TS EAMCET 2024 : 9th May Evening Shift

If $A = [\begin{array}{lll} 1 & 2 & 2 \\ 3 & 2 & 3 \\ 1 & 1 & 2 \end{array}]$ and $A^{- 1} = [\begin{array}{lll} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{array}]$ , then $\sum_{\begin{matrix} 1 \leq i \leq 3 \\ 1 \leq j \leq 3 \end{matrix}} a_{i j} =$

Q.6 Correct

Q.6 In-correct

Q.6 Unattempt

A X = D

represents the system of linear equations

3 x - 4 y + 7 z + 6 = 0, 5 x + 2 y - 4 z + 9 = 0

and

8 x - 6 y - z + 5 = 0

, then

A X = D

represents the system of linear equations

3 x - 4 y + 7 z + 6 = 0, 5 x + 2 y - 4 z + 9 = 0

and

8 x - 6 y - z + 5 = 0

(x, y, z) = (α, β, γ)

is the unique solution of the system of simultaneous linear equations

3 x - 4 y + z + 7 = 0

2 x + 3 y - z = 10

and

x - 2 y - 3 z = 3

, then

α =

(x, y, z) = (α, β, γ)

is the unique solution of the system of simultaneous linear equations

3 x - 4 y + z + 7 = 0

2 x + 3 y - z = 10

and

x - 2 y - 3 z = 3

, then

α =

Q.8 Correct

Q.8 In-correct

Q.8 Unattempt

\frac{(2 - i) x + (1 + i)}{2 + i} + \frac{(1 - 2 i) y + (1 - i)}{1 + 2 i} = 1 - 2 i

, then

2 x + 4 y =

\frac{(2 - i) x + (1 + i)}{2 + i} + \frac{(1 - 2 i) y + (1 - i)}{1 + 2 i} = 1 - 2 i

, then

2 x + 4 y =

Q.9 Correct

Q.9 In-correct

Q.9 Unattempt

z = 1 - \sqrt{3} i

, then

z^{3} - 3 z^{2} + 3 z =

z = 1 - \sqrt{3} i

, then

z^{3} - 3 z^{2} + 3 z =

Q.10 Correct

Q.10 In-correct

Q.10 Unattempt

The product of all the values of

(\sqrt{3} - i)^{\frac{2}{5}}

The product of all the values of

(\sqrt{3} - i)^{\frac{2}{5}}

Q.11 Correct

Q.11 In-correct

Q.11 Unattempt

The number of common roots among the 12 th and 30th roots of unity is

Q.12 Correct

Q.12 In-correct

Q.12 Unattempt

α

is a root of the equation

\frac{x - 1}{\sqrt{2 x^{2} - 5 x + 2}} = \frac{41}{60}

. If

- \frac{1}{2} < α < 0

, then

α

is equal to

α

is a root of the equation

\frac{x - 1}{\sqrt{2 x^{2} - 5 x + 2}} = \frac{41}{60}

. If

- \frac{1}{2} < α < 0

, then

α

4 + 3 x - 7 x^{2}

attains its maximum value

M

x = α

and

5 x^{2} - 2 x + 1

attains its minimum value

m

x = β

, then

\frac{28 (M - a)}{5 (m + β)} =

4 + 3 x - 7 x^{2}

attains its maximum value

M

x = α

and

5 x^{2} - 2 x + 1

attains its minimum value

m

x = β

, then

\frac{28 (M - a)}{5 (m + β)} =

Q.14 Correct

Q.14 In-correct

Q.14 Unattempt

α, β, γ

are the roots of the equation

2 x^{3} - 5 x^{2} + 4 x - 3 = 0

, then

Σ α β (α + β) =

α, β, γ

are the roots of the equation

2 x^{3} - 5 x^{2} + 4 x - 3 = 0

, then

Σ α β (α + β) =

Q.15 Correct

Q.15 In-correct

Q.15 Unattempt

$α, β, γ, 2$ and $ε$ are the roots of the equation

$\begin{aligned} α, β, γ + 4 x^{4} - 13 x^{3} - 52 x^{2} + 36 x + 144 = 0 . If \\ α < β < γ < 2 < ε, then α + 2 β + 3 γ + 5 ε = \end{aligned}$

