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Solution
Q.1 Correct
Q.1 In-correct
Q.1 Unattempt
Match the functions of List - I with their nature in List - II and choose the correct option.

Then the correct match is
Match the functions of List - I with their nature in List - II and choose the correct option.

Then the correct match is
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt
If [x] denotes the greatest integer function, then the domain of the function
f (x) = √
x−[x]
log(x2−x)
 is
If [x] denotes the greatest integer function, then the domain of the function
f (x) = √
x−[x]
log(x2−x)
 is
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt
Assertion (A) : If |x| < 1 , then
∞
Σ
n=0
(−1)nxn+1 =
x
x+1
Reason (R) : If |x| < 1 , then (1+x)−1 = 1 - x + x2−x3 + ...
Which one of the following is true?
Assertion (A) : If |x| < 1 , then
∞
Σ
n=0
(−1)nxn+1 =
x
x+1
Reason (R) : If |x| < 1 , then (1+x)−1 = 1 - x + x2−x3 + ...
Which one of the following is true?
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt
If A = [
123
135
216
] , then (Adj(Adj‌A))−1 =
If A = [
123
135
216
] , then (Adj(Adj‌A))−1 =
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt
If |
x2+3xx+1x−3
x−12−xx+4
x−3x−33x
| = a0+a1x+a2x2+a3x2+a4x4 , then (a1+a3) + 2 (a0+a2+a4) =
If |
x2+3xx+1x−3
x−12−xx+4
x−3x−33x
| = a0+a1x+a2x2+a3x2+a4x4 , then (a1+a3) + 2 (a0+a2+a4) =
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt
Let AX = D be a system of three linear non homogeneous equations. If |A| = 0 and rank (A) = rank ([AD]) = α, then
Let AX = D be a system of three linear non homogeneous equations. If |A| = 0 and rank (A) = rank ([AD]) = α, then
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt
If x + iy = (1+i)6−(1−i)6 , then which one of the following is true ?
If x + iy = (1+i)6−(1−i)6 , then which one of the following is true ?
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt
i2+i3 + ... + i4000 =
i2+i3 + ... + i4000 =
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt
If 1, ω and ω2 are the cube roots of unity, then (a + b + c) (a + bω + cω2) (a + bω2 + cω) =
If 1, ω and ω2 are the cube roots of unity, then (a + b + c) (a + bω + cω2) (a + bω2 + cω) =
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt
If ak = cos αk + i sin αk , k = 1 , 2 , 3 and a1,a2,a3 are the roots of the equation x3+bx+c = 0 , then the real part of b =
If ak = cos αk + i sin αk , k = 1 , 2 , 3 and a1,a2,a3 are the roots of the equation x3+bx+c = 0 , then the real part of b =
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt
The set of all values of 'a' for which the expression
ax2−2x+3
2x−3x2+a
 assumes all real values for real values of x is
The set of all values of 'a' for which the expression
ax2−2x+3
2x−3x2+a
 assumes all real values for real values of x is
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt
If both the roots of the equation x2 - 4ax + 1 - 3a + 4a2 = 0 exceed 1, then a lies in the interval
If both the roots of the equation x2 - 4ax + 1 - 3a + 4a2 = 0 exceed 1, then a lies in the interval
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt
If the cubic equation x3−ax2 + ax - 1 = 0 is identical with the cubic equation whose roots are the squares of the roots of the given cubic equation, then the non zero real value of 'a' is
If the cubic equation x3−ax2 + ax - 1 = 0 is identical with the cubic equation whose roots are the squares of the roots of the given cubic equation, then the non zero real value of 'a' is
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt
If α , β , γ are the roots of the equation x3+px2 + qx + r = 0 , then (α + β) (β + γ) (γ + α) =
If α , β , γ are the roots of the equation x3+px2 + qx + r = 0 , then (α + β) (β + γ) (γ + α) =
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt
Let x denote the number of ways of arranging w boys and m girls in a row so that no two boys sit together. If y and r give the number of ways of arranging m boys and m girls in a row and around a circular table respectively so that boys and girls sit alternately, then x : y : z =
Let x denote the number of ways of arranging w boys and m girls in a row so that no two boys sit together. If y and r give the number of ways of arranging m boys and m girls in a row and around a circular table respectively so that boys and girls sit alternately, then x : y : z =
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt
The number of even numbers greater than 1000000 that can be formed using all the digits 1, 2, 0, 2, 4, 2 and 4 is
The number of even numbers greater than 1000000 that can be formed using all the digits 1, 2, 0, 2, 4, 2 and 4 is
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt
The greatest integer less than or equal to (√3+2)5 is
The greatest integer less than or equal to (√3+2)5 is
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt
The sixth term in the expansion of (3−√
17
4
+3√2)10 is a
The sixth term in the expansion of (3−√
17
4
+3√2)10 is a
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt
Let
1
(x2−3)2
 =
A1
x−√3
+
A2
(x−√3)2
 +
A3
x+√3
 +
A4
(x+√3)2
. Then consider the following statements :
i) All the Ai's are not distinct
ii) There exists a pair, Ap and Aq such that Ap2 = Aq2 (p ≠ q)
iii)
4
Σ
i=1
Ai =
1
6
iv)
4
Σ
i=1
Ai = 1
Which one of the following is true?
Let
1
(x2−3)2
 =
A1
x−√3
+
A2
(x−√3)2
 +
A3
x+√3
 +
A4
(x+√3)2
. Then consider the following statements :
i) All the Ai's are not distinct
ii) There exists a pair, Ap and Aq such that Ap2 = Aq2 (p ≠ q)
iii)
4
Σ
i=1
Ai =
1
6
iv)
4
Σ
i=1
Ai = 1
Which one of the following is true?
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt
The period of cos (x + 8x + 27x + ... + n3x) is
The period of cos (x + 8x + 27x + ... + n3x) is
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt
sin2 (3°) + sin2 (6°) + sin2 (9°) + ... + sin2 (84°) + sin2 (87°) + sin2 (90°) =
sin2 (3°) + sin2 (6°) + sin2 (9°) + ... + sin2 (84°) + sin2 (87°) + sin2 (90°) =
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt
cos
π
7
 + cos
2π
7
 + cos
3π
7
 - cos
4π
7
 + cos
5π
7
 - cos
6π
7
 =
cos
π
7
 + cos
2π
7
 + cos
3π
7
 - cos
4π
7
 + cos
5π
7
 - cos
6π
7
 =
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt
The number of integral values of k for which the equation 7 cos x + 5 sin x = 2k + 1 has a solution is
The number of integral values of k for which the equation 7 cos x + 5 sin x = 2k + 1 has a solution is
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt
sec (tan−1
y
2
) =
sec (tan−1
y
2
) =
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt
The number of roots of the equation √2+ecosh−1x−esinh−1x = 0 is
The number of roots of the equation √2+ecosh−1x−esinh−1x = 0 is
Q.26 Correct
Q.26 In-correct
Q.26 Unattempt
A wire of length 44 cm is bent into an arc of a circle of radius 12 cm. The angle (in degrees) subtended by the arc at the centre of the circle is
A wire of length 44 cm is bent into an arc of a circle of radius 12 cm. The angle (in degrees) subtended by the arc at the centre of the circle is
Q.27 Correct
Q.27 In-correct
Q.27 Unattempt
In any triangle ABC, if a : b : c = 2 : 3 : 4, then R : r =
In any triangle ABC, if a : b : c = 2 : 3 : 4, then R : r =
Q.28 Correct
Q.28 In-correct
Q.28 Unattempt
Corresponding to a triangle .ABC. match the items given in List - I with the items given in List - II.

The correct match is
Corresponding to a triangle .ABC. match the items given in List - I with the items given in List - II.

