densities of two substances is 5:6 and the ratio of their specific heat capacities is 3:5, then the ratio of heat energies required per unit volume so that the two substances can have same temperature rise is
If the ratio of densities of two substances is 5:6 and the ratio of their specific heat capacities is 3:5, then the ratio of heat energies required per unit volume so that the two substances can have same temperature rise is
Q.97 Correct
Q.97 In-correct
Q.97 Unattempt
In a process, the work done by the system is equal to the decrease in its internal energy. The process that the system undergoes is
In a process, the work done by the system is equal to the decrease in its internal energy. The process that the system undergoes is
Q.98 Correct
Q.98 In-correct
Q.98 Unattempt
N molecules each of mass m of gas A and 2N molecules each of mass 2m of gas B are contained in a vessel which is maintained at a temperature T. The mean square velocity of the molecules of gas B is denoted by V22 and the mean square of the x-component velocity of the molecules of gas A is denoted by V12, then
V1
V2
is
N molecules each of mass m of gas A and 2N molecules each of mass 2m of gas B are contained in a vessel which is maintained at a temperature T. The mean square velocity of the molecules of gas B is denoted by V22 and the mean square of the x-component velocity of the molecules of gas A is denoted by V12, then
V1
V2
is
Q.99 Correct
Q.99 In-correct
Q.99 Unattempt
Among the following statements, the correct statement for a wave is
Among the following statements, the correct statement for a wave is
Q.100 Correct
Q.100 In-correct
Q.100 Unattempt
A source and an observer move away from each other with same velocity of 10ms1 with respect to ground. If the observer finds the frequency of sound coming from the source as 1980Hz, then actual frequency of the source is (speed of sound in air =340ms1 )
A source and an observer move away from each other with same velocity of 10ms1 with respect to ground. If the observer finds the frequency of sound coming from the source as 1980Hz, then actual frequency of the source is (speed of sound in air =340ms1 )
Q.101 Correct
Q.101 In-correct
Q.101 Unattempt
Two convex lenses of focal lengths 20cm and 30cm are placed in contact with each other co-axially. The focal length of the combination is
Two convex lenses of focal lengths 20cm and 30cm are placed in contact with each other co-axially. The focal length of the combination is
Q.102 Correct
Q.102 In-correct
Q.102 Unattempt
A point source of light is placed at the focus of a concave mirror. Consider only paraxial rays. The shapes of the wavefronts of incident and reflected lights respectively are
A point source of light is placed at the focus of a concave mirror. Consider only paraxial rays. The shapes of the wavefronts of incident and reflected lights respectively are
Q.103 Correct
Q.103 In-correct
Q.103 Unattempt
If the electric potential at a point on the surface of a hollow conducting sphere of radius R is V, then the electric potential at a point which is at distance
R
3
from the centre of the sphere is
If the electric potential at a point on the surface of a hollow conducting sphere of radius R is V, then the electric potential at a point which is at distance
R
3
from the centre of the sphere is
Q.104 Correct
Q.104 In-correct
Q.104 Unattempt
The effective capacitance between points A and B shown in the circuit is

The effective capacitance between points A and B shown in the circuit is

Q.105 Correct
Q.105 In-correct
Q.105 Unattempt
The Wheatstone bridge shown in the diagram is balanced. If P3 is the power dissipated by R3 and P1 is the power dissipated by R1, then the ratio
P3
P1
is

The Wheatstone bridge shown in the diagram is balanced. If P3 is the power dissipated by R3 and P1 is the power dissipated by R1, then the ratio
P3
P1
is

Q.106 Correct
Q.106 In-correct
Q.106 Unattempt
A wire of resistance 2R is stretched such that its length is doubled. Then the increase in its resistance is
A wire of resistance 2R is stretched such that its length is doubled. Then the increase in its resistance is
Q.107 Correct
Q.107 In-correct
Q.107 Unattempt
It is found that a non-zero current element is unable to produce any magnetic field at a particular point. Then the angle between the current element and the position vector of that point with respect to the current element is
It is found that a non-zero current element is unable to produce any magnetic field at a particular point. Then the angle between the current element and the position vector of that point with respect to the current element is
Q.108 Correct
Q.108 In-correct
Q.108 Unattempt
Three long, straight, parallel wires carrying different currents are arranged as shown in the diagram. In the given arrangement, let the net force per unit length on the wire ' C ' be
F
. If the wire ' B ' is removed without disturbing the other two wires, then the force per unit length on wire ' A ' is

Three long, straight, parallel wires carrying different currents are arranged as shown in the diagram. In the given arrangement, let the net force per unit length on the wire ' C ' be
F
. If the wire ' B ' is removed without disturbing the other two wires, then the force per unit length on wire ' A ' is

