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Solution
Q.1 Correct
Q.1 In-correct
Q.1 Unattempt
If f : R → [-1,1] and g : R → A are two subjective mappings and sin(g(x)−
π
3
)=
f(x)
2
√4−f2(x) , then A =
©
If f : R → [-1,1] and g : R → A are two subjective mappings and sin(g(x)−
π
3
)=
f(x)
2
√4−f2(x) , then A =
©
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt
The domain of the function f(x)=√
4−x2
[x]+2
, where [x] denotes the greatest integer not more than x , is
©
The domain of the function f(x)=√
4−x2
[x]+2
, where [x] denotes the greatest integer not more than x , is
©
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt
If an=√7+√7+√7+...n‌times , then which one of the following is true?
©
If an=√7+√7+√7+...n‌times , then which one of the following is true?
©
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt
If A is a square matrix of order 3, and A2+A+2I=0 , then
©
If A is a square matrix of order 3, and A2+A+2I=0 , then
©
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt
If A is a square matrix of order 3, then consider the following statements
I : If |A|=0 then |Adj‌A|=0
II: If |A|≠0 then |A−1|=|A−1|
Which of the above statement is/are true?
©
If A is a square matrix of order 3, then consider the following statements
I : If |A|=0 then |Adj‌A|=0
II: If |A|≠0 then |A−1|=|A−1|
Which of the above statement is/are true?
©
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt
The system of equations x−2y+3z=5,2x−2y+z=0, −x+2y−3z=6 has
©
The system of equations x−2y+3z=5,2x−2y+z=0, −x+2y−3z=6 has
©
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt
The amplitude of sin‌
π
5
+i(1+cos‌
π
5
) is
©
The amplitude of sin‌
π
5
+i(1+cos‌
π
5
) is
©
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt
If a point P denotes a complex number z=x+iy in the Argand plane and if
z+1
z+i
 is a purely real number, then the locus of P is
©
If a point P denotes a complex number z=x+iy in the Argand plane and if
z+1
z+i
 is a purely real number, then the locus of P is
©
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt
If ω is a complex cube root of unity, then
[
51+73ω+87ω2
73+87ω+51ω2
+
51+73ω+87ω2
87+51ω+73ω2
]15=

©
If ω is a complex cube root of unity, then
[
51+73ω+87ω2
73+87ω+51ω2
+
51+73ω+87ω2
87+51ω+73ω2
]15=

©
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt
If z∈C and iz3+4z2−z+4i=0 , then a complex root of this equation having minimum magnitude is
©
If z∈C and iz3+4z2−z+4i=0 , then a complex root of this equation having minimum magnitude is
©
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt
If α,β are the root of the equation 2x2−4x+5=0, then the quadratic equation whose roots are α2+β and α+β2 is
©
If α,β are the root of the equation 2x2−4x+5=0, then the quadratic equation whose roots are α2+β and α+β2 is
©
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt
If a,b,c∈R be such that 4a+2b+c>0 and ax2+bx+c=0 has no real roots, then the value of (c+a)(c+b) is
©
If a,b,c∈R be such that 4a+2b+c>0 and ax2+bx+c=0 has no real roots, then the value of (c+a)(c+b) is
©
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt
The minimum degree of a polynomial equation with rational coefficients having √3+√27,√2+5i as two of its roots is
©
The minimum degree of a polynomial equation with rational coefficients having √3+√27,√2+5i as two of its roots is
©
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt
If all the digits in the number 53426 are permuted in all possible ways and are arranged in decreasing order, then the number having rank 89, is
©
If all the digits in the number 53426 are permuted in all possible ways and are arranged in decreasing order, then the number having rank 89, is
©
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt
Three parallel straight lines L1,L2 and L3 lie on the sameplane. Consider 5 points on L1 , 7 points on L2 and 9 points on L3. Then the maximum possible number of triangles formed with vertices at these points, is
©
Three parallel straight lines L1,L2 and L3 lie on the sameplane. Consider 5 points on L1 , 7 points on L2 and 9 points on L3. Then the maximum possible number of triangles formed with vertices at these points, is
©
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt
If a > 0 and the coefficient of x2 in the expression of (ax3+
c
x
)6 is 60, then ac2=
©
If a > 0 and the coefficient of x2 in the expression of (ax3+
c
x
)6 is 60, then ac2=
©
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt
If x=
3
4.8
+
3.5
4.8.12
+
3.5.7
4.8.12.16
+..., then 2x2+5x=
©
If x=
3
4.8
+
3.5
4.8.12
+
3.5.7
4.8.12.16
+..., then 2x2+5x=
©
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt
If
3x2+1
(x2+1)(x2+2)
=
Ax+B
x2+1
 +
Cx+D
x2+2
+
Ex+F
(x2+2)2
, then A+C+E=
©
If
3x2+1
(x2+1)(x2+2)
=
Ax+B
x2+1
 +
Cx+D
x2+2
+
Ex+F
(x2+2)2
, then A+C+E=
©
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt
If tan(
π
4
+
y
2
)=tan3(
π
4
+
x
2
), then
3‌sin‌x+sin3x
1+3sin2x
=
©
If tan(
π
4
+
y
2
)=tan3(
π
4
+
x
2
), then
3‌sin‌x+sin3x
1+3sin2x
=
©
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt
[(cos‌252°−sin‌126°)(cos‌252°+sin‌126°) (sin2126°+sin2186°+sin266°)]=
©
[(cos‌252°−sin‌126°)(cos‌252°+sin‌126°) (sin2126°+sin2186°+sin266°)]=
©
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt
If α,β,γ are any three angles, then cos‌α+cos‌β−cos‌γ−cos(α+β+γ)=
©
If α,β,γ are any three angles, then cos‌α+cos‌β−cos‌γ−cos(α+β+γ)=
©
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt
The general solution of the equation √3−5‌sin‌x+sin2x+cos‌x=0 is
©
The general solution of the equation √3−5‌sin‌x+sin2x+cos‌x=0 is
©
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt
Consider the following statements
I. sin−1(y2−4y+6)+cos−1(y2−4y+6) =
π
2
,∀y∈R
II. sec−1(y2−4y+6)+cosec−1(y2−4y+6) =
π
2
,∀y∈R
Which of the above statements is/are true?
©
Consider the following statements
I. sin−1(y2−4y+6)+cos−1(y2−4y+6) =
π
2
,∀y∈R
II. sec−1(y2−4y+6)+cosec−1(y2−4y+6) =
π
2
,∀y∈R
Which of the above statements is/are true?
©
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt
If sec‌θ‌cosh‌y=cosec‌x and cosec‌θ‌sinh‌y=sec‌x, then sinh2y=
©
If sec‌θ‌cosh‌y=cosec‌x and cosec‌θ‌sinh‌y=sec‌x, then sinh2y=
©
Q.26 Correct
Q.26 In-correct
Q.26 Unattempt
Consider the following statements:
In triangle ABC, if c = 6 and cosC=−
11
25
 then R=
25
2√14

II. In triangle ABC, if a=3,b=4,c=6, then ABC is acute angled triangle.
Which of the above statements is/are true?
©
Consider the following statements:
In triangle ABC, if c = 6 and cosC=−
11
25
 then R=
25
2√14