The correct match is
Q.29 Correct
Q.29 In-correct
Q.29 Unattempt
Let the position vectors of two points A and B be
→
a
+
→
b
+
→
c
 and
→
a
−2
→
b
+3
→
c
 respectively. If the points P and Q divide AB in the ratio 1 : 3 internally and externally respectively, then 3 |
→
AB
| =
Let the position vectors of two points A and B be
→
a
+
→
b
+
→
c
 and
→
a
−2
→
b
+3
→
c
 respectively. If the points P and Q divide AB in the ratio 1 : 3 internally and externally respectively, then 3 |
→
AB
| =
Q.30 Correct
Q.30 In-correct
Q.30 Unattempt
If
→
a
,
→
b
 and
→
c
 are three non-collinear points and k
→
a
+2
→
b
+3
→
c
 is a point in the plane of
→
a
,
→
b
,
→
c
 then k =
If
→
a
,
→
b
 and
→
c
 are three non-collinear points and k
→
a
+2
→
b
+3
→
c
 is a point in the plane of
→
a
,
→
b
,
→
c
 then k =
Q.31 Correct
Q.31 In-correct
Q.31 Unattempt
If the vector
→
a
 = 3
^
j
+4
^
k
 is the sum of two vectors
→
a
1 and
→
a2
, vector
→
a
1 is parallel to
→
b
 =
^
i
+
^
j
 and vector
→
a
2 is perpendicular to
→
b
 , then
→
a
 =
If the vector
→
a
 = 3
^
j
+4
^
k
 is the sum of two vectors
→
a
1 and
→
a2
, vector
→
a
1 is parallel to
→
b
 =
^
i
+
^
j
 and vector
→
a
2 is perpendicular to
→
b
 , then
→
a
 =
Q.32 Correct
Q.32 In-correct
Q.32 Unattempt
The angle between the line of intersection of the two planes
→
r
.(2
^
i
+2
^
j
−3
^
k
) = 5 ,
→
r
.(3
^
i
+3
^
j
−5
^
k
) and the line
→
r
 = 3
^
i
+2
^
j
+
^
k
 + t(5
^
i
+5
^
j
−4
^
k
) is
The angle between the line of intersection of the two planes
→
r
.(2
^
i
+2
^
j
−3
^
k
) = 5 ,
→
r
.(3
^
i
+3
^
j
−5
^
k
) and the line
→
r
 = 3
^
i
+2
^
j
+
^
k
 + t(5
^
i
+5
^
j
−4
^
k
) is
Q.33 Correct
Q.33 In-correct
Q.33 Unattempt
Let
→
x
 =
^
i
+
^
j
 and
^
y
 = 3
^
i
−2
^
k
. Then the vectoe
→
r
 of magnitude √21 satisfying
→
r
×
→
x
 =
→
y
×
→
x
 and
→
r
×
→
y
 =
→
x
×
→
y
 is
Let
→
x
 =
^
i
+
^
j
 and
^
y
 = 3
^
i
−2
^
k
. Then the vectoe
→
r
 of magnitude √21 satisfying
→
r
×
→
x
 =
→
y
×
→
x
 and
→
r
×
→
y
 =
→
x
×
→
y
 is
Q.34 Correct
Q.34 In-correct
Q.34 Unattempt
The acute angle between
→
r
 = (−
^
i
+3
^
k
) + λ(2
^
i
+3
^
j
+6
^
k
) and
→
r
.(10
^
i
+2
^
j
−11
^
k
) = 3 is
The acute angle between
→
r
 = (−
^
i
+3
^
k
) + λ(2
^
i
+3
^
j
+6
^
k
) and
→
r
.(10
^
i
+2
^
j
−11
^
k
) = 3 is
Q.35 Correct
Q.35 In-correct
Q.35 Unattempt
In a data with 15 number of observations x1,x2,x3 , ... x15 ,
15
Σ
i=1
xi2 = 3600 and
15
Σ
i=1
x1 = 175. If the value of one observation 20 was found wrong and was replaced by its correct value 40, then the collected variance of that data is
In a data with 15 number of observations x1,x2,x3 , ... x15 ,
15
Σ
i=1
xi2 = 3600 and
15
Σ
i=1
x1 = 175. If the value of one observation 20 was found wrong and was replaced by its correct value 40, then the collected variance of that data is
Q.36 Correct
Q.36 In-correct
Q.36 Unattempt
If the coefficient of variation and variance of a frequency distribution are 7.2 and 3.24 respectively, then its mean is
If the coefficient of variation and variance of a frequency distribution are 7.2 and 3.24 respectively, then its mean is
Q.37 Correct
Q.37 In-correct
Q.37 Unattempt
If five dice are thrown simultaneously, then the probability that atleast three of them show the same numbered face is
If five dice are thrown simultaneously, then the probability that atleast three of them show the same numbered face is
Q.38 Correct
Q.38 In-correct
Q.38 Unattempt
If two unbiased dice are rolled simultaneously until a sum of the number appeared on these dice is either 7 or 11, then the probability that 7 comes before 11, is
If two unbiased dice are rolled simultaneously until a sum of the number appeared on these dice is either 7 or 11, then the probability that 7 comes before 11, is
Q.39 Correct
Q.39 In-correct
Q.39 Unattempt
A box contains 10 mangoes out of which 4 are spoiled. 2 mangoes are taken together at random. If one of them is found to be good, then the probability that the other is also good, is
A box contains 10 mangoes out of which 4 are spoiled. 2 mangoes are taken together at random. If one of them is found to be good, then the probability that the other is also good, is
Q.40 Correct
Q.40 In-correct
Q.40 Unattempt
Two dice are rolled. If a random variable X is defined as the absolute difference of the two numbers that appear on them, then the mean of X is
Two dice are rolled. If a random variable X is defined as the absolute difference of the two numbers that appear on them, then the mean of X is
Q.41 Correct
Q.41 In-correct
Q.41 Unattempt
If getting a head on a coin when it is tossed is considered as success, then the probability of having more number of failures when ten fan coins are tossed simultaneously, is
If getting a head on a coin when it is tossed is considered as success, then the probability of having more number of failures when ten fan coins are tossed simultaneously, is
Q.42 Correct
Q.42 In-correct
Q.42 Unattempt
The set of all points that forms a triangle of area 15 sq. units with the points (1, - 2) and (- 5, 3) lies on
The set of all points that forms a triangle of area 15 sq. units with the points (1, - 2) and (- 5, 3) lies on
Q.43 Correct
Q.43 In-correct
Q.43 Unattempt
Suppose the new axes X, Y are generated by rotating the coordinate axes y. y about the origin through an angle of 30° in the anticlockwise direction. Then the transformed equation of x2+2√3 xy - y2 = 2a2 with respect to new axes, X , Y is
Suppose the new axes X, Y are generated by rotating the coordinate axes y. y about the origin through an angle of 30° in the anticlockwise direction. Then the transformed equation of x2+2√3 xy - y2 = 2a2 with respect to new axes, X , Y is
Q.44 Correct
Q.44 In-correct
Q.44 Unattempt
A line L makes intercepts a and b on the coordinate axes. The axes are rotated through an angle θ in the positive direction, keeping the origin fixed. If the line L makes intercepts p and q on the new coordinate axes, then
1
a2
+
1
b2
=
A line L makes intercepts a and b on the coordinate axes. The axes are rotated through an angle θ in the positive direction, keeping the origin fixed. If the line L makes intercepts p and q on the new coordinate axes, then
1
a2
+
1
b2
=
Q.45 Correct
Q.45 In-correct
Q.45 Unattempt
If m1,m2 (m1 > m2) are the slopes of the lines which make an angle of 30° with the line joining the points (1 , 2) and (3 , 4) , then
m1
m2
 =
If m1,m2 (m1 > m2) are the slopes of the lines which make an angle of 30° with the line joining the points (1 , 2) and (3 , 4) , then
m1
m2
 =
Q.46 Correct
Q.46 In-correct
Q.46 Unattempt
If A (-2, 1), B (0, -2), C (1, 2) are the vertices of a triangle ABC, then the perpendicular distance from its circumcentre to the side BC is
If A (-2, 1), B (0, -2), C (1, 2) are the vertices of a triangle ABC, then the perpendicular distance from its circumcentre to the side BC is
Q.47 Correct
Q.47 In-correct
Q.47 Unattempt
If one of the lines ax2+2hxy+by2 = 0 bisects the angle between the positive coordinate axes, then
If one of the lines ax2+2hxy+by2 = 0 bisects the angle between the positive coordinate axes, then
Q.48 Correct
Q.48 In-correct
Q.48 Unattempt
The equation of the pair of perpendicular lines passing through origin and forming an isoceles triangle with the line 2x + 3y = 6 is
The equation of the pair of perpendicular lines passing through origin and forming an isoceles triangle with the line 2x + 3y = 6 is
Q.49 Correct
Q.49 In-correct
Q.49 Unattempt
If one of the diameters of the circle x2+y2 - 2x + 6y + 6 = 0 is a chord to the circle with centre (2, 1), then the radius of the bigger circle is
If one of the diameters of the circle x2+y2 - 2x + 6y + 6 = 0 is a chord to the circle with centre (2, 1), then the radius of the bigger circle is
Q.50 Correct
Q.50 In-correct
Q.50 Unattempt
The line 3x - y + k = 0 touches the circle x2+y2 + 4x - 6y + 3 = 0. If k1,k2 (k1 < k2) are the two values of k, then the equation of the chord of contact of the point (k1,k2) with respect to the given circle is
The line 3x - y + k = 0 touches the circle x2+y2 + 4x - 6y + 3 = 0. If k1,k2 (k1 < k2) are the two values of k, then the equation of the chord of contact of the point (k1,k2) with respect to the given circle is
Q.51 Correct
Q.51 In-correct
Q.51 Unattempt
If the line ax + by = 1 is a tangent to this circle Sr = x2+y2−r2 = 0 , then which one of the following is true?