Q.109 Correct
Q.109 In-correct
Q.109 Unattempt
If χ is the susceptibility and µr is the relative permeability of a ferromagnetic substance, then
If χ is the susceptibility and µr is the relative permeability of a ferromagnetic substance, then
Q.110 Correct
Q.110 In-correct
Q.110 Unattempt
Metal detector works on the principle of
Metal detector works on the principle of
Q.111 Correct
Q.111 In-correct
Q.111 Unattempt
A copper disc of radius 0.1m rotates about an axis passing through its centre and perpendicular to its plane with 10 revolutions per second in a uniform transverse magnetic field of 0.1T. The emf induced across the radius of the disc is
A copper disc of radius 0.1m rotates about an axis passing through its centre and perpendicular to its plane with 10 revolutions per second in a uniform transverse magnetic field of 0.1T. The emf induced across the radius of the disc is
Q.112 Correct
Q.112 In-correct
Q.112 Unattempt
At very high frequencies, the current (i) in the given circuit is

At very high frequencies, the current (i) in the given circuit is

Q.113 Correct
Q.113 In-correct
Q.113 Unattempt
Electromagnetic radiation of intensity 0.6Wm2 is falling on a black surface. The radiation pressure on the surface is
Electromagnetic radiation of intensity 0.6Wm2 is falling on a black surface. The radiation pressure on the surface is
Q.114 Correct
Q.114 In-correct
Q.114 Unattempt
Radiations of wavelength 400nm incidents on a photo sensitive material of work function 2.2eV. The stopping potential is nearly
Radiations of wavelength 400nm incidents on a photo sensitive material of work function 2.2eV. The stopping potential is nearly
Q.115 Correct
Q.115 In-correct
Q.115 Unattempt
In a hypothetical Bohr hydrogen atom, if the mass of the electron is doubled then the energy of the electron in the first orbit is
In a hypothetical Bohr hydrogen atom, if the mass of the electron is doubled then the energy of the electron in the first orbit is
Q.116 Correct
Q.116 In-correct
Q.116 Unattempt
The half-life period of element X is same as the mean life time of element Y. Assume initially X and Y have same number of atoms. Then
The half-life period of element X is same as the mean life time of element Y. Assume initially X and Y have same number of atoms. Then
Q.117 Correct
Q.117 In-correct
Q.117 Unattempt
Heavy water is used as moderator in nuclear reactor because
Heavy water is used as moderator in nuclear reactor because
Q.118 Correct
Q.118 In-correct
Q.118 Unattempt
Photodiodes are mostly operated in reverse biased condition because
Photodiodes are mostly operated in reverse biased condition because
Q.119 Correct
Q.119 In-correct
Q.119 Unattempt
Which of the following statements is true about LEDs?
Which of the following statements is true about LEDs?
Q.120 Correct
Q.120 In-correct
Q.120 Unattempt
An amplitude modulated wave is represented by cm(t)=10[1+0.6sin(1250t)]sin(108t).
Then the modulation index is
An amplitude modulated wave is represented by cm(t)=10[1+0.6sin(1250t)]sin(108t).
Then the modulation index is
Q.121 Correct
Q.121 In-correct
Q.121 Unattempt
The energy of second orbit of hydrogen atom is 5.45×1019J. What is the energy of first orbit of Li2+ ion (in J)?
The energy of second orbit of hydrogen atom is 5.45×1019J. What is the energy of first orbit of Li2+ ion (in J)?
Q.122 Correct
Q.122 In-correct
Q.122 Unattempt
The number of electrons with (n+l) values equal to 3,4 and 5 in an element with atomic number (z) 24 are respectively ( n= principal quantum number and l= azimuthal quantum number)
The number of electrons with (n+l) values equal to 3,4 and 5 in an element with atomic number (z) 24 are respectively ( n= principal quantum number and l= azimuthal quantum number)
Q.123 Correct
Q.123 In-correct
Q.123 Unattempt
Match the following