II. In triangle ABC, if a=3,b=4,c=6, then ABC is acute angled triangle.
Which of the above statements is/are true?
©
Q.27 Correct
Q.27 In-correct
Q.27 Unattempt
In triangle ABC, if a=3,b=4,c=6, then
cot‌
A
2
+cot‌
B
2
+cot‌
C
2
cot‌A+cot‌B+cot‌C
=
©
In triangle ABC, if a=3,b=4,c=6, then
cot‌
A
2
+cot‌
B
2
+cot‌
C
2
cot‌A+cot‌B+cot‌C
=
©
Q.28 Correct
Q.28 In-correct
Q.28 Unattempt
If the reciprocals of the lengths of the sides of a ∆ABC are in harmonic progression, then its exradii r1,r2,r3 are in
©
If the reciprocals of the lengths of the sides of a ∆ABC are in harmonic progression, then its exradii r1,r2,r3 are in
©
Q.29 Correct
Q.29 In-correct
Q.29 Unattempt
If P an Q are two points on the cuarve y=2x+2 such that OP.i=−1 and OQ.i=2, then the mnagnbitude of (OQ−4OP) is
©
If P an Q are two points on the cuarve y=2x+2 such that OP.i=−1 and OQ.i=2, then the mnagnbitude of (OQ−4OP) is
©
Q.30 Correct
Q.30 In-correct
Q.30 Unattempt
P and Q are points on the straight line passing through the point A(3i+j−k) and parallel to the vector (2i−j+2k) . IfAP=AQ=3 , then the vector equation of the plane OPQ is
©
P and Q are points on the straight line passing through the point A(3i+j−k) and parallel to the vector (2i−j+2k) . IfAP=AQ=3 , then the vector equation of the plane OPQ is
©
Q.31 Correct
Q.31 In-correct
Q.31 Unattempt
Let m be the unit vector orthogonal to the vector i−j+k and coplanar with the vectors 2i+j and j−k . Ifa=i−k , then the length of thel perpendicular from theorigin to thel plane r.m=a.m is
©
Let m be the unit vector orthogonal to the vector i−j+k and coplanar with the vectors 2i+j and j−k . Ifa=i−k , then the length of thel perpendicular from theorigin to thel plane r.m=a.m is
©
Q.32 Correct
Q.32 In-correct
Q.32 Unattempt
If a,b,c are non-coplanar unit vectors such that a×(b×c)=
b+c
√2
, then the angle between a and b is
©
If a,b,c are non-coplanar unit vectors such that a×(b×c)=
b+c
√2
, then the angle between a and b is
©
Q.33 Correct
Q.33 In-correct
Q.33 Unattempt
If a and b are two unit vectors such that c=(a×c)+b, then the maximum value of [a b c] is
©
If a and b are two unit vectors such that c=(a×c)+b, then the maximum value of [a b c] is
©
Q.34 Correct
Q.34 In-correct
Q.34 Unattempt
α,β‌and‌γ are non zero vectors such that |β|=|γ|=1 and|α|=10, then
(α×(β+γ))×(β×γ).(β−γ)=
©
α,β‌and‌γ are non zero vectors such that |β|=|γ|=1 and|α|=10, then
(α×(β+γ))×(β×γ).(β−γ)=
©
Q.35 Correct
Q.35 In-correct
Q.35 Unattempt
The arithmetic mean and standard deviation of a data of nine numbers are 13 and 5 respectively. If 3 is included as the 10‌th item of the data, then the variance of the data of the ten number is
©
The arithmetic mean and standard deviation of a data of nine numbers are 13 and 5 respectively. If 3 is included as the 10‌th item of the data, then the variance of the data of the ten number is
©
Q.36 Correct
Q.36 In-correct
Q.36 Unattempt
The variance of the following distribution is
 Marks  1-3  3-5  5-7  7-9
 Number of students  40  30  20  10

©
The variance of the following distribution is
 Marks  1-3  3-5  5-7  7-9
 Number of students  40  30  20  10

©
Q.37 Correct
Q.37 In-correct
Q.37 Unattempt
A and B are two events such that P(A) = 0.58, P(B) = 0.32 and P(A∩B)=0.28 . Then the probability that neither A nor B occurs is
©
A and B are two events such that P(A) = 0.58, P(B) = 0.32 and P(A∩B)=0.28 . Then the probability that neither A nor B occurs is
©
Q.38 Correct
Q.38 In-correct
Q.38 Unattempt
Two dice are thrown simultaneously. If A is event of getting the sum of the numbers on two dice as greater than or equal to 8 and B is the event of getting a number less than or equal to 3 on atleast one of the die. Then P(B∕A)=
©
Two dice are thrown simultaneously. If A is event of getting the sum of the numbers on two dice as greater than or equal to 8 and B is the event of getting a number less than or equal to 3 on atleast one of the die. Then P(B∕A)=
©
Q.39 Correct
Q.39 In-correct
Q.39 Unattempt
A bag contains 6 balls. If 4 balls are drawn at a time and all of them are found to be red, then the probability that exactly 5 of the balls in the bag are red is
©
A bag contains 6 balls. If 4 balls are drawn at a time and all of them are found to be red, then the probability that exactly 5 of the balls in the bag are red is
©
Q.40 Correct
Q.40 In-correct
Q.40 Unattempt
If the probability distribution of a random variable X isgiven by
X=xi:0123
P(X=xi):
1
8
3
8
3KK

Then the variance of X is
©
If the probability distribution of a random variable X isgiven by
X=xi:0123
P(X=xi):
1
8
3
8
3KK