$α, β, γ, 2$ and $ε$ are the roots of the equation

$\begin{aligned} α, β, γ + 4 x^{4} - 13 x^{3} - 52 x^{2} + 36 x + 144 = 0 . If \\ α < β < γ < 2 < ε, then α + 2 β + 3 γ + 5 ε = \end{aligned}$

Q.16 Correct

Q.16 In-correct

Q.16 Unattempt

Among the 4 -digit numbers that can be formed using the digits

1, 2, 3, 4, 5

and 6 without repeating any digit, the number of numbers which are divisible by 6 is

Among the 4 -digit numbers that can be formed using the digits

1, 2, 3, 4, 5

and 6 without repeating any digit, the number of numbers which are divisible by 6 is

Q.17 Correct

Q.17 In-correct

Q.17 Unattempt

If the number of circular permutations of 9 distinct things taken 5 at a time is

n_{1}

and the number of linear permutation of 8 distinct things taken 4 at a time is

n_{2}

, then

\frac{n_{1}}{n_{2}} =

If the number of circular permutations of 9 distinct things taken 5 at a time is

n_{1}

and the number of linear permutation of 8 distinct things taken 4 at a time is

n_{2}

, then

\frac{n_{1}}{n_{2}} =

Q.18 Correct

Q.18 In-correct

Q.18 Unattempt

The number of ways in which 4 different things can be distributed to 6 persons so that no person gets all the things is

Q.19 Correct

Q.19 In-correct

Q.19 Unattempt

If the coefficients of 3 consecutive terms in the expansion of

(1 + x)^{23}

are in arithmetic progression, then those terms are

If the coefficients of 3 consecutive terms in the expansion of

(1 + x)^{23}

are in arithmetic progression, then those terms are

Q.20 Correct

Q.20 In-correct

Q.20 Unattempt

The numerically greatest term in the expansion of

(3 x - 16 y)^{15}

, when

x = \frac{2}{3}

and

y = \frac{3}{2}

, is

The numerically greatest term in the expansion of

(3 x - 16 y)^{15}

, when

x = \frac{2}{3}

and

y = \frac{3}{2}

\frac{3 x^{4} - 2 x^{2} + 1}{(x - 2)^{4}} = A + \frac{B}{x - 2} + \frac{C}{(x - 2)^{2}}

+ \frac{D}{(x - 2)^{3}} + \frac{E}{(x - 2)^{4}}

, then

2 A + 3 B - C - D + E =

\frac{3 x^{4} - 2 x^{2} + 1}{(x - 2)^{4}} = A + \frac{B}{x - 2} + \frac{C}{(x - 2)^{2}}