The correct answer is
Match the following

The correct answer is
Q.124 Correct
Q.124 In-correct
Q.124 Unattempt
According to MO theory, the molecule which contains only π - bonds between the atoms is
According to MO theory, the molecule which contains only π - bonds between the atoms is
Q.125 Correct
Q.125 In-correct
Q.125 Unattempt
In which of the following changes there is no change in hybridisation of the central atom?
In which of the following changes there is no change in hybridisation of the central atom?
Q.126 Correct
Q.126 In-correct
Q.126 Unattempt
The rate of diffusion of a gas A is 5 times more than that of gas B. If the molar mass of A is xgmol1, the molar mass of B(. in gmol1) is
The rate of diffusion of a gas A is 5 times more than that of gas B. If the molar mass of A is xgmol1, the molar mass of B(. in gmol1) is
Q.127 Correct
Q.127 In-correct
Q.127 Unattempt
Which one of the following has the same number of atoms as are in 6g of H2O ?
Which one of the following has the same number of atoms as are in 6g of H2O ?
Q.128 Correct
Q.128 In-correct
Q.128 Unattempt
For the reaction at 25C,X2O4(l)2XO2(g),U and S are 2.1K.Cal and 20CalK respectively. What is G for the reaction at the same temperature? (R=2CalK1mol1)
For the reaction at 25C,X2O4(l)2XO2(g),U and S are 2.1K.Cal and 20CalK respectively. What is G for the reaction at the same temperature? (R=2CalK1mol1)
Q.129 Correct
Q.129 In-correct
Q.129 Unattempt
Which of the following does not form a buffer solution?
Which of the following does not form a buffer solution?
Q.130 Correct
Q.130 In-correct
Q.130 Unattempt
The hydrides of which group elements of the periodic table form electron precise hydrides?
The hydrides of which group elements of the periodic table form electron precise hydrides?
Q.131 Correct
Q.131 In-correct
Q.131 Unattempt
The alkali metal with lowest EMM0(V) is X and the alkali metal with highest EM+M(V) is Y. Then X and Y are respectively
The alkali metal with lowest EMM0(V) is X and the alkali metal with highest EM+M(V) is Y. Then X and Y are respectively
Q.132 Correct
Q.132 In-correct
Q.132 Unattempt
Assertion (A): Be and Mg do not impart any colour to the flame
Reason (R): The electrons in them are strongly bound to get excited by flame
Assertion (A): Be and Mg do not impart any colour to the flame
Reason (R): The electrons in them are strongly bound to get excited by flame
Q.133 Correct
Q.133 In-correct
Q.133 Unattempt
Aluminium reacts with dilute HCl and liberates a gas ' A ' and with aqueous alkali liberates a gas ' B '. A and B respectively are
Aluminium reacts with dilute HCl and liberates a gas ' A ' and with aqueous alkali liberates a gas ' B '. A and B respectively are
Q.134 Correct
Q.134 In-correct
Q.134 Unattempt
Identify the incorrect statement about the oxidation states of group 14 elements
Identify the incorrect statement about the oxidation states of group 14 elements
Q.135 Correct
Q.135 In-correct
Q.135 Unattempt
The IUPAC name of the given compound is

The IUPAC name of the given compound is

Q.136 Correct
Q.136 In-correct
Q.136 Unattempt
The aromatic compound / species with maximum number of π - electrons is
The aromatic compound / species with maximum number of π - electrons is
Q.137 Correct
Q.137 In-correct
Q.137 Unattempt
In the conversion of A to B, the electrophile involved is
C2H2
Redhot
Irontube
873K
A
CH3
O
||
C
Cl
Anhy3,AlCl3
B
In the conversion of A to B, the electrophile involved is
C2H2
Redhot
Irontube
873K
A
CH3
O
||
C
Cl
Anhy3,AlCl3
B
Q.138 Correct
Q.138 In-correct
Q.138 Unattempt
An alkene X on ozonolysis gives a mixture of Propan-2-one and methanal. What is X ?
An alkene X on ozonolysis gives a mixture of Propan-2-one and methanal. What is X ?
Q.139 Correct
Q.139 In-correct
Q.139 Unattempt
The formula of a metal oxide is M0.96O1. The fractions of metal that exists as M3+ and M2+ ions in that oxide are respectively
The formula of a metal oxide is M0.96O1. The fractions of metal that exists as M3+ and M2+ ions in that oxide are respectively
Q.140 Correct
Q.140 In-correct
Q.140 Unattempt
At 50C, the vapour pressure of pure benzene is 268 torr. The number of moles of non-volatile solute per mole of benzene required to prepare a solution having a vapour pressure of 167 torr at the same temperature is
(molar mass of benzene =78gmol1 )
At 50C, the vapour pressure of pure benzene is 268 torr. The number of moles of non-volatile solute per mole of benzene required to prepare a solution having a vapour pressure of 167 torr at the same temperature is
(molar mass of benzene =78gmol1 )
Q.141 Correct
Q.141 In-correct
Q.141 Unattempt
The rate law for the decomposition of hydrogen iodide is
d[HI]
dt
=k[HI]2
. The units of rate constant k are
The rate law for the decomposition of hydrogen iodide is
d[HI]
dt
=k[HI]2
. The units of rate constant k are
Q.142 Correct
Q.142 In-correct
Q.142 Unattempt
A current of 15.0 amperes is passed through a solution of CrCl2 for 45 minutes. The volume of Cl2 (in L) obtained at the anode at 1atm and 273K is around
A current of 15.0 amperes is passed through a solution of CrCl2 for 45 minutes. The volume of Cl2 (in L) obtained at the anode at 1atm and 273K is around
Q.143 Correct
Q.143 In-correct
Q.143 Unattempt
Which of the following can form ionic micelles in water?
Which of the following can form ionic micelles in water?
Q.144 Correct
Q.144 In-correct
Q.144 Unattempt
The ore which is purified by Leaching process is
The ore which is purified by Leaching process is
Q.145 Correct
Q.145 In-correct
Q.145 Unattempt
P4+3NaOH+3H2O
CO2
3
X
+PH3
X
HCl(aq)
Y
+NaCl