If the line ax + by = 1 is a tangent to this circle Sr = x2+y2−r2 = 0 , then which one of the following is true?
Q.52 Correct
Q.52 In-correct
Q.52 Unattempt
Each of the two orthogonal circles C1 and C2 passes through both the points (2 , 0) and (- 2 , 0). If y = mx + c is a common tangent to these circles, then
Each of the two orthogonal circles C1 and C2 passes through both the points (2 , 0) and (- 2 , 0). If y = mx + c is a common tangent to these circles, then
Q.53 Correct
Q.53 In-correct
Q.53 Unattempt
The equation of the circle whose diameter is the common chord of the circles x2+y2 - 3x + y - 10 = 0 and x2+y2 - x + 2y - 20 = 0 is
The equation of the circle whose diameter is the common chord of the circles x2+y2 - 3x + y - 10 = 0 and x2+y2 - x + 2y - 20 = 0 is
Q.54 Correct
Q.54 In-correct
Q.54 Unattempt
Study the following statements.
I. The vertex of the parabola x = ly2 + my + n is (n−
m2
4l
,−
m
2l
)
II. The focus of the parabola y = lx2 + mx + n is (n+
1−m2
4l
,−
m
2l
)
III. The pole of the line lx + my + n = 0 with respect to the parabola x2 = 4ay is (−
2al
m
,
n
m
)
Then, the collect option among the following is
Study the following statements.
I. The vertex of the parabola x = ly2 + my + n is (n−
m2
4l
,−
m
2l
)
II. The focus of the parabola y = lx2 + mx + n is (n+
1−m2
4l
,−
m
2l
)
III. The pole of the line lx + my + n = 0 with respect to the parabola x2 = 4ay is (−
2al
m
,
n
m
)
Then, the collect option among the following is
Q.55 Correct
Q.55 In-correct
Q.55 Unattempt
Let P represent the point (3 , 6) on the parabola y2 = 12x. For the parabola y2 = 12x, if l1 is the length of the normal chord drawn at P and l2 is the length of the focal chord drawn through P, then
l1
l2
 =
Let P represent the point (3 , 6) on the parabola y2 = 12x. For the parabola y2 = 12x, if l1 is the length of the normal chord drawn at P and l2 is the length of the focal chord drawn through P, then
l1
l2
 =
Q.56 Correct
Q.56 In-correct
Q.56 Unattempt
A tangent is drawn at (3√3cosθ,sinθ) (0<θ<
π
2
) to the ellipse
x2
27
+
y2
1
 = 1. The value of θ for which the sum of the intercepts on the coordinate axes made by this tangent attains the minimum, is
A tangent is drawn at (3√3cosθ,sinθ) (0<θ<
π
2
) to the ellipse
x2
27
+
y2
1
 = 1. The value of θ for which the sum of the intercepts on the coordinate axes made by this tangent attains the minimum, is
Q.57 Correct
Q.57 In-correct
Q.57 Unattempt
A line perpendicular to the X-axis cuts the circle x2+y2 = 9 at A and the ellipse 4x2+9y2 = 36 at B such that A and B lie in the same quadrant. If θ is the greatest acute angle between the tangents drawn to the curves at A and B, then tan θ =
A line perpendicular to the X-axis cuts the circle x2+y2 = 9 at A and the ellipse 4x2+9y2 = 36 at B such that A and B lie in the same quadrant. If θ is the greatest acute angle between the tangents drawn to the curves at A and B, then tan θ =
Q.58 Correct
Q.58 In-correct
Q.58 Unattempt
If e1 is the eccentricity of the ellipse
x2
16
+
y2
15
 = 1 and e2 is the eccentricity of a hyperbola passing through the foci of the given ellipse and e1e2 = 1, then the equation of such a hyperbola among the following is
If e1 is the eccentricity of the ellipse
x2
16
+
y2
15
 = 1 and e2 is the eccentricity of a hyperbola passing through the foci of the given ellipse and e1e2 = 1, then the equation of such a hyperbola among the following is
Q.59 Correct
Q.59 In-correct
Q.59 Unattempt
If (1 , 0 , 3), (2 , 1 , 5), (- 2 , 3 , 6) are the midpoints of the sides of a triangle, then the centroid of the triangle is
If (1 , 0 , 3), (2 , 1 , 5), (- 2 , 3 , 6) are the midpoints of the sides of a triangle, then the centroid of the triangle is
Q.60 Correct
Q.60 In-correct
Q.60 Unattempt
If a plane P passes through the points (1 , 0 , 0) , (0 , 1 , 0) and makes an angle
π
4
 with the plane x + y = 3 , then the direction ratios of a normal to the plane P is
If a plane P passes through the points (1 , 0 , 0) , (0 , 1 , 0) and makes an angle
π
4
 with the plane x + y = 3 , then the direction ratios of a normal to the plane P is
Q.61 Correct
Q.61 In-correct
Q.61 Unattempt
A variable plane is at a distance of 6 units from the origin. If it meets the coordinate axes in A, B and C. then the equation of the locus of the centroid of the Δ ABC is
A variable plane is at a distance of 6 units from the origin. If it meets the coordinate axes in A, B and C. then the equation of the locus of the centroid of the Δ ABC is
Q.62 Correct
Q.62 In-correct
Q.62 Unattempt
lim
x→∞
(
2x2+3x+4
x2−3x+5
)
3|x|+1
2|x|−1
 =
lim
x→∞
(
2x2+3x+4
x2−3x+5
)
3|x|+1
2|x|−1
 =
Q.63 Correct
Q.63 In-correct
Q.63 Unattempt
If 'a' is the point of discontinuity of the function f (x) =
{
cos2xfor−∞<x<0
e3xfor‌0≤x<3
x2−4x+3for‌3≤x≤6
log(15x−89)
x−6
for‌x>6
then ,
lim
x→a
x2−9
x3−5x2+9x−9
 =
If 'a' is the point of discontinuity of the function f (x) =
{
cos2xfor−∞<x<0
e3xfor‌0≤x<3
x2−4x+3for‌3≤x≤6
log(15x−89)
x−6
for‌x>6
then ,
lim
x→a
x2−9
x3−5x2+9x−9
 =
Q.64 Correct
Q.64 In-correct
Q.64 Unattempt
If y = (x + 1) (x2 + 1) (x4 + 1) (x8 + 1), then
lim
x→−1
dy
dx
 =
If y = (x + 1) (x2 + 1) (x4 + 1) (x8 + 1), then
lim
x→−1
dy
dx
 =
Q.65 Correct
Q.65 In-correct
Q.65 Unattempt
f (x) is a twice differentiable function such that f" (x) = - f (x) and f' (x) = g (x). If h (x) = (f(x))2+(g(x))2 and h (1) = 2 , then h (2) =
f (x) is a twice differentiable function such that f" (x) = - f (x) and f' (x) = g (x). If h (x) = (f(x))2+(g(x))2 and h (1) = 2 , then h (2) =
Q.66 Correct
Q.66 In-correct
Q.66 Unattempt
If y = √x+√y+√x+√y+...∞ , then
dy
dx
 =
If y = √x+√y+√x+√y+...∞ , then
dy
dx
 =
Q.67 Correct
Q.67 In-correct
Q.67 Unattempt
The Tangent of the angle between the curves xy = 1 and x2 + 8y = 0 is
The Tangent of the angle between the curves xy = 1 and x2 + 8y = 0 is
Q.68 Correct
Q.68 In-correct
Q.68 Unattempt
The slope of the tangent at (1 , 2) to the curve x = t2 - 7t + 7 and y = t2 - 4t - 10 is
The slope of the tangent at (1 , 2) to the curve x = t2 - 7t + 7 and y = t2 - 4t - 10 is
Q.69 Correct
Q.69 In-correct
Q.69 Unattempt
Consider the function f (x) = 2x3−3x2 - x + 1 and the intervals
I1 = [- 1 , 0] , I2 = [0 , 1] , I3 = [1 , 2] , I4 = [- 2 , - 1].
Then,
Consider the function f (x) = 2x3−3x2 - x + 1 and the intervals
I1 = [- 1 , 0] , I2 = [0 , 1] , I3 = [1 , 2] , I4 = [- 2 , - 1].
Then,
Q.70 Correct
Q.70 In-correct
Q.70 Unattempt
If f (x) =
x+1
∫
x
e−t2 dt , then the interval in which f (x) is decreasing is
If f (x) =
x+1
∫
x
e−t2 dt , then the interval in which f (x) is decreasing is
Q.71 Correct
Q.71 In-correct
Q.71 Unattempt
If ∫
cosx+x
1+sinx
 dx = f (x) + ∫
3cos
x
2
−sin
x
2
cos
x
2
+sin
x
2
 dx + c , then f (x) =
If ∫
cosx+x
1+sinx
 dx = f (x) + ∫
3cos
x
2
−sin
x
2
cos
x
2
+sin
x
2
 dx + c , then f (x) =
Q.72 Correct
Q.72 In-correct
Q.72 Unattempt
∫
√cos2x
sinx
 dx =
∫
√cos2x
sinx
 dx =
Q.73 Correct
Q.73 In-correct
Q.73 Unattempt
If ∫
(2x+3)
x(x+1)(x+2)(x+3)+1
 dx = -
1
px2+qr+r
 + c , then
2p−q
r
 =
If ∫
(2x+3)
x(x+1)(x+2)(x+3)+1
 dx = -
1
px2+qr+r
 + c , then
2p−q
r
 =
Q.74 Correct
Q.74 In-correct
Q.74 Unattempt
∫ (logx)2 dx =
∫ (logx)2 dx =
Q.75 Correct
Q.75 In-correct
Q.75 Unattempt
lim
n→∞
k
n2+k2
 =
lim
n→∞
k
n2+k2
 =
Q.76 Correct
Q.76 In-correct
Q.76 Unattempt
10
∫
0
(5−√10x−x2) dx =
10
∫
0
(5−√10x−x2) dx =
Q.77 Correct
Q.77 In-correct
Q.77 Unattempt
Area of the region (in square units) bounded by the curves y = √x , x = √y and the lines x = 1 , x = 4 is
Area of the region (in square units) bounded by the curves y = √x , x = √y and the lines x = 1 , x = 4 is
Q.78 Correct
Q.78 In-correct
Q.78 Unattempt
The differential equation representing the family of circles of constant radius r is
The differential equation representing the family of circles of constant radius r is
Q.79 Correct
Q.79 In-correct
Q.79 Unattempt
The solution of the differential equation (2x - 3y + 5) dx + (9y - 6x - 7) dy = 0 is
The solution of the differential equation (2x - 3y + 5) dx + (9y - 6x - 7) dy = 0 is
Q.80 Correct
Q.80 In-correct
Q.80 Unattempt
The solution of the differential equation √1−y2 dx + x dy - sin−1y dy = 0 is
The solution of the differential equation √1−y2 dx + x dy - sin−1y dy = 0 is
Q.81 Correct
Q.81 In-correct
Q.81 Unattempt
Match the following fundamental forces of nature with their relative strength.