+ \frac{D}{(x - 2)^{3}} + \frac{E}{(x - 2)^{4}}

, then

2 A + 3 B - C - D + E =

Q.22 Correct

Q.22 In-correct

Q.22 Unattempt

The maximum value of the function

f (x) = 3 \sin^{12} x + 4 \cos^{16} x

The maximum value of the function

f (x) = 3 \sin^{12} x + 4 \cos^{16} x

Q.23 Correct

Q.23 In-correct

Q.23 Unattempt

A + B + C = 2 S

, then

\sin (S - A) \cos (S - B) - \sin (S - C) \cos S =

A + B + C = 2 S

, then

\sin (S - A) \cos (S - B) - \sin (S - C) \cos S =

Q.24 Correct

Q.24 In-correct

Q.24 Unattempt

\cos x + \cos y = \frac{2}{3}

and

\sin x - \sin y = \frac{3}{4}

, then

\sin (x - y) + \cos (x - y) =

\cos x + \cos y = \frac{2}{3}

and

\sin x - \sin y = \frac{3}{4}

, then

\sin (x - y) + \cos (x - y) =

Q.25 Correct

Q.25 In-correct

Q.25 Unattempt

The solution set of the equation

\cos^{2} 2 x + \sin^{2} 3 x = 1

The solution set of the equation

\cos^{2} 2 x + \sin^{2} 3 x = 1

Q.26 Correct

Q.26 In-correct

Q.26 Unattempt

2 \tan^{- 1} x = 3 \sin^{- 1} x

and

x \neq 0

, then

8 x^{2} + 1 =

2 \tan^{- 1} x = 3 \sin^{- 1} x

and

x \neq 0

, then

8 x^{2} + 1 =

Q.27 Correct

Q.27 In-correct

Q.27 Unattempt

Match the functions given in List I with their relevant characteristics from List II.

List I	List II
(A) sinh x	(I) Domains is (-1,1), even function
(B) sec hx	(II) Domain is [1,∞), neither even nor odd function
(C) tan hx	(III) Even function
(D) cosec h⁻¹x	(IV) Range is R, odd function
	(V) Range is (-1,1), odd function

The correct answer is

Match the functions given in List I with their relevant characteristics from List II.

List I	List II
(A) sinh x	(I) Domains is (-1,1), even function
(B) sec hx	(II) Domain is [1,∞), neither even nor odd function
(C) tan hx	(III) Even function
(D) cosec h⁻¹x	(IV) Range is R, odd function
	(V) Range is (-1,1), odd function

The correct answer is

△ A B C

, if

\tan \frac{A}{2} : \tan \frac{B}{2} : \tan \frac{C}{2} = 15 : 10 : 6

, then

\frac{a}{b - c} =

In a

△ A B C

, if

\tan \frac{A}{2} : \tan \frac{B}{2} : \tan \frac{C}{2} = 15 : 10 : 6

, then

\frac{a}{b - c} =

△ A B C, \frac{a (r_{1} + r_{2} r_{3})}{r_{1} - r + r_{2} + r_{3}} =

In a

△ A B C, \frac{a (r_{1} + r_{2} r_{3})}{r_{1} - r + r_{2} + r_{3}} =

Q.30 Correct

Q.30 In-correct

Q.30 Unattempt

a, b, c

are non-coplanar vectors. If the three points

λ a - 2 b + c, 2 a + λ b - 2 c

and

4 a + 7 b - 8 c

are collinear, then

λ =

a, b, c

are non-coplanar vectors. If the three points

λ a - 2 b + c, 2 a + λ b - 2 c

and

4 a + 7 b - 8 c

are collinear, then

λ =

Q.31 Correct

Q.31 In-correct

Q.31 Unattempt

\hat{i} + \hat{j}, \hat{j} + \hat{k}, \hat{k} + \hat{i}, \hat{i} - \hat{j}, \hat{j} - \hat{k}

are the position vectors of the points

A, B, C, D, E

respectively, then the point of intersection of the line

A B

and the plane passing through

C, D, E

is.

\hat{i} + \hat{j}, \hat{j} + \hat{k}, \hat{k} + \hat{i}, \hat{i} - \hat{j}, \hat{j} - \hat{k}