Then the variance of X is
©
Q.41 Correct
Q.41 In-correct
Q.41 Unattempt
A manufacturer of locks knows that 2% of his product is defective. If he sells the locks in boxes each with 100 locks and guarantees that not more than 2 locks will be defective in box, then the probability that a box will fail to meet the guaranteed quality is
©
A manufacturer of locks knows that 2% of his product is defective. If he sells the locks in boxes each with 100 locks and guarantees that not more than 2 locks will be defective in box, then the probability that a box will fail to meet the guaranteed quality is
©
Q.42 Correct
Q.42 In-correct
Q.42 Unattempt
The equation of the locus of a point (2‌cos‌θ−3,3‌sin‌θ−4) is
©
The equation of the locus of a point (2‌cos‌θ−3,3‌sin‌θ−4) is
©
Q.43 Correct
Q.43 In-correct
Q.43 Unattempt
When the origin is shifted to the point (2, 3) and then the coordinate axes are rotated through an angle
π
3
 in the counter clockwise sense, then the transformed equation of3x2+2xy+3y2−18x −22+50=0 is
©
When the origin is shifted to the point (2, 3) and then the coordinate axes are rotated through an angle
π
3
 in the counter clockwise sense, then the transformed equation of3x2+2xy+3y2−18x −22+50=0 is
©
Q.44 Correct
Q.44 In-correct
Q.44 Unattempt
A straight line L with negative slope passes through the point (1,1) and cuts the positive coordinate axes at the points A and B. If O is the origin, then the minimum value of OA + OB as L varies, is
©
A straight line L with negative slope passes through the point (1,1) and cuts the positive coordinate axes at the points A and B. If O is the origin, then the minimum value of OA + OB as L varies, is
©
Q.45 Correct
Q.45 In-correct
Q.45 Unattempt
If the straight line L≡3x+4y−k=0 cuts the line segment joining the points P(2, -1) and Q(1,1) in the ration 4:1, then the equation of the parallel to the line y=x and concurrent with the lines PQ and L = 0 is
©
If the straight line L≡3x+4y−k=0 cuts the line segment joining the points P(2, -1) and Q(1,1) in the ration 4:1, then the equation of the parallel to the line y=x and concurrent with the lines PQ and L = 0 is
©
Q.46 Correct
Q.46 In-correct
Q.46 Unattempt
The orthocenter and the centroid of ΔABC are (5, 8) and (3,
14
3
) respectively. The equation of the side BC is x−y=0. Given that the image of the orthocenter of a triangle with respect to any side lies on the circumcircle of that triangle, then the diameter of the circumcircle of ∆ABC is
©
The orthocenter and the centroid of ΔABC are (5, 8) and (3,
14
3
) respectively. The equation of the side BC is x−y=0. Given that the image of the orthocenter of a triangle with respect to any side lies on the circumcircle of that triangle, then the diameter of the circumcircle of ∆ABC is
©
Q.47 Correct
Q.47 In-correct
Q.47 Unattempt
If a pair of perpendicular lines through the origin together with the straight line 2x+3y=6 from an isosceles triangle then the area of that triangle (in sq. units) is
©
If a pair of perpendicular lines through the origin together with the straight line 2x+3y=6 from an isosceles triangle then the area of that triangle (in sq. units) is
©
Q.48 Correct
Q.48 In-correct
Q.48 Unattempt
If the equation 3x2+7xy+2y2+2gx+2fy+2=0 represents a pair of intersecting lines and the square of the distance of their point of intersection from the origin is
2
5
 then f2+g2=
©
If the equation 3x2+7xy+2y2+2gx+2fy+2=0 represents a pair of intersecting lines and the square of the distance of their point of intersection from the origin is
2
5
 then f2+g2=
©
Q.49 Correct
Q.49 In-correct
Q.49 Unattempt
From a point P(0, b) tow tangents are drawn to the circle x2+y2=16 and these two tangents intersect x − axis at two points A and B. If the area of the triangle ∆PAB is minimum, then the equation of its circumcircle is
©
From a point P(0, b) tow tangents are drawn to the circle x2+y2=16 and these two tangents intersect x − axis at two points A and B. If the area of the triangle ∆PAB is minimum, then the equation of its circumcircle is
©
Q.50 Correct
Q.50 In-correct
Q.50 Unattempt
If the angle between the tangents drawn to the circle x2+y2−12x−16=0 at the points where the line 5y=5x+k cut the circle is 60°, then the value of k is,
©
If the angle between the tangents drawn to the circle x2+y2−12x−16=0 at the points where the line 5y=5x+k cut the circle is 60°, then the value of k is,
©
Q.51 Correct
Q.51 In-correct
Q.51 Unattempt
If a circle S with radius 5 touches the circle x2+y2−6x−4y−12=0 at (−1,−1) then the length of the tangent from the centre of the circle S to the given circle is
©
If a circle S with radius 5 touches the circle x2+y2−6x−4y−12=0 at (−1,−1) then the length of the tangent from the centre of the circle S to the given circle is
©
Q.52 Correct
Q.52 In-correct
Q.52 Unattempt
If a circle S passing through the point (3, 4) cuts the circle x2+y2=36 orthogonally, then the locus of the centre of S is
©
If a circle S passing through the point (3, 4) cuts the circle x2+y2=36 orthogonally, then the locus of the centre of S is
©
Q.53 Correct
Q.53 In-correct
Q.53 Unattempt
The line x−2=0 cuts the circle x2+y2−8x−2y+8=0 at A and B. The equation of the circle passing through the points A and B and having least radius is
©
The line x−2=0 cuts the circle x2+y2−8x−2y+8=0 at A and B. The equation of the circle passing through the points A and B and having least radius is
©
Q.54 Correct
Q.54 In-correct
Q.54 Unattempt
If a perpendicular drawn through the vertex O of the parabola y=4ax to any of its tangent meets the tangent at N and the parabola at M, then ON . OM =
©
If a perpendicular drawn through the vertex O of the parabola y=4ax to any of its tangent meets the tangent at N and the parabola at M, then ON . OM =
©
Q.55 Correct
Q.55 In-correct
Q.55 Unattempt
Let α1 and α2 be the ordinates of two points A and B on a parabola y2=4ax and let α3 be the ordinate of the point of intersection of its tangents at A and B. Then α3−α2=
©
Let α1 and α2 be the ordinates of two points A and B on a parabola y2=4ax and let α3 be the ordinate of the point of intersection of its tangents at A and B. Then α3−α2=
©
Q.56 Correct
Q.56 In-correct
Q.56 Unattempt
The equations of the latus recta of the ellipse 9x2+4y2−18x−8y−23=0 are
©
The equations of the latus recta of the ellipse 9x2+4y2−18x−8y−23=0 are
©
Q.57 Correct
Q.57 In-correct
Q.57 Unattempt
The equation of the tangent to the ellipse 4x2+9y2=36 atthe end of the latus rectum lying in the second quadrant, is
©
The equation of the tangent to the ellipse 4x2+9y2=36 atthe end of the latus rectum lying in the second quadrant, is
©
Q.58 Correct
Q.58 In-correct
Q.58 Unattempt
If the product of the lengths of the perpendiculars from anypoint on the hyperbola 16x2−25y2=400 to its asymptotes is p and the angle between the two asymptotes is θ then p tan
θ
2

©
If the product of the lengths of the perpendiculars from anypoint on the hyperbola 16x2−25y2=400 to its asymptotes is p and the angle between the two asymptotes is θ then p tan
θ
2

©
Q.59 Correct
Q.59 In-correct
Q.59 Unattempt
A(3,2,−1),B(4,1,1),C(6,2,5) and D(3,3,3) are four points G1,G2,G3 and G4 respectively are the centroids of the triangles BCD, CDA, DAB and ABC. The point of concurrence of the lines AG1,BG2,CG3 and DG4 is
©
A(3,2,−1),B(4,1,1),C(6,2,5) and D(3,3,3) are four points G1,G2,G3 and G4 respectively are the centroids of the triangles BCD, CDA, DAB and ABC. The point of concurrence of the lines AG1,BG2,CG3 and DG4 is
©
Q.60 Correct
Q.60 In-correct
Q.60 Unattempt
The acute angle between the lines whose direction cosines are given by the equations l+m+n=0 and 2lm+2ln−mn=0 is
©
The acute angle between the lines whose direction cosines are given by the equations l+m+n=0 and 2lm+2ln−mn=0 is
©
Q.61 Correct
Q.61 In-correct
Q.61 Unattempt
A variable plane passes through a fixed point (α,β,γ) and meets the coordinate axes in A, B, and C. Let P1,P2‌and‌P3 be the planes passing through A, B, C and parallel to the coordinate planes YZ, ZX, XY respectively. Then the locus of the point of intersection of the planes P1,P2‌and‌P3 is
©
A variable plane passes through a fixed point (α,β,γ) and meets the coordinate axes in A, B, and C. Let P1,P2‌and‌P3 be the planes passing through A, B, C and parallel to the coordinate planes YZ, ZX, XY respectively. Then the locus of the point of intersection of the planes P1,P2‌and‌P3 is
©
Q.62 Correct
Q.62 In-correct
Q.62 Unattempt
lim
x→
π
2
1+cos‌2‌x
cot‌3‌x(3sin‌2‌x−1)=

©
lim
x→
π
2
1+cos‌2‌x
cot‌3‌x(3sin‌2‌x−1)=

©
Q.63 Correct
Q.63 In-correct
Q.63 Unattempt
lim
n→∞
n−nk{(n+1)(n+
1
2
)(n+
1
22
).....(n+
1
2k−1
)}n=

©
lim
n→∞
n−nk{(n+1)(n+
1
2
)(n+
1
22
).....(n+
1
2k−1
)}n=

©
Q.64 Correct
Q.64 In-correct
Q.64 Unattempt

If a and b (a>b) are points of discontinuity of the function

then 3a - b =

If a and b (a>b) are points of discontinuity of the function

then 3a - b =
Q.65 Correct
Q.65 In-correct
Q.65 Unattempt
For $− 1< 1
©
For $− 1< 1
©
Q.66 Correct
Q.66 In-correct
Q.66 Unattempt
f:R→R is a function such that f(0)=1 and for all x,y∈R
f(xy+1)=f(x)f(y)−f(y)−x+2 then
df
dx
 at x=e is
©
f:R→R is a function such that f(0)=1 and for all x,y∈R
f(xy+1)=f(x)f(y)−f(y)−x+2 then
df
dx
 at x=e is
©
Q.67 Correct
Q.67 In-correct
Q.67 Unattempt
y=sin(log(x2+2x+1))⇒(x+1)2
d2y
dx2
+(x+1)
dy
dx
=