The correct match is
Match the following fundamental forces of nature with their relative strength.

The correct match is
Q.82 Correct
Q.82 In-correct
Q.82 Unattempt
Identify the incorrect statement among the following.
Identify the incorrect statement among the following.
Q.83 Correct
Q.83 In-correct
Q.83 Unattempt
Ball-1 is dropped from the top of a building from rest. At the same moment, ball- 2 is thrown upward towards ball- 1 with a speed 14m∕s from a point 21m below the top of building. How far will the ball-1 have dropped when it passes ball-2. (Assume g=10m∕s2 )
Ball-1 is dropped from the top of a building from rest. At the same moment, ball- 2 is thrown upward towards ball- 1 with a speed 14m∕s from a point 21m below the top of building. How far will the ball-1 have dropped when it passes ball-2. (Assume g=10m∕s2 )
Q.84 Correct
Q.84 In-correct
Q.84 Unattempt
Rain is falling at an angle of 30° from the vertical clue to the wind with a speed of 40 m/s. A car is travelling horizontally in the direction opposite to the wind, at a speed of 40 m/s. At what angle from the vertical will it experience the ram falling from?

Rain is falling at an angle of 30° from the vertical clue to the wind with a speed of 40 m/s. A car is travelling horizontally in the direction opposite to the wind, at a speed of 40 m/s. At what angle from the vertical will it experience the ram falling from?