are the position vectors of the points

A, B, C, D, E

respectively, then the point of intersection of the line

A B

and the plane passing through

C, D, E

a, b

are two vectors such that

| a | = 3, | b | = 4

| a + b | = \sqrt{37}, | a - b | = k

and

(a, b) = θ

, then

\frac{4}{13} (k \sin θ)^{2} =

a, b

are two vectors such that

| a | = 3, | b | = 4

| a + b | = \sqrt{37}, | a - b | = k

and

(a, b) = θ

, then

\frac{4}{13} (k \sin θ)^{2} =

Q.33 Correct

Q.33 In-correct

Q.33 Unattempt

r

is a vector perpendicular to the planet, determined by the vectors

2 \hat{i} - \hat{j}

and

\hat{j} + 2 \hat{k}

, If the magnitude of the projection of

r

on the vector

2 \hat{i} + \hat{j} + 2 \hat{k}

is l , then

| r | =

r

is a vector perpendicular to the planet, determined by the vectors

2 \hat{i} - \hat{j}

and

\hat{j} + 2 \hat{k}

, If the magnitude of the projection of

r

on the vector

2 \hat{i} + \hat{j} + 2 \hat{k}

is l , then

| r | =

Q.34 Correct

Q.34 In-correct

Q.34 Unattempt

b = \hat{i} - \hat{j} + 2 k, c = \hat{i} + 2 \hat{j} - \hat{k}

are two vectors and

a

is a vector such that

\cos (a, b \times c) = \sqrt{\frac{2}{3}}

. If

a

is a unit vector, then

| a \times (b \times c) | =

b = \hat{i} - \hat{j} + 2 k, c = \hat{i} + 2 \hat{j} - \hat{k}

are two vectors and

a

is a vector such that

\cos (a, b \times c) = \sqrt{\frac{2}{3}}

. If

a

is a unit vector, then

| a \times (b \times c) | =

Q.35 Correct

Q.35 In-correct

Q.35 Unattempt

The variance of the following continuous frequency distribution is

Classinterval	0-4	4-8	8-12	12-16
Frequency	2	3	2	1

The variance of the following continuous frequency distribution is

Classinterval	0-4	4-8	8-12	12-16
Frequency	2	3	2	1

Q.36 Correct

Q.36 In-correct

Q.36 Unattempt

Among the 5 married couples, if the names of 5 men are matched with the names of their wives randomly, then the probability that no man is matched with name of his wife is

Q.37 Correct

Q.37 In-correct

Q.37 Unattempt

If 3 dice are thrown, the probability of getting 10 as the sum of the three numbers that appeared on the top faces of the dice is

A, B, C

contain 2 red and 3 white balls; 3 red and 2 white balls; 1 red and 4 white balls respectively. If a ball selected at random from one of the urns is found to be red, then the probability that it is drawn from urn

C

Three similar urns

A, B, C

C

Q.39 Correct

Q.39 In-correct

Q.39 Unattempt

If a random variable X has the following probability distribution, then the mean of

X

\begin{array}{ccccc} X = x_{1} & 1 & 2 & 3 & 5 \\ p (X = x_{i}) & 2 k^{2} & k & k & k^{2} \end{array}

If a random variable X has the following probability distribution, then the mean of

X

\begin{array}{ccccc} X = x_{1} & 1 & 2 & 3 & 5 \\ p (X = x_{i}) & 2 k^{2} & k & k & k^{2} \end{array}

Q.40 Correct

Q.40 In-correct

Q.40 Unattempt

A A fair coin is tossed a fixed number of times. If the probability of getting 5 heads is equal to the probability of getting 4 heads, then the probability of getting 6 heads is

Q.41 Correct

Q.41 In-correct

Q.41 Unattempt

If the ratio of the distances of a variable point

P

from the point

(1, 1)

and the line

x - y + 2 = 0

1 : \sqrt{2}

, then the equation of the locus of

P

If the ratio of the distances of a variable point

P

from the point

(1, 1)

and the line

x - y + 2 = 0

1 : \sqrt{2}

, then the equation of the locus of

P

Q.42 Correct

Q.42 In-correct

Q.42 Unattempt

If the origin is shifted to the point

(\frac{3}{2}, - 2)

by the translation of axes, then the transformed equation of

2 x^{2} + 4 x y + y^{2} + 2 x - 2 y + 1 = 0

If the origin is shifted to the point

(\frac{3}{2}, - 2)