©
y=sin(log(x2+2x+1))⇒(x+1)2
d2y
dx2
+(x+1)
dy
dx
=

©
Q.68 Correct
Q.68 In-correct
Q.68 Unattempt
The acute angle between the tangents drawn at the point at the point of intersection (other than the origin) of the curves x2=4y and y2=4x is
©
The acute angle between the tangents drawn at the point at the point of intersection (other than the origin) of the curves x2=4y and y2=4x is
©
Q.69 Correct
Q.69 In-correct
Q.69 Unattempt
If x>0 then
x
1+x
−log(1+x)
©
If x>0 then
x
1+x
−log(1+x)
©
Q.70 Correct
Q.70 In-correct
Q.70 Unattempt
On the curve y=x3 , the point at which the tangent line is parallel to the chord joining the points (−1,−1) and (2,8), is
©
On the curve y=x3 , the point at which the tangent line is parallel to the chord joining the points (−1,−1) and (2,8), is
©
Q.71 Correct
Q.71 In-correct
Q.71 Unattempt
If the petrol burnt in driving a motor boat varies as the cube of the velocity, then the speed (in km/hour) of the boat going against a water flow of C kms/hour so that the quantity of petrol burnt is minimum is
©
If the petrol burnt in driving a motor boat varies as the cube of the velocity, then the speed (in km/hour) of the boat going against a water flow of C kms/hour so that the quantity of petrol burnt is minimum is
©
Q.72 Correct
Q.72 In-correct
Q.72 Unattempt
For x<1,∫
x−x2
√1−x
dx=
©
For x<1,∫
x−x2
√1−x
dx=
©
Q.73 Correct
Q.73 In-correct
Q.73 Unattempt
∫
dx
(2‌sin‌x+sec‌x)4
=A(1+tan‌x)−5 +B(1+tan‌x)−6+C(1+tan‌x)−7+k, then A + B + C =
©
∫
dx
(2‌sin‌x+sec‌x)4
=A(1+tan‌x)−5 +B(1+tan‌x)−6+C(1+tan‌x)−7+k, then A + B + C =
©
Q.74 Correct
Q.74 In-correct
Q.74 Unattempt
∫
2x2−1+x2√x2+4
x2(x2+4)
dx=
©
∫
2x2−1+x2√x2+4
x2(x2+4)
dx=
©
Q.75 Correct
Q.75 In-correct
Q.75 Unattempt
For n≥2, let In=
∫
π
4
0
tann xdx and Fn=In+In−2. then Fn−Fn+1=
©
For n≥2, let In=
∫
π
4
0
tann xdx and Fn=In+In−2. then Fn−Fn+1=
©
Q.76 Correct
Q.76 In-correct
Q.76 Unattempt
lim
n→∞
n[
1
3n2+8n+4
+
1
3n2+16n+16
 +......+
1
15n2
]=
©
lim
n→∞
n[
1
3n2+8n+4
+
1
3n2+16n+16
 +......+
1
15n2
]=
©
Q.77 Correct
Q.77 In-correct
Q.77 Unattempt
∫|x2−3x+2|dx=
©
∫|x2−3x+2|dx=
©
Q.78 Correct
Q.78 In-correct
Q.78 Unattempt
OABC is a unit square where O is the origin and B = (1, 1).
The curves 2y2=x and x2=y divide the area of the square into three parts OABO, OBO, and OBCO. If a1,a2,a3 are the areas (in sq. units) of these parts respectively, then a1+2a2+3a3=
©
OABC is a unit square where O is the origin and B = (1, 1).
The curves 2y2=x and x2=y divide the area of the square into three parts OABO, OBO, and OBCO. If a1,a2,a3 are the areas (in sq. units) of these parts respectively, then a1+2a2+3a3=
©
Q.79 Correct
Q.79 In-correct
Q.79 Unattempt
The differential equation corresponding to the family of parabolas y2=4a(x+a) , where a is the parameter, is
©
The differential equation corresponding to the family of parabolas y2=4a(x+a) , where a is the parameter, is
©
Q.80 Correct
Q.80 In-correct
Q.80 Unattempt
The general solution; of
dy
dx
+y‌tan‌x=2x+x2‌tan‌x
©
The general solution; of
dy
dx
+y‌tan‌x=2x+x2‌tan‌x
©
Q.81 Correct
Q.81 In-correct
Q.81 Unattempt
In a system, unit of mass is A kg, length is B m and time is C s, then the value of 10 N in this system is
©
In a system, unit of mass is A kg, length is B m and time is C s, then the value of 10 N in this system is
©
Q.82 Correct
Q.82 In-correct
Q.82 Unattempt
Assertion (A) : The angle between acceleration and velocity of a body in one dimensional motion is always zero.
Reason (R) : One dimensional motion is along a straight line.
©
Assertion (A) : The angle between acceleration and velocity of a body in one dimensional motion is always zero.
Reason (R) : One dimensional motion is along a straight line.
©
Q.83 Correct
Q.83 In-correct
Q.83 Unattempt
A projectile is given an initial velocity of (
^
i
+2
^
j
)ms−1 . The equation of its path is (g=10ms−1)
©
A projectile is given an initial velocity of (
^
i
+2
^
j
)ms−1 . The equation of its path is (g=10ms−1)
©
Q.84 Correct
Q.84 In-correct
Q.84 Unattempt
A body projected with some velocity at an angle 45° with the horizontal from the origin in X-Y plane passes through a point at (4, 3) m. Its horizontal range is
©
A body projected with some velocity at an angle 45° with the horizontal from the origin in X-Y plane passes through a point at (4, 3) m. Its horizontal range is
©
Q.85 Correct
Q.85 In-correct
Q.85 Unattempt
A block of mass 10 kg is placed on a horizontal frictionless surface and is attached to a cord which passes over two light frictionless pulleys as shown in the figure. The hanging block tied to the other end of the cord is initially at rest 2 m above the horizontal floor. If the hanging block strikes the 2 s after the system is released, the weight of the hanging block is ____ (g = 10 ms‌−2)
 
©
A block of mass 10 kg is placed on a horizontal frictionless surface and is attached to a cord which passes over two light frictionless pulleys as shown in the figure. The hanging block tied to the other end of the cord is initially at rest 2 m above the horizontal floor. If the hanging block strikes the 2 s after the system is released, the weight of the hanging block is ____ (g = 10 ms‌−2)
 
©
Q.86 Correct
Q.86 In-correct
Q.86 Unattempt
A double inclined plane as shown in figure has fixed horizontal base and smooth faces with the same angle of inclination of 30° . A block of mass 300 g is on one face and is connected by a cord passing over a frictionless pulley to a second block of mass 200 g kept on another face. The acceleration with which thesystem of the blocks moves is _____% of acceleration due to gravity.
 
©
A double inclined plane as shown in figure has fixed horizontal base and smooth faces with the same angle of inclination of 30° . A block of mass 300 g is on one face and is connected by a cord passing over a frictionless pulley to a second block of mass 200 g kept on another face. The acceleration with which thesystem of the blocks moves is _____% of acceleration due to gravity.
 