Q.85 Correct
Q.85 In-correct
Q.85 Unattempt
Two touching blocks 1 and 2 are placed on an inclined plane forming an angle 60° with the horizontal. The masses are m1 and m2 and the coefficient of friction between the inclined plane and the two blocks are 1.5 µ and 1.0 µ respectively. The force of reaction between blocks during the motion is
(g = acceleration due to gravity)
Two touching blocks 1 and 2 are placed on an inclined plane forming an angle 60° with the horizontal. The masses are m1 and m2 and the coefficient of friction between the inclined plane and the two blocks are 1.5 µ and 1.0 µ respectively. The force of reaction between blocks during the motion is
(g = acceleration due to gravity)
Q.86 Correct
Q.86 In-correct
Q.86 Unattempt
Three blocks are connected by massless strings on a frictionless inclined plane of 30° as shown in the figure. A force of 104 N is applied upward along the incline to mass m3 causing an upward motion of the blocks. What is the acceleration of the blocks?
(Assume g = 10 m/‌2)

Three blocks are connected by massless strings on a frictionless inclined plane of 30° as shown in the figure. A force of 104 N is applied upward along the incline to mass m3 causing an upward motion of the blocks. What is the acceleration of the blocks?
(Assume g = 10 m/‌2)

Q.87 Correct
Q.87 In-correct
Q.87 Unattempt
Consider a system of two masses and a pulley shown in the figure. The coefficient of friction between the two blocks and also between block and table is 0.1. Find the force. F. that must be given to the 0.8 kg block such that it attains acceleration of 5 m/s2.
(Assume g = 10 m/s2)

Consider a system of two masses and a pulley shown in the figure. The coefficient of friction between the two blocks and also between block and table is 0.1. Find the force. F. that must be given to the 0.8 kg block such that it attains acceleration of 5 m/s2.
(Assume g = 10 m/s2)

Q.88 Correct
Q.88 In-correct
Q.88 Unattempt
A box of mass 3 kg moves on a horizontal frictionless table and collides with another box of mass 3 kg initially at rest on the edge of the table at height 1 m. The speed of the moving box just before the collision is 4 m/s. The two boxes stick together and fall from the table. The kinetic energy just before the boxes strike the floor is
(Assume g = 10 m/s2)
A box of mass 3 kg moves on a horizontal frictionless table and collides with another box of mass 3 kg initially at rest on the edge of the table at height 1 m. The speed of the moving box just before the collision is 4 m/s. The two boxes stick together and fall from the table. The kinetic energy just before the boxes strike the floor is
(Assume g = 10 m/s2)
Q.89 Correct
Q.89 In-correct
Q.89 Unattempt
A ball of mass 2 kg is thrown from a tall building with velocity
→
v
 = (20 m/s)
^
i
 + (24 m/s)
^
j
 at time t = 0 s. Change in the potential energy of the ball after t = 8 s is
(The ball is assumed to be in air during its motion between 0 s and 8 s,
^
i
 is along the horizontal and
^
j
 is along the vertical direction, let g = 10 m/s2)
A ball of mass 2 kg is thrown from a tall building with velocity
→
v
 = (20 m/s)
^
i
 + (24 m/s)
^
j
 at time t = 0 s. Change in the potential energy of the ball after t = 8 s is
(The ball is assumed to be in air during its motion between 0 s and 8 s,
^
i
 is along the horizontal and
^
j
 is along the vertical direction, let g = 10 m/s2)
Q.90 Correct
Q.90 In-correct
Q.90 Unattempt
Three balls A, B and C of masses 50 g, 100 g and 150 g respectively are placed at the vertices of an equilateral triangle. The length of each side is 1 m. If A is placed at (0, 0) and B is placed at (1, 0) m, find the coordinates (x, y) for the centre of mass of this system of balls
Three balls A, B and C of masses 50 g, 100 g and 150 g respectively are placed at the vertices of an equilateral triangle. The length of each side is 1 m. If A is placed at (0, 0) and B is placed at (1, 0) m, find the coordinates (x, y) for the centre of mass of this system of balls
Q.91 Correct
Q.91 In-correct
Q.91 Unattempt
Three bodies, a ring, a solid disc and a solid sphere roll down the same inclined plane without slipping. The radii of the bodies are identical and they start from rest. If VS, VR and VD are the speeds of the sphere, ring and disc respectively when they reach the bottom, then the collect option is
Three bodies, a ring, a solid disc and a solid sphere roll down the same inclined plane without slipping. The radii of the bodies are identical and they start from rest. If VS, VR and VD are the speeds of the sphere, ring and disc respectively when they reach the bottom, then the collect option is
Q.92 Correct
Q.92 In-correct
Q.92 Unattempt
A vertical spring mass system has the same time-period as a simple pendulum undergoing small oscillations. Now both of them are put in an elevator going downwards with an acceleration 5 m/s2. The ratio of time-period of the spring mass system to the time-period of the pendulum is (Assume g = 10 m/s2)

A vertical spring mass system has the same time-period as a simple pendulum undergoing small oscillations. Now both of them are put in an elevator going downwards with an acceleration 5 m/s2. The ratio of time-period of the spring mass system to the time-period of the pendulum is (Assume g = 10 m/s2)

Q.93 Correct
Q.93 In-correct
Q.93 Unattempt
Consider a spherical planet which is rotating about its axis such that the speed of a point on its equator is 'V' and the effective acceleration due to gravity on the equator is
1
3
 of its value at the poles. What is the escape velocity for a particle at the pole of this planet.
Consider a spherical planet which is rotating about its axis such that the speed of a point on its equator is 'V' and the effective acceleration due to gravity on the equator is
1
3
 of its value at the poles. What is the escape velocity for a particle at the pole of this planet.
Q.94 Correct
Q.94 In-correct
Q.94 Unattempt
Consider a system of blocks X. A and B as shown in the figure. The blocks A and B have equal mass and are connected by a massless string through a massless pully. The coefficient of friction between block A & X and B & X is 0.5. If block ‘X' moves on horizontal frictionless surface, what should be its minimum acceleration such that blocks A and B remain stationary,
(g = acceleration due to gravity)

Consider a system of blocks X. A and B as shown in the figure. The blocks A and B have equal mass and are connected by a massless string through a massless pully. The coefficient of friction between block A & X and B & X is 0.5. If block ‘X' moves on horizontal frictionless surface, what should be its minimum acceleration such that blocks A and B remain stationary,
(g = acceleration due to gravity)