The incorrect statement about Y is
P4+3NaOH+3H2O
CO2
3
X
+PH3
X
HCl(aq)
Y
+NaCl

The incorrect statement about Y is
Q.146 Correct
Q.146 In-correct
Q.146 Unattempt
The ratio of lone pair of electrons to bond pair of electrons in ozone molecule is
The ratio of lone pair of electrons to bond pair of electrons in ozone molecule is
Q.147 Correct
Q.147 In-correct
Q.147 Unattempt
Consider the following statements about the oxides of halogens
A. At room temperature, OF2 is thermally stable
B. Order of stability of oxides of halogens is I>Br>Cl
C. I2O5 is used in the estimation of CO
D. ClO2 is used as a bleaching agent
The correct statements are
Consider the following statements about the oxides of halogens
A. At room temperature, OF2 is thermally stable
B. Order of stability of oxides of halogens is I>Br>Cl
C. I2O5 is used in the estimation of CO
D. ClO2 is used as a bleaching agent
The correct statements are
Q.148 Correct
Q.148 In-correct
Q.148 Unattempt
XeF4+O2F2X+O2
X+
H2O
(1mole)
Y+2HF

The shapes of molecules of X and Y respectively are
XeF4+O2F2X+O2
X+
H2O
(1mole)
Y+2HF

The shapes of molecules of X and Y respectively are
Q.149 Correct
Q.149 In-correct
Q.149 Unattempt
Among the following the incorrect statement about transition metals is
Among the following the incorrect statement about transition metals is
Q.150 Correct
Q.150 In-correct
Q.150 Unattempt
Match the following

The correct answer is
Match the following

The correct answer is
Q.151 Correct
Q.151 In-correct
Q.151 Unattempt
Ziegler-Natta Catalyst is used in the manufacture of
Ziegler-Natta Catalyst is used in the manufacture of
Q.152 Correct
Q.152 In-correct
Q.152 Unattempt
The deficiency of which vitamin causes pernicious anaemia?
The deficiency of which vitamin causes pernicious anaemia?
Q.153 Correct
Q.153 In-correct
Q.153 Unattempt
The following molecule with the structure acts as

The following molecule with the structure acts as

Q.154 Correct
Q.154 In-correct
Q.154 Unattempt
Which of the following is least reactive towards SN1 reactions?
Which of the following is least reactive towards SN1 reactions?
Q.155 Correct
Q.155 In-correct
Q.155 Unattempt
Consider the following sequence of reactionsC2H4
(i)O3
(ii)Zn/H2O
P
(i)CH3MgBr/Ether
(ii)H2O/H+
Q
PCC
CH2Cl2
R

The incorrect statement about R is
Consider the following sequence of reactionsC2H4
(i)O3
(ii)Zn/H2O
P
(i)CH3MgBr/Ether
(ii)H2O/H+
Q
PCC
CH2Cl2
R

The incorrect statement about R is
Q.156 Correct
Q.156 In-correct
Q.156 Unattempt
The common name of benzene -1,3-diol is
The common name of benzene -1,3-diol is
Q.157 Correct
Q.157 In-correct
Q.157 Unattempt
Identify the major product C in the given sequence of reactions

Identify the major product C in the given sequence of reactions

Q.158 Correct
Q.158 In-correct
Q.158 Unattempt
Arrange the following in the correct order of their reactivity towards nucleophilic addition reactions
I) CH3
C
|
H
=O

II) CH3
C
|
NH2
=O

III) CH2=O
IV) CH3
C
|
CH3
=O
Arrange the following in the correct order of their reactivity towards nucleophilic addition reactions
I) CH3
C
|
H
=O

II) CH3
C
|
NH2
=O

III) CH2=O
IV) CH3
C
|
CH3
=O
Q.159 Correct
Q.159 In-correct
Q.159 Unattempt
R is one of the monomers for the formation of a polymer called

R is one of the monomers for the formation of a polymer called

Q.160 Correct
Q.160 In-correct
Q.160 Unattempt
What is B in the given reaction?C2H5Br
excess
NH3
A
Br2|
KOH
B
What is B in the given reaction?C2H5Br
excess
NH3
A
Br2|
KOH
B
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