©
Q.87 Correct
Q.87 In-correct
Q.87 Unattempt
A canon shell fired breaks into two equal parts at its highest point. If one part retraces the path to the canon with kinetic energy E1 and kinetic energy of the second part is E2 then
©
A canon shell fired breaks into two equal parts at its highest point. If one part retraces the path to the canon with kinetic energy E1 and kinetic energy of the second part is E2 then
©
Q.88 Correct
Q.88 In-correct
Q.88 Unattempt

A uniform chain of mass ‘m’ and length ‘l’ is on a smooth horizontal table with (1/n)th part of its length is hanging from one end of the table. The velocity of the chain when it completely slips off the table is

A uniform chain of mass ‘m’ and length ‘l’ is on a smooth horizontal table with (1/n)th part of its length is hanging from one end of the table. The velocity of the chain when it completely slips off the table is
Q.89 Correct
Q.89 In-correct
Q.89 Unattempt
Two particles of masses in the ratio 1 : 2 are placed along a vertical line. The lighter particle is raised through a height of 9 cm. To raise the centre of mass of the system by 2 cm, the heavier particle should be _____
©
Two particles of masses in the ratio 1 : 2 are placed along a vertical line. The lighter particle is raised through a height of 9 cm. To raise the centre of mass of the system by 2 cm, the heavier particle should be _____
©
Q.90 Correct
Q.90 In-correct
Q.90 Unattempt
A solid sphere and a ring of same radius roll down an inclined plane without slipping. Both start from rest from the top of the inclined plane. If the sphere and the ring reach the bottom of the inclined plane with velocities vr and vs respectively,then
vr2
vs2
 is
©
A solid sphere and a ring of same radius roll down an inclined plane without slipping. Both start from rest from the top of the inclined plane. If the sphere and the ring reach the bottom of the inclined plane with velocities vr and vs respectively,then
vr2
vs2
 is
©
Q.91 Correct
Q.91 In-correct
Q.91 Unattempt

A particle is executing S.H.M. The time taken for (3/8)th of oscillation from extreme position is ‘X’. Then the time taken for the particle to complete (5/8)th of oscillation from mean positions is ©

A particle is executing S.H.M. The time taken for (3/8)th of oscillation from extreme position is ‘X’. Then the time taken for the particle to complete (5/8)th of oscillation from mean positions is ©
Q.92 Correct
Q.92 In-correct
Q.92 Unattempt
An object is thrown vertically upward from the surface of the earth with a velocity x times the escape velocity on the earth (x<1) , the maximum height to which to which it raises from the centre of the earth is (radius of earth is R)
©
An object is thrown vertically upward from the surface of the earth with a velocity x times the escape velocity on the earth (x<1) , the maximum height to which to which it raises from the centre of the earth is (radius of earth is R)
©
Q.93 Correct
Q.93 In-correct
Q.93 Unattempt
A sphere of mass 2 kg and diameter 4.5 cm is attached to the lower end of steel wire of 2 m length and area of cross section 6 2 0.24 10 m− × . The wire is suspended from 205 cm high ceiling of a room. When the system is made to oscillate as a simple pendulum, the sphere just grazes the floor at its lowest position. The velocity of the sphere at the lowest position is
(Young’s modulus of steel =2×1011Nm−2 and acceleration due to gravity = 10 ms‌−2)
©
A sphere of mass 2 kg and diameter 4.5 cm is attached to the lower end of steel wire of 2 m length and area of cross section 6 2 0.24 10 m− × . The wire is suspended from 205 cm high ceiling of a room. When the system is made to oscillate as a simple pendulum, the sphere just grazes the floor at its lowest position. The velocity of the sphere at the lowest position is
(Young’s modulus of steel =2×1011Nm−2 and acceleration due to gravity = 10 ms‌−2)
©
Q.94 Correct
Q.94 In-correct
Q.94 Unattempt
A spherical body of density ρ is floating half immersed in a liquid of density d . If σ is the surface tension of the liquid, then the diameter of the body is
©
A spherical body of density ρ is floating half immersed in a liquid of density d . If σ is the surface tension of the liquid, then the diameter of the body is
©
Q.95 Correct
Q.95 In-correct
Q.95 Unattempt
As shown in the figure, an equilateral triangle ABC is formed by joining three rods of equal length and D is the midpoint of AB. Coefficient of linear expansion of the material of AB is α1 and that of AC and BC is α2. If the length DC remains constant for small changes in temperature, then
 
©
As shown in the figure, an equilateral triangle ABC is formed by joining three rods of equal length and D is the midpoint of AB. Coefficient of linear expansion of the material of AB is α1 and that of AC and BC is α2. If the length DC remains constant for small changes in temperature, then
 
©
Q.96 Correct
Q.96 In-correct
Q.96 Unattempt
Match the following List-I with List-II.
 List-I  List-II
 (A) When ice melt into water  (I) Volume increases
 (B) When water changes intosteam  (II) Volume decreases
 (C) Melting point of ice  (III) Increases withincrease of pressure
 (D) Boiling point of water  (IV) Decreases with increase of pressure

©
Match the following List-I with List-II.
 List-I  List-II
 (A) When ice melt into water  (I) Volume increases
 (B) When water changes intosteam  (II) Volume decreases
 (C) Melting point of ice  (III) Increases withincrease of pressure
 (D) Boiling point of water  (IV) Decreases with increase of pressure

©
Q.97 Correct
Q.97 In-correct
Q.97 Unattempt
A cylindrical vessel of uniform cross section consisting of a gas of γ=1.5 is divided into two part A and B using a piston. Initially the piston is kept fixed such that part A has pressure P and volume 5V and the part B has pressure 8P and volume V. If the piston is let free and the gas is allowed to undergo adiabatic process, the final volume of the gas in part A is _____
©
A cylindrical vessel of uniform cross section consisting of a gas of γ=1.5 is divided into two part A and B using a piston. Initially the piston is kept fixed such that part A has pressure P and volume 5V and the part B has pressure 8P and volume V. If the piston is let free and the gas is allowed to undergo adiabatic process, the final volume of the gas in part A is _____
©
Q.98 Correct
Q.98 In-correct
Q.98 Unattempt
A diatomic ideal gas is used in a Carnot’s engine as working substance. During adiabatic expansion of the cycle, if the volume of the gas increases from V to 32V then the efficiency of the engine is
©
A diatomic ideal gas is used in a Carnot’s engine as working substance. During adiabatic expansion of the cycle, if the volume of the gas increases from V to 32V then the efficiency of the engine is
©
Q.99 Correct
Q.99 In-correct
Q.99 Unattempt
The absolute temperature at which the rms speed of a hydrogen molecule is equal to its escape speed from the Moon’s surface is
(radius of Moon is R, g is acceleration due to gravity on Moon’s surface, m is the mass of hydrogen molecule and k is Boltzmann constant)
©
The absolute temperature at which the rms speed of a hydrogen molecule is equal to its escape speed from the Moon’s surface is
(radius of Moon is R, g is acceleration due to gravity on Moon’s surface, m is the mass of hydrogen molecule and k is Boltzmann constant)
©
Q.100 Correct
Q.100 In-correct
Q.100 Unattempt
An object of density 2000 kgm‌−3 is hung from a thin light wire. The fundamental frequency of the transverse waves in the wire is 200 Hz. If the object is immersed in water such that half of its volume is submerged, then the fundamental frequency of the transverse waves in the wire is ______
©
An object of density 2000 kgm‌−3 is hung from a thin light wire. The fundamental frequency of the transverse waves in the wire is 200 Hz. If the object is immersed in water such that half of its volume is submerged, then the fundamental frequency of the transverse waves in the wire is ______
©
Q.101 Correct
Q.101 In-correct
Q.101 Unattempt
An observer and a source emitting sound of frequency 120 Hz are on the X-axis. The observer is stationary while the source of sound is in motion given by the equation x=3‌sin‌ω‌t ( x inmeters and t in second). If the difference between the maximum and minimum frequencies of the sound observed by the observer is 22 Hz, then the value of ω is (Speed of sound in air = 330 ms‌−1 )
©
An observer and a source emitting sound of frequency 120 Hz are on the X-axis. The observer is stationary while the source of sound is in motion given by the equation x=3‌sin‌ω‌t ( x inmeters and t in second). If the difference between the maximum and minimum frequencies of the sound observed by the observer is 22 Hz, then the value of ω is (Speed of sound in air = 330 ms‌−1 )
©
Q.102 Correct
Q.102 In-correct
Q.102 Unattempt
As shown in the figure, a parallel beam of light incident on the upper part of a prism of angle 1.8° and material of refractive index 1.5. The light immerging out from the prism falls on a concave mirror of radius of curvature 40 cm. The distance of the point from the principle axis of the mirror where the light rays are focussed after reflection from the mirror is
 