Q.95 Correct
Q.95 In-correct
Q.95 Unattempt
How much pressure (in atm) is needed to compress a sample of water by 0.4%?
(Assume Bulk modulus of water ~ 2.0 x 109 Pa)
How much pressure (in atm) is needed to compress a sample of water by 0.4%?
(Assume Bulk modulus of water ~ 2.0 x 109 Pa)
Q.96 Correct
Q.96 In-correct
Q.96 Unattempt
The tension in a massless cable connected to an iron ball of 100 kg when it is submerged in sea water is (ρiron = 8 × 103 kg/m3 and ρsea‌water = 1000 kg/m3 , g = 10 m/s2)
The tension in a massless cable connected to an iron ball of 100 kg when it is submerged in sea water is (ρiron = 8 × 103 kg/m3 and ρsea‌water = 1000 kg/m3 , g = 10 m/s2)
Q.97 Correct
Q.97 In-correct
Q.97 Unattempt
The area of a circular copper coin increases by 0.4% when its temperature is raised by 100 °C. The coefficient of linear expansion of the coin is
The area of a circular copper coin increases by 0.4% when its temperature is raised by 100 °C. The coefficient of linear expansion of the coin is
Q.98 Correct
Q.98 In-correct
Q.98 Unattempt
A 210 W heater is used to heat 100 g water. The time required to raise the temperature of this water from 25 °C to 100 °C is (specific heat capacity of water = 4200 J/kg°C)
A 210 W heater is used to heat 100 g water. The time required to raise the temperature of this water from 25 °C to 100 °C is (specific heat capacity of water = 4200 J/kg°C)
Q.99 Correct
Q.99 In-correct
Q.99 Unattempt
One mole of nitrogen gas being initially at a temperature of T0 = 300 K is adiabatically compressed to increase its pressure 10 times. The final gas temperature after compression is (Assume nitrogen gas molecules as rigid diatomic and 100
1
7
 = 1.9)
One mole of nitrogen gas being initially at a temperature of T0 = 300 K is adiabatically compressed to increase its pressure 10 times. The final gas temperature after compression is (Assume nitrogen gas molecules as rigid diatomic and 100
1
7
 = 1.9)
Q.100 Correct
Q.100 In-correct
Q.100 Unattempt
Two gases A and B are contained in two separate, but otherwise identical containers. Gas A consists of monoatomic molecules, each with atomic mass of 4 u whereas, Gas B consists of rigid diatomic molecules, each with atomic mass of 20 u. If Gas A is kept at 27 °C, at what temperature should Gas B be kept so that both have the same r.m.s. speed?
Two gases A and B are contained in two separate, but otherwise identical containers. Gas A consists of monoatomic molecules, each with atomic mass of 4 u whereas, Gas B consists of rigid diatomic molecules, each with atomic mass of 20 u. If Gas A is kept at 27 °C, at what temperature should Gas B be kept so that both have the same r.m.s. speed?
Q.101 Correct
Q.101 In-correct
Q.101 Unattempt
Standing waves are produced in a string 16 m long. If there are 9 nodes between the two fixed ends of the string and the speed of the wave is 32 m/s, what is the frequency of the wave?
Standing waves are produced in a string 16 m long. If there are 9 nodes between the two fixed ends of the string and the speed of the wave is 32 m/s, what is the frequency of the wave?
Q.102 Correct
Q.102 In-correct
Q.102 Unattempt
A highway truck has two horns A and B. When sounded together, the driver records 50 beats in 10 seconds with horn B blowing and the truck moving towards a wall at a speed of 10 m/s, the driver noticed a beat frequency of 5 Hz with the echo. When frequency of A is decreased the beat frequency with two horns sounded together increases. Calculate the frequency of horn A. (Speed of sound = 330 m/s)
A highway truck has two horns A and B. When sounded together, the driver records 50 beats in 10 seconds with horn B blowing and the truck moving towards a wall at a speed of 10 m/s, the driver noticed a beat frequency of 5 Hz with the echo. When frequency of A is decreased the beat frequency with two horns sounded together increases. Calculate the frequency of horn A. (Speed of sound = 330 m/s)
Q.103 Correct
Q.103 In-correct
Q.103 Unattempt
When light of an unknown polarization is examined with a polaroid. it is found to exhibit maximum intensity I0 along y-axis and minimum intensity
2I0
3
 along x-axis. The intensity transmitted through a polaroid with pass axis at 45° to y-axis (in xy plane) is
When light of an unknown polarization is examined with a polaroid. it is found to exhibit maximum intensity I0 along y-axis and minimum intensity
2I0
3
 along x-axis. The intensity transmitted through a polaroid with pass axis at 45° to y-axis (in xy plane) is
Q.104 Correct
Q.104 In-correct
Q.104 Unattempt
In a Young’s double slit experiment, mth order and nth order of bright fringes are formed at point P on a distant screen, if monochromatic source of wavelength 400 nm and 600 nm are used respectively. The minimum value of and are. respectively
In a Young’s double slit experiment, mth order and nth order of bright fringes are formed at point P on a distant screen, if monochromatic source of wavelength 400 nm and 600 nm are used respectively. The minimum value of and are. respectively
Q.105 Correct
Q.105 In-correct
Q.105 Unattempt
Two small conducting balls of identical mass 20 g and identical charge 10−10 C hang from non conducting threads of length L = 300 cm. If the equilibrium separation of balls is and x ≪ L, then the magnitude of y is (Assume 4π∊0 =
1
9×109
 F/m and g = 10 m/s2)
Two small conducting balls of identical mass 20 g and identical charge 10−10 C hang from non conducting threads of length L = 300 cm. If the equilibrium separation of balls is and x ≪ L, then the magnitude of y is (Assume 4π∊0 =
1
9×109
 F/m and g = 10 m/s2)
Q.106 Correct
Q.106 In-correct
Q.106 Unattempt
The space between the two large parallel plates is filled with a material of uniform charge density 'ρ'. Assume that one of the plate is kept at x = 0. The potential at any point 'x' between these plates is given by
(A and B are constants)

The space between the two large parallel plates is filled with a material of uniform charge density 'ρ'. Assume that one of the plate is kept at x = 0. The potential at any point 'x' between these plates is given by
(A and B are constants)

Q.107 Correct
Q.107 In-correct
Q.107 Unattempt
Identify the correct statement among the following.
Identify the correct statement among the following.
Q.108 Correct
Q.108 In-correct
Q.108 Unattempt
For the circuits A and B as shown in the figure, identify the correct option

For the circuits A and B as shown in the figure, identify the correct option

Q.109 Correct
Q.109 In-correct
Q.109 Unattempt
Two infinitely long straight wires A and B. each carrying current I are placed on x and y axis respectively. The current in wires A and B flow along −
^
i
 and
^
j
 directions respectively. The force on a charged particle having charge q moving from position
→
r
 = d (
^
i
+
^
j
) with velocity
→
v
 = v
^
i
 is
Two infinitely long straight wires A and B. each carrying current I are placed on x and y axis respectively. The current in wires A and B flow along −
^
i
 and
^
j
 directions respectively. The force on a charged particle having charge q moving from position
→
r
 = d (
^
i
+
^
j
) with velocity
→
v
 = v
^
i
 is
Q.110 Correct
Q.110 In-correct
Q.110 Unattempt
Along straight wire carrying current 16 A is bent at 90° such that half of the wire lies along the positive x-axis and other half lies along the positive y-axis. What is the magnitude of magnetic field at the point
→
r
 = (−2
^
i
+0
^
j
) mm. (Assume
µ0
4π
 = 10−7Hm−1)
Along straight wire carrying current 16 A is bent at 90° such that half of the wire lies along the positive x-axis and other half lies along the positive y-axis. What is the magnitude of magnetic field at the point
→
r
 = (−2
^
i
+0
^
j
) mm. (Assume
µ0
4π
 = 10−7Hm−1)
Q.111 Correct
Q.111 In-correct
Q.111 Unattempt
The magnitude of the force vector acting on a unit length of a thin wire carrying a current I = 8 A at a point O. if the wire is bent as shown in the figure with a radius R = 10 π cm, is

The magnitude of the force vector acting on a unit length of a thin wire carrying a current I = 8 A at a point O. if the wire is bent as shown in the figure with a radius R = 10 π cm, is