©
As shown in the figure, a parallel beam of light incident on the upper part of a prism of angle 1.8° and material of refractive index 1.5. The light immerging out from the prism falls on a concave mirror of radius of curvature 40 cm. The distance of the point from the principle axis of the mirror where the light rays are focussed after reflection from the mirror is
 
©
Q.103 Correct
Q.103 In-correct
Q.103 Unattempt
A microscope has an objective of aperture 8 mm and focal length of 5 cm. The minimum separation between two object to be just resolved by the microscope is
(Wavelength of light used = 5500 Å)
©
A microscope has an objective of aperture 8 mm and focal length of 5 cm. The minimum separation between two object to be just resolved by the microscope is
(Wavelength of light used = 5500 Å)
©
Q.104 Correct
Q.104 In-correct
Q.104 Unattempt
The electric field due to short electric dipole at a distance ‘r’ on the axial line from its mid point is x times the electric field at a distance 2r on the equatorial line from the mid-point of dipole.
Then the value of x is
©
The electric field due to short electric dipole at a distance ‘r’ on the axial line from its mid point is x times the electric field at a distance 2r on the equatorial line from the mid-point of dipole.
Then the value of x is
©
Q.105 Correct
Q.105 In-correct
Q.105 Unattempt
A point charge ‘q’ is placed at origin. Let
→
E
A,
→
E
B‌and‌
→
E
C be the electric fields at three points A (1, 2, 3), B(1, 1, -1) and (2, 2, 2) respectively due to the charge ‘q’. Then the relation between them is
(a)
→
E
A⊥
→
E
B
(b)
→
E
A∥
→
E
C
(c) |
→
E
B|=4|
→
E
C|
(d) |
→
E
B|=8|
→
E
C|
©
A point charge ‘q’ is placed at origin. Let
→
E
A,
→
E
B‌and‌
→
E
C be the electric fields at three points A (1, 2, 3), B(1, 1, -1) and (2, 2, 2) respectively due to the charge ‘q’. Then the relation between them is
(a)
→
E
A⊥
→
E
B
(b)
→
E
A∥
→
E
C
(c) |
→
E
B|=4|
→
E
C|
(d) |
→
E
B|=8|
→
E
C|
©
Q.106 Correct
Q.106 In-correct
Q.106 Unattempt
An electric dipole consists of two particles each of mass 1 kg separated by 1 m carrying charges 1 μC and –1 μC respectively. It is equilibrium in a uniform electric field of 2×104Vm−1 . If it is deflected by a small angle 2°, minimum time taken by it to come back again to the mean position is ( in seconds )
©
An electric dipole consists of two particles each of mass 1 kg separated by 1 m carrying charges 1 μC and –1 μC respectively. It is equilibrium in a uniform electric field of 2×104Vm−1 . If it is deflected by a small angle 2°, minimum time taken by it to come back again to the mean position is ( in seconds )
©
Q.107 Correct
Q.107 In-correct
Q.107 Unattempt
One plate of a parallel plate capacitor is connected to a spring as shown in the figure. The area of each plate of the capacitor is A and the distance between the plates is d when the battery is not connected and the spring is unstretched. After connecting the battery, in the steady state, the distance between the plates is 0.74d, then the force constant of the spring is
 
©
One plate of a parallel plate capacitor is connected to a spring as shown in the figure. The area of each plate of the capacitor is A and the distance between the plates is d when the battery is not connected and the spring is unstretched. After connecting the battery, in the steady state, the distance between the plates is 0.74d, then the force constant of the spring is
 
©
Q.108 Correct
Q.108 In-correct
Q.108 Unattempt
Two cell P and Q each of emf 2.16 V are connected in series with a resistor of 19.6 Ω. An ideal voltmeter reads 2 V when connected across the cell P and 1.92 V when connected across the cell Q. The ratio of the internal resistance of the cells P and Q is
©
Two cell P and Q each of emf 2.16 V are connected in series with a resistor of 19.6 Ω. An ideal voltmeter reads 2 V when connected across the cell P and 1.92 V when connected across the cell Q. The ratio of the internal resistance of the cells P and Q is
©
Q.109 Correct
Q.109 In-correct
Q.109 Unattempt
A resistor has bands with colours orange, green, silver and gold.Then the resistance of the resistor is
©
A resistor has bands with colours orange, green, silver and gold.Then the resistance of the resistor is
©
Q.110 Correct
Q.110 In-correct
Q.110 Unattempt
A beam of protons enters a uniform magnetic field of 0.314T with a velocity 4×105ms−1 in a direction making an angle 60° with the direction of the magnetic field. The path of the beam is (mass of proton =1.6×10−27‌kg )
©
A beam of protons enters a uniform magnetic field of 0.314T with a velocity 4×105ms−1 in a direction making an angle 60° with the direction of the magnetic field. The path of the beam is (mass of proton =1.6×10−27‌kg )
©
Q.111 Correct
Q.111 In-correct
Q.111 Unattempt
The magnetic field due to a current carrying loop of radius 3 cm at a point on its axis at a distance of 4 cm from its centre is 54 μT. Then the value of magnetic field at the centre of the loop is _____
©
The magnetic field due to a current carrying loop of radius 3 cm at a point on its axis at a distance of 4 cm from its centre is 54 μT. Then the value of magnetic field at the centre of the loop is _____
©
Q.112 Correct
Q.112 In-correct
Q.112 Unattempt
A short bar magnet of magnetic moment 0.21 Am‌2 is placed with its axis perpendicular to the direction of the horizontal components of the Earth’s magnetic field. The distance of the point on the axis of the magnet from the centre of the magnet where the resultant magnetic field is inclined at 45° with the horizontal component of the Earth’s field direction is _____
(Horizontal component of the Earth’s magnetic field = 4.2×10−5 T )
©
A short bar magnet of magnetic moment 0.21 Am‌2 is placed with its axis perpendicular to the direction of the horizontal components of the Earth’s magnetic field. The distance of the point on the axis of the magnet from the centre of the magnet where the resultant magnetic field is inclined at 45° with the horizontal component of the Earth’s field direction is _____
(Horizontal component of the Earth’s magnetic field = 4.2×10−5 T )
©
Q.113 Correct
Q.113 In-correct
Q.113 Unattempt
The length of a wire required to make a solenoid of length ‘l’ and self induction ‘L’ is
©
The length of a wire required to make a solenoid of length ‘l’ and self induction ‘L’ is
©
Q.114 Correct
Q.114 In-correct
Q.114 Unattempt
An inductor and a resistor are connected in series to an ac source. The current in the circuit is 500 mA if the applied ac voltage is 8√2V at a frequency of
175
π
 Hz and the current in the circuit is 400 mA if the same ac voltage at a frequency of
225
π
 Hz is applied. The values of the inductance and resistance are respectively
©
An inductor and a resistor are connected in series to an ac source. The current in the circuit is 500 mA if the applied ac voltage is 8√2V at a frequency of
175
π
 Hz and the current in the circuit is 400 mA if the same ac voltage at a frequency of
225
π
 Hz is applied. The values of the inductance and resistance are respectively
©
Q.115 Correct
Q.115 In-correct
Q.115 Unattempt
An electromagnetic waves of frequency 2 MHz propagates from vacuum to a non magnetic medium of relative permittivity 9.
Then its wavelength
©
An electromagnetic waves of frequency 2 MHz propagates from vacuum to a non magnetic medium of relative permittivity 9.
Then its wavelength
©
Q.116 Correct
Q.116 In-correct
Q.116 Unattempt
The figure shows the variation of photocurrent (i) with anode potential (V) for three different radiations. Let Ia,Ib‌and‌Ic be the intensities and fa,fb‌and‌fc be the frequencies for the curves a, b and c respectively. Then
 