Q.112 Correct
Q.112 In-correct
Q.112 Unattempt
A 10 Ω coil of 180 turns and diameter 4 cm is placed in a uniform magnetic field so that the magnetic flux is maximum through the coil's cross-sectional area. Mien the field is suddenly removed a charge of 360 µC flows through a 618 Ω galvanometer connected to the coil, find the magnetic field:
A 10 Ω coil of 180 turns and diameter 4 cm is placed in a uniform magnetic field so that the magnetic flux is maximum through the coil's cross-sectional area. Mien the field is suddenly removed a charge of 360 µC flows through a 618 Ω galvanometer connected to the coil, find the magnetic field:
Q.113 Correct
Q.113 In-correct
Q.113 Unattempt
An inductor coil is connected to a capacitor and an AC source of r.m.s. voltage 8 V in series. The r.m.s. current in the circuit is 16 A and is in phase with e.m.f. If this inductor coil is connected to 6 V DC battery, the magnitude of steady current is
An inductor coil is connected to a capacitor and an AC source of r.m.s. voltage 8 V in series. The r.m.s. current in the circuit is 16 A and is in phase with e.m.f. If this inductor coil is connected to 6 V DC battery, the magnitude of steady current is
Q.114 Correct
Q.114 In-correct
Q.114 Unattempt
An electromagnetic wave of frequency 3.0 MHz passes from vacuum into a non-magnetic medium with permittivity ∊ = 16 ∊0. Where ∊0 is the free-space permittivity. The change in wavelength is
An electromagnetic wave of frequency 3.0 MHz passes from vacuum into a non-magnetic medium with permittivity ∊ = 16 ∊0. Where ∊0 is the free-space permittivity. The change in wavelength is
Q.115 Correct
Q.115 In-correct
Q.115 Unattempt
A particle of charge q , mass m and energy E has de - Broglie wavelength λ. For a particle of charge 2q , mass 2m and energy 2E, the de - Broglie wavelength is
A particle of charge q , mass m and energy E has de - Broglie wavelength λ. For a particle of charge 2q , mass 2m and energy 2E, the de - Broglie wavelength is
Q.116 Correct
Q.116 In-correct
Q.116 Unattempt
The collision of an electron with kinetic energy 5.5 eV and a hydrogen atom in its ground state can be described as
The collision of an electron with kinetic energy 5.5 eV and a hydrogen atom in its ground state can be described as
Q.117 Correct
Q.117 In-correct
Q.117 Unattempt
An alloy is composed of two radioactive materials A and B having equal weight. The half life of A and B are 10 yrs and 20 yrs respectively. After a time 't', the alloy was found to consist of (
1
e
) kg of 'A' and 1 kg of B. If the atomic weight of A and B are same, then the value of 't' is (Assume ln 2 = 0.7)
An alloy is composed of two radioactive materials A and B having equal weight. The half life of A and B are 10 yrs and 20 yrs respectively. After a time 't', the alloy was found to consist of (
1
e
) kg of 'A' and 1 kg of B. If the atomic weight of A and B are same, then the value of 't' is (Assume ln 2 = 0.7)
Q.118 Correct
Q.118 In-correct
Q.118 Unattempt
When a zener diode is used as a regulator with zener voltage of 10 V. nearly five times the load current passes through the zener diode. What should be the series resistance for the zener diode, if load resistance is 2 kΩ and the unregulated voltage supplied is 16 V
When a zener diode is used as a regulator with zener voltage of 10 V. nearly five times the load current passes through the zener diode. What should be the series resistance for the zener diode, if load resistance is 2 kΩ and the unregulated voltage supplied is 16 V
Q.119 Correct
Q.119 In-correct
Q.119 Unattempt
The logic circuit below has the truth table, same as that of

The logic circuit below has the truth table, same as that of

Q.120 Correct
Q.120 In-correct
Q.120 Unattempt
A message signal is used to modulate a carrier frequency. If the peak voltages of message signal and carrier signal are increased by 0.1% and 0.3% respectively, then the percentage change in modulation index is
A message signal is used to modulate a carrier frequency. If the peak voltages of message signal and carrier signal are increased by 0.1% and 0.3% respectively, then the percentage change in modulation index is
Q.121 Correct
Q.121 In-correct
Q.121 Unattempt
From the following energy levels of hydrogen atom, the values of E∞ and E3 in J are, respectively

From the following energy levels of hydrogen atom, the values of E∞ and E3 in J are, respectively

Q.122 Correct
Q.122 In-correct
Q.122 Unattempt
Match the following

The correct answer is
Match the following

The correct answer is
Q.123 Correct
Q.123 In-correct
Q.123 Unattempt
In which group of the periodic table the element with Z = 120 be placed?
In which group of the periodic table the element with Z = 120 be placed?
Q.124 Correct
Q.124 In-correct
Q.124 Unattempt
Common oxidation state of f-block elements is in. The other stable oxidation states of
63
‌
Eu and
65
‌
Tb are respectively.
Common oxidation state of f-block elements is in. The other stable oxidation states of
63
‌
Eu and
65
‌
Tb are respectively.
Q.125 Correct
Q.125 In-correct
Q.125 Unattempt
How many of the following species are diamagnetic?
He2+,H2,H2+,H2−,He
How many of the following species are diamagnetic?
He2+,H2,H2+,H2−,He
Q.126 Correct
Q.126 In-correct
Q.126 Unattempt
In which of the following, hydrogen bonding is strongest?
In which of the following, hydrogen bonding is strongest?
Q.127 Correct
Q.127 In-correct
Q.127 Unattempt
What is the approximate most probable velocity of oxygen? If the kinetic energy of one mole of oxygen is 3741.3 J.
What is the approximate most probable velocity of oxygen? If the kinetic energy of one mole of oxygen is 3741.3 J.
Q.128 Correct
Q.128 In-correct
Q.128 Unattempt
What is the correction term in the pressure for real gas in comparison to the ideal gas?
What is the correction term in the pressure for real gas in comparison to the ideal gas?
Q.129 Correct
Q.129 In-correct
Q.129 Unattempt
In a 1 L vessel, 10 moles of methane and 50 moles of O2 are present. The number of moles of O2, water and CO2 present in the vessel are respectively after the vessel was heated to bum methane completely.
In a 1 L vessel, 10 moles of methane and 50 moles of O2 are present. The number of moles of O2, water and CO2 present in the vessel are respectively after the vessel was heated to bum methane completely.
Q.130 Correct
Q.130 In-correct
Q.130 Unattempt
Identify die oxidation states of Mn when MnO42− ion undergoes disproportionation reaction under acidic medium
Identify die oxidation states of Mn when MnO42− ion undergoes disproportionation reaction under acidic medium
Q.131 Correct
Q.131 In-correct
Q.131 Unattempt
Find the heat required to make water of 30 °C from 10 g of ice at 0.0 °C. (enthalpy of fusion of ice = 333.55 J g−1. Cp of water = 4.18 J g−1K−1)
Find the heat required to make water of 30 °C from 10 g of ice at 0.0 °C. (enthalpy of fusion of ice = 333.55 J g−1. Cp of water = 4.18 J g−1K−1)
Q.132 Correct
Q.132 In-correct
Q.132 Unattempt
For the reaction
0.5 C (s) + 0.5 CO2 (g) ⇌ CO (g)
the equilibrium pressure is 12 atm. If CO2 conversion is 50%, the value of Kp, in atm is
For the reaction
0.5 C (s) + 0.5 CO2 (g) ⇌ CO (g)
the equilibrium pressure is 12 atm. If CO2 conversion is 50%, the value of Kp, in atm is
Q.133 Correct
Q.133 In-correct
Q.133 Unattempt
What is the solubility product (Ksp) of calcium phosphate in pure water?
[S = molar solubility]
What is the solubility product (Ksp) of calcium phosphate in pure water?
[S = molar solubility]
Q.134 Correct
Q.134 In-correct
Q.134 Unattempt
What is the approximate volume (inmL) of 10 vol H2O2 solution that will react completely with 1 L of 0.02 M KMnO4 solution in acid medium?
What is the approximate volume (inmL) of 10 vol H2O2 solution that will react completely with 1 L of 0.02 M KMnO4 solution in acid medium?
Q.135 Correct
Q.135 In-correct
Q.135 Unattempt
Which of the following products are formed on hydrolysis of NaO2 ?
a) NaOH
b) H2O2
c) O2
d) H2O
Which of the following products are formed on hydrolysis of NaO2 ?
a) NaOH
b) H2O2
c) O2
d) H2O
Q.136 Correct
Q.136 In-correct
Q.136 Unattempt
Hie oxidation state (n) and coordination number (C.N.) of Al and number of valence electrons around Al (N) in Al2Cl6 are respectively
Hie oxidation state (n) and coordination number (C.N.) of Al and number of valence electrons around Al (N) in Al2Cl6 are respectively
Q.137 Correct
Q.137 In-correct
Q.137 Unattempt
ΔH°f values (in kJ mol−1) for graphite, diamond and C60 are respectively
ΔH°f values (in kJ mol−1) for graphite, diamond and C60 are respectively
Q.138 Correct
Q.138 In-correct
Q.138 Unattempt
What is the formula of the product formed when F− reacts with enamel on teeth?
What is the formula of the product formed when F− reacts with enamel on teeth?
Q.139 Correct
Q.139 In-correct
Q.139 Unattempt
Which one of the following methods can be used to find out the percentage composition of halogen present in an organic compound?
Which one of the following methods can be used to find out the percentage composition of halogen present in an organic compound?
Q.140 Correct
Q.140 In-correct
Q.140 Unattempt
Which of the following reactions produce alkane as the product?
I. E−COO−Na+ + NaOH
CaO
────────▶
Δ

II. CH3−
O
||
C
−CH3
Zn−Hg
────────▶
conc.HCl

III. CH3C ≡ CCH3
LiAlH4
────────▶

IV. CH3−
CH3
|
C
|
CH3
−Cl
NaBH4
────────▶
Which of the following reactions produce alkane as the product?
I. E−COO−Na+ + NaOH
CaO
────────▶
Δ

II. CH3−
O
||
C
−CH3
Zn−Hg
────────▶
conc.HCl

III. CH3C ≡ CCH3
LiAlH4
────────▶

IV. CH3−
CH3
|
C
|
CH3
−Cl
NaBH4
────────▶
Q.141 Correct
Q.141 In-correct
Q.141 Unattempt
Which of the following are not aromatic?

Which of the following are not aromatic?

Q.142 Correct
Q.142 In-correct
Q.142 Unattempt
How many of the following compounds show ferrimagnetism?
Fe3O4 ; MgFe2O4 ; NiFe2O4 ; MnO ; CrO2
How many of the following compounds show ferrimagnetism?
Fe3O4 ; MgFe2O4 ; NiFe2O4 ; MnO ; CrO2
Q.143 Correct
Q.143 In-correct
Q.143 Unattempt
The molality (in mol kg−1) of 1 mole of solute in 50 g of solvent is:
The molality (in mol kg−1) of 1 mole of solute in 50 g of solvent is:
Q.144 Correct
Q.144 In-correct
Q.144 Unattempt
The freezing point of solution containing 10 mL of non-volatile and non - electrolyte liquid “A" in 500 g of water is - 0.413 °C. If Kf of water is 1.86 K kg mol−1 and the molecular weight of A = 60 g mol−1, what is the density of the solution in g mL−1 ?
(Assume Δmix V = 0)
The freezing point of solution containing 10 mL of non-volatile and non - electrolyte liquid “A" in 500 g of water is - 0.413 °C. If Kf of water is 1.86 K kg mol−1 and the molecular weight of A = 60 g mol−1, what is the density of the solution in g mL−1 ?
(Assume Δmix V = 0)
Q.145 Correct
Q.145 In-correct
Q.145 Unattempt
A current of 19296 C is passed through, an aqueous solution of copper sulphate using copper electrodes. What is the mass (in g) of copper deposited at the cathode?
(molar mass of Cu = 63.5 g mol−1)
A current of 19296 C is passed through, an aqueous solution of copper sulphate using copper electrodes. What is the mass (in g) of copper deposited at the cathode?
(molar mass of Cu = 63.5 g mol−1)
Q.146 Correct
Q.146 In-correct
Q.146 Unattempt
For a zero-order reaction, the correct expression for rate constant (k) at half - life time (t
1
2
) is (R0 = initial concentration of reactant)
For a zero-order reaction, the correct expression for rate constant (k) at half - life time (t
1
2
) is (R0 = initial concentration of reactant)
Q.147 Correct
Q.147 In-correct
Q.147 Unattempt
Which one of the following is used as an eye lotion?
Which one of the following is used as an eye lotion?
Q.148 Correct
Q.148 In-correct
Q.148 Unattempt
Identify A and B respectively in the following reactions.
4 Au (s) + 8 CN(aq)− + 2H2O (aq)
O2(g)
────▶
A(aq)
↓
B+2Au(s)
Zn(s)
 + 4OH(aq)−
Identify A and B respectively in the following reactions.
4 Au (s) + 8 CN(aq)− + 2H2O (aq)
O2(g)
────▶
A(aq)
↓
B+2Au(s)
Zn(s)
 + 4OH(aq)−
Q.149 Correct
Q.149 In-correct
Q.149 Unattempt
Statement (A): Sulphur vapour is paramagnetic.
Statement (B): Reaction of dil. HCl with finely divided iron forms FeCl3 and H2 gas.
The correct answer is
Statement (A): Sulphur vapour is paramagnetic.
Statement (B): Reaction of dil. HCl with finely divided iron forms FeCl3 and H2 gas.
The correct answer is
Q.150 Correct
Q.150 In-correct
Q.150 Unattempt
The reason for the noble gases to have low boiling and low melting point is
The reason for the noble gases to have low boiling and low melting point is
Q.151 Correct
Q.151 In-correct
Q.151 Unattempt
Match the following

The correct answer is
Match the following

The correct answer is
Q.152 Correct
Q.152 In-correct
Q.152 Unattempt
Which one of the following complex has the highest magnitude of Crystal Field Splitting Energy (Δ0)?
Which one of the following complex has the highest magnitude of Crystal Field Splitting Energy (Δ0)?
Q.153 Correct
Q.153 In-correct
Q.153 Unattempt
A polymer contains 50 molecules with molecular mass 5000, 100 molecules with molecular mass 10,000 and 50 molecules with molecular mass 15,000. Calculate number average molecular mass?
A polymer contains 50 molecules with molecular mass 5000, 100 molecules with molecular mass 10,000 and 50 molecules with molecular mass 15,000. Calculate number average molecular mass?
Q.154 Correct
Q.154 In-correct
Q.154 Unattempt
Which of the following are reducing sugars?
(A) Sucrose
(B) Maltose
(C) Lactose
(D) Fructose
Which of the following are reducing sugars?
(A) Sucrose
(B) Maltose
(C) Lactose
(D) Fructose
Q.155 Correct
Q.155 In-correct
Q.155 Unattempt
Identify opiates from the following
(A) Codeine
(B) Thymine
(C) Epinephrine
(D) Morphine
(E) Thiamine
(F) Heroin
Identify opiates from the following
(A) Codeine
(B) Thymine
(C) Epinephrine
(D) Morphine
(E) Thiamine
(F) Heroin
Q.156 Correct
Q.156 In-correct
Q.156 Unattempt
Match the following.

The correct answer is
Match the following.

The correct answer is
Q.157 Correct
Q.157 In-correct
Q.157 Unattempt
Find the suitable product for the following reaction.
R - CO2H
(i)B2H6
────────▶
(ii)H2O∕H+
Find the suitable product for the following reaction.
R - CO2H
(i)B2H6
────────▶
(ii)H2O∕H+
Q.158 Correct
Q.158 In-correct
Q.158 Unattempt
What is the product “E" in the following reaction ?

What is the product “E" in the following reaction ?

Q.159 Correct
Q.159 In-correct
Q.159 Unattempt
The decreasing order of acidic strength for following acids is
a) CH3COOH
b) CH3CHclCH2COOH
c) ClCH2COOH
d) Cl2CHCOOH
The decreasing order of acidic strength for following acids is
a) CH3COOH
b) CH3CHclCH2COOH
c) ClCH2COOH
d) Cl2CHCOOH
Q.160 Correct
Q.160 In-correct
Q.160 Unattempt
Identify X, Y and Z respectively in the following reaction sequence
Acetic acid
1)‌N‌H3,2)‌Δ
────────▶
3)‌C6‌H5‌S‌O2‌C‌l,Pyridine∕343K
 X + Y + Z
Identify X, Y and Z respectively in the following reaction sequence
Acetic acid
1)‌N‌H3,2)‌Δ
────────▶
3)‌C6‌H5‌S‌O2‌C‌l,Pyridine∕343K
 X + Y + Z
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