©
The figure shows the variation of photocurrent (i) with anode potential (V) for three different radiations. Let Ia,Ib‌and‌Ic be the intensities and fa,fb‌and‌fc be the frequencies for the curves a, b and c respectively. Then
 
©
Q.117 Correct
Q.117 In-correct
Q.117 Unattempt
A stationary hydrogen atom undergoes a transition from n = 5 to n = 4. Recoil speed of the atom is (R = Rydberg constant, h = Plank’s constant, m = mass of the proton)
©
A stationary hydrogen atom undergoes a transition from n = 5 to n = 4. Recoil speed of the atom is (R = Rydberg constant, h = Plank’s constant, m = mass of the proton)
©
Q.118 Correct
Q.118 In-correct
Q.118 Unattempt
The half life of 92238U against α − decay is 13.86×1016s . Theactivity of 1g sample of 92238U is _____
©
The half life of 92238U against α − decay is 13.86×1016s . Theactivity of 1g sample of 92238U is _____
©
Q.119 Correct
Q.119 In-correct
Q.119 Unattempt
An npn transistor is connected in common emitter configuration as shown in the figure. If the collector current is 5 mA, VBE=0.6V,VCE=3V and common emitter current amplification factor is 50, then the values of R1 and R2 are respectively
 
©
An npn transistor is connected in common emitter configuration as shown in the figure. If the collector current is 5 mA, VBE=0.6V,VCE=3V and common emitter current amplification factor is 50, then the values of R1 and R2 are respectively
 
©
Q.120 Correct
Q.120 In-correct
Q.120 Unattempt
The maximum distance between the transmitting and receiving TV towers is 65 km. If the ratio of the heights of the transmitting and receiving towers respectively are (Radius of earth 6400 km)
©
The maximum distance between the transmitting and receiving TV towers is 65 km. If the ratio of the heights of the transmitting and receiving towers respectively are (Radius of earth 6400 km)
©
Q.121 Correct
Q.121 In-correct
Q.121 Unattempt
The wavelength corresponding to electronic transition between two orbits of hydrogen atom is 912 Å. The wavelength (in Å) for the same electronic transition in Li‌+2 is
©
The wavelength corresponding to electronic transition between two orbits of hydrogen atom is 912 Å. The wavelength (in Å) for the same electronic transition in Li‌+2 is
©
Q.122 Correct
Q.122 In-correct
Q.122 Unattempt
The ratio of lowest energy in terms of wave numbers of Balmer and Lyman series of lines of atomic spectrum of hydrogen is
©
The ratio of lowest energy in terms of wave numbers of Balmer and Lyman series of lines of atomic spectrum of hydrogen is
©
Q.123 Correct
Q.123 In-correct
Q.123 Unattempt
Which of the following represents the correct order of ionic radii?
©
Which of the following represents the correct order of ionic radii?
©
Q.124 Correct
Q.124 In-correct
Q.124 Unattempt
The species, which has the bond order same as that of F2 molecule is
©
The species, which has the bond order same as that of F2 molecule is
©
Q.125 Correct
Q.125 In-correct
Q.125 Unattempt
The hybridization of an atom ‘X’ with atomic number 27 in [XF6]3− is
©
The hybridization of an atom ‘X’ with atomic number 27 in [XF6]3− is
©
Q.126 Correct
Q.126 In-correct
Q.126 Unattempt
The temperature of 4.0 moles of a gas occupying 5dm‌3 at 3.32 bar is
(R=0.083‌bar‌dm3‌K−1‌mol−1)
©
The temperature of 4.0 moles of a gas occupying 5dm‌3 at 3.32 bar is
(R=0.083‌bar‌dm3‌K−1‌mol−1)
©
Q.127 Correct
Q.127 In-correct
Q.127 Unattempt
To 50mL of 0.1 N Na2CO3 solution 150 mL of water is added.
What is the molarity of resultant solution?
©
To 50mL of 0.1 N Na2CO3 solution 150 mL of water is added.
What is the molarity of resultant solution?
©
Q.128 Correct
Q.128 In-correct
Q.128 Unattempt
Match the following
  List-I  List-II
  A) At constant volume the change in internal energy of a system   I) W=−2.30‌nRT‌log‌
Vf
Vi
 B) Isothermal irreversible change  II) Wadia=ΔU
 C) Isothermal reversible change  III) qv=ΔU
 D) Adiabatic change  IV) W=−Pex(Vf−Vi)
   V) ΔU=ΔH−nRT

©
Match the following
  List-I  List-II
  A) At constant volume the change in internal energy of a system   I) W=−2.30‌nRT‌log‌
Vf
Vi
 B) Isothermal irreversible change  II) Wadia=ΔU
 C) Isothermal reversible change  III) qv=ΔU
 D) Adiabatic change  IV) W=−Pex(Vf−Vi)
   V) ΔU=ΔH−nRT

©
Q.129 Correct
Q.129 In-correct
Q.129 Unattempt
The pH of a buffer solution formed by mixing 30 mL of 0.1 M NH4OH and 30 mL of 1 M NH4Cl solution is 8.6. The pKb of NH4OH is
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The pH of a buffer solution formed by mixing 30 mL of 0.1 M NH4OH and 30 mL of 1 M NH4Cl solution is 8.6. The pKb of NH4OH is
©
Q.130 Correct
Q.130 In-correct
Q.130 Unattempt
The solubility products of three sparingly soluble salts AB, A2B and AB3 are respectively 4.0×10−20,3.2×10−11 and 2.7×10−31. The increasing order of their solubility is
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The solubility products of three sparingly soluble salts AB, A2B and AB3 are respectively 4.0×10−20,3.2×10−11 and 2.7×10−31. The increasing order of their solubility is
©
Q.131 Correct
Q.131 In-correct
Q.131 Unattempt
Identify the correct statements from the following
a) Zn reacts with dilute HCl and aqueous NaOH solution separately and liberates hydrogen
b) Ti and Zr form interstitial hydrides
c) The viscosity of H2O is more than the viscosity of D2O
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Identify the correct statements from the following
a) Zn reacts with dilute HCl and aqueous NaOH solution separately and liberates hydrogen
b) Ti and Zr form interstitial hydrides
c) The viscosity of H2O is more than the viscosity of D2O
©
Q.132 Correct
Q.132 In-correct
Q.132 Unattempt
What are X, Y and Z in the following reactions?
CaCO3
Δ
⇄
 CO2+X
X+H2O→Y
Y+Cl2→Z
©
What are X, Y and Z in the following reactions?
CaCO3
Δ
⇄
 CO2+X
X+H2O→Y
Y+Cl2→Z
©
Q.133 Correct
Q.133 In-correct
Q.133 Unattempt
Identify the correct set of 13‌th group elements which do not form amphoteric oxides
©
Identify the correct set of 13‌th group elements which do not form amphoteric oxides
©
Q.134 Correct
Q.134 In-correct
Q.134 Unattempt
Identify X, Y and Z in the following reaction
2CH3Cl+X
Y
–––––––🢖
570K
Z
©
Identify X, Y and Z in the following reaction
2CH3Cl+X
Y
–––––––🢖
570K
Z
©
Q.135 Correct
Q.135 In-correct
Q.135 Unattempt
Which of the following is not a greenhouse gas?
©
Which of the following is not a greenhouse gas?
©
Q.136 Correct
Q.136 In-correct
Q.136 Unattempt
The order of priortiy of the following functional groups in IUPAC method of naming organic compounds is
 
©
The order of priortiy of the following functional groups in IUPAC method of naming organic compounds is
 
©
Q.137 Correct
Q.137 In-correct
Q.137 Unattempt
What are X, Y and Z in the following reactions?
CH3−CH2−CO‌
⊖
O
‌
⊕
Na
‌
X
––––🢖
‌Y‌
Kolbe′s‌Electrolysis
◂––––––––––––
‌ ‌Z+H2O

©
What are X, Y and Z in the following reactions?
CH3−CH2−CO‌
⊖
O
‌
⊕
Na
‌
X
––––🢖
‌Y‌
Kolbe′s‌Electrolysis
◂––––––––––––
‌ ‌Z+H2O

©
Q.138 Correct
Q.138 In-correct
Q.138 Unattempt
Which one of the following compounds will not show geometrical isomerism?
©
Which one of the following compounds will not show geometrical isomerism?
©
Q.139 Correct
Q.139 In-correct
Q.139 Unattempt
A compound is formed by X and Y elements. Atoms of Y (anions) form hcp lattice. Atoms of X (cations) are in some octahedral holes. The formula of the compound is XY3 . What is the fraction of octahedral holes unoccupied by X?
©
A compound is formed by X and Y elements. Atoms of Y (anions) form hcp lattice. Atoms of X (cations) are in some octahedral holes. The formula of the compound is XY3 . What is the fraction of octahedral holes unoccupied by X?
©
Q.140 Correct
Q.140 In-correct
Q.140 Unattempt
At T(K), the vapour pressure of pure benzene is 0.85 bar. A non-volatile, non-electrolyte substance weighing 0.5 g when added to 39 g of benzene, the vapour pressure of the solution is 0.845 bar. The molar mass ( in g mol‌−1 ) of the substance is
©
At T(K), the vapour pressure of pure benzene is 0.85 bar. A non-volatile, non-electrolyte substance weighing 0.5 g when added to 39 g of benzene, the vapour pressure of the solution is 0.845 bar. The molar mass ( in g mol‌−1 ) of the substance is
©
Q.141 Correct
Q.141 In-correct
Q.141 Unattempt
0.1 m solution each of sodium sulphate, urea and sodium chloride are taken. The correct ratio of elevation of boiling point of these solutions is
©
0.1 m solution each of sodium sulphate, urea and sodium chloride are taken. The correct ratio of elevation of boiling point of these solutions is
©
Q.142 Correct
Q.142 In-correct
Q.142 Unattempt
Using the standard electrode potentials given below identify the correct statements from the following
Fe2++2e−→Fe;E°=−0.44V
Cu2++2e−→Cu;E°=+0.34V
Ag++e−→Ag;E°=+0.80V
a) Copper can displace iron from FeSO‌4 solution
b) Iron can displace copper from CuSO‌4 solution
c) Silver can displace copper from CuSO‌4 solution
d) Iron can displace silver from AgNO‌3 solution
©
Using the standard electrode potentials given below identify the correct statements from the following
Fe2++2e−→Fe;E°=−0.44V
Cu2++2e−→Cu;E°=+0.34V
Ag++e−→Ag;E°=+0.80V
a) Copper can displace iron from FeSO‌4 solution
b) Iron can displace copper from CuSO‌4 solution
c) Silver can displace copper from CuSO‌4 solution
d) Iron can displace silver from AgNO‌3 solution
©
Q.143 Correct
Q.143 In-correct
Q.143 Unattempt
At T(K) if the rate constant for a zero order reaction is 2.5×10−3Ms−1 , the time required for the initial concentration of reactant, R to fall from 0.10 M to 0.075 M at the same temperature in seconds is
©
At T(K) if the rate constant for a zero order reaction is 2.5×10−3Ms−1 , the time required for the initial concentration of reactant, R to fall from 0.10 M to 0.075 M at the same temperature in seconds is
©
Q.144 Correct
Q.144 In-correct
Q.144 Unattempt
The temperature above which, formation of micelles takes place is called
©
The temperature above which, formation of micelles takes place is called
©
Q.145 Correct
Q.145 In-correct
Q.145 Unattempt
The method used for producing semiconductor grade metals of high purity is
©
The method used for producing semiconductor grade metals of high purity is
©
Q.146 Correct
Q.146 In-correct
Q.146 Unattempt
The element X on reaction with conc. HNO‌3 forms two acidic oxides A and B of different shapes. Element Z on reaction with conc. H‌2 SO‌4 forms two acidic oxides A and D of different shapes. What are X and Z?
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The element X on reaction with conc. HNO‌3 forms two acidic oxides A and B of different shapes. Element Z on reaction with conc. H‌2 SO‌4 forms two acidic oxides A and D of different shapes. What are X and Z?
©
Q.147 Correct
Q.147 In-correct
Q.147 Unattempt
Identify the correct statement from the following
©
Identify the correct statement from the following
©
Q.148 Correct
Q.148 In-correct
Q.148 Unattempt
Identify the reaction in which monobasic and dibasic acids are formed
©
Identify the reaction in which monobasic and dibasic acids are formed
©
Q.149 Correct
Q.149 In-correct
Q.149 Unattempt
Catalyst used in the manufacture of high density polythene is
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Catalyst used in the manufacture of high density polythene is
©
Q.150 Correct
Q.150 In-correct
Q.150 Unattempt
Identify the corret statements from the following
a) Eu2+‌and‌Y‌b2+ are reducing agents
b) The elctronic configuration of Pr3+ is [Xe]4f3
c) Aqueous solution of LaCl‌3 is colourless
©
Identify the corret statements from the following
a) Eu2+‌and‌Y‌b2+ are reducing agents
b) The elctronic configuration of Pr3+ is [Xe]4f3
c) Aqueous solution of LaCl‌3 is colourless
©
Q.151 Correct
Q.151 In-correct
Q.151 Unattempt
The polydispersity index of a polymer containing 10 molecules with molecular mass 1.0×104 and 10 molecules with molecular mass 1.0×105 is approximately
©
The polydispersity index of a polymer containing 10 molecules with molecular mass 1.0×104 and 10 molecules with molecular mass 1.0×105 is approximately
©
Q.152 Correct
Q.152 In-correct
Q.152 Unattempt
β−D−(−)− Fructofuranose is
©
β−D−(−)− Fructofuranose is
©
Q.153 Correct
Q.153 In-correct
Q.153 Unattempt
Assertion (A) : Shape of the receptor changes after attachment of chemical messenger
Reason (R) : Receptor does not regain original shape after removal of chemical messenger
The correct answer is
©
Assertion (A) : Shape of the receptor changes after attachment of chemical messenger
Reason (R) : Receptor does not regain original shape after removal of chemical messenger
The correct answer is
©
Q.154 Correct
Q.154 In-correct
Q.154 Unattempt
Identify chiral molecules from the following
 
©
Identify chiral molecules from the following
 
©
Q.155 Correct
Q.155 In-correct
Q.155 Unattempt
Isopropyl benzene on aerial oxidation followed by acid hydrolysis of the resulting compound yields
©
Isopropyl benzene on aerial oxidation followed by acid hydrolysis of the resulting compound yields
©
Q.156 Correct
Q.156 In-correct
Q.156 Unattempt
Reimer-Tiemann reaction involves the formation of X from phenol through intermediate Y. What are X and Y?
©
Reimer-Tiemann reaction involves the formation of X from phenol through intermediate Y. What are X and Y?
©
Q.157 Correct
Q.157 In-correct
Q.157 Unattempt
Q.158 Correct
Q.158 In-correct
Q.158 Unattempt

The hydrogen atom bonded to the carbon designated by which number in  is most acidic?

The hydrogen atom bonded to the carbon designated by which number in  is most acidic?
Q.159 Correct
Q.159 In-correct
Q.159 Unattempt
The order of strengths of the following carboxylic acids is
a) CH3−CH2‌COOH
b) CH3−COOH
c) C6H5−COOH
d) C6H5−CH2‌COOH
©
The order of strengths of the following carboxylic acids is
a) CH3−CH2‌COOH
b) CH3−COOH
c) C6H5−COOH
d) C6H5−CH2‌COOH
©
Q.160 Correct
Q.160 In-correct
Q.160 Unattempt

What are A, B and C in the following reaction? Arene diazonium fluoroborate 

What are A, B and C in the following reaction? Arene diazonium fluoroborate 
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