by the translation of axes, then the transformed equation of

2 x^{2} + 4 x y + y^{2} + 2 x - 2 y + 1 = 0

Q.43 Correct

Q.43 In-correct

Q.43 Unattempt

L \equiv x \cos α + y \sin α - p = 0

represents a line perpendicular to the line

x + y + 1 = 0

. If

p

is positive,

α

lies in the fourth quadrant and perpendicular distance from

(\sqrt{2}, \sqrt{2})

to the line,

L = 0

is 5 units, then

p =

L \equiv x \cos α + y \sin α - p = 0

represents a line perpendicular to the line

x + y + 1 = 0

. If

p

is positive,

α

lies in the fourth quadrant and perpendicular distance from

(\sqrt{2}, \sqrt{2})

to the line,

L = 0

is 5 units, then

p =

Q.44 Correct

Q.44 In-correct

Q.44 Unattempt

(- 2, - 1), (2, 5)

are two vertices of a triangle and

(2, \frac{5}{3})

is its orthocenter. If

(m, n)

is the third vertex of that triangle, then

m + n

is equal to.

(- 2, - 1), (2, 5)

are two vertices of a triangle and

(2, \frac{5}{3})

is its orthocenter. If

(m, n)

is the third vertex of that triangle, then

m + n

L_{1} \equiv 2 x + y - 3 = 0

and

L_{2} \equiv a x + b y + c = 0

are two equal sides of an isosceles triangle. If

L_{3} \equiv x + 2 y + 1 = 0

is the third side of this triangle and

(5, 1)

is a point on

L_{2} =

0 , then

\frac{b^{2}}{| a c |} =

L_{1} \equiv 2 x + y - 3 = 0

and

L_{2} \equiv a x + b y + c = 0

are two equal sides of an isosceles triangle. If

L_{3} \equiv x + 2 y + 1 = 0

is the third side of this triangle and

(5, 1)

is a point on

L_{2} =

0 , then

\frac{b^{2}}{| a c |} =

Q.46 Correct

Q.46 In-correct

Q.46 Unattempt

The slope of one of the pair of lines

2 x^{2} + h x y + 6 y^{2} = 0

is thrice the slope of the other line, then

h =

The slope of one of the pair of lines

2 x^{2} + h x y + 6 y^{2} = 0

is thrice the slope of the other line, then

h =

Q.47 Correct

Q.47 In-correct

Q.47 Unattempt

P (\frac{π}{4}), Q (\frac{π}{3})

are two points on the circle

x^{2} + y^{2} - 2 x - 2 y - 1 = 0

, then the slope of the tangent to this circle which is parallel to the chord

P Q

P (\frac{π}{4}), Q (\frac{π}{3})

are two points on the circle

x^{2} + y^{2} - 2 x - 2 y - 1 = 0

, then the slope of the tangent to this circle which is parallel to the chord

P Q

(2, 0)

with respect to a circle

S

is -4 and the length of the tangent drawn from the point

(1, 1)

S

is 2 . If the circle

S

passes through the point

(- 1, - 1)

, then the radius of the circle

S

The power of a point

(2, 0)

with respect to a circle

S

is -4 and the length of the tangent drawn from the point

(1, 1)

S

is 2 . If the circle

S

passes through the point

(- 1, - 1)

, then the radius of the circle

S

x - 5 y - 7 = 0

with respect to the circle

S \equiv x^{2} + y^{2} - 2 x + 4 y + 1 = 0

P (a, b)

. If

C

is the centre of the circle

S = 0

, then

P C =

The pole of the line

x - 5 y - 7 = 0

with respect to the circle

S \equiv x^{2} + y^{2} - 2 x + 4 y + 1 = 0

P (a, b)

. If

C

is the centre of the circle

S = 0

, then

P C =

Q.50 Correct

Q.50 In-correct

Q.50 Unattempt

The equation of the pair of transverse common tangents drawn to the circles

x^{2} + y^{2} + 2 x + 2 y + 1 = 0

and

x^{2} + y^{2} - 2 x - 2 y + 1 = 0

The equation of the pair of transverse common tangents drawn to the circles

x^{2} + y^{2} + 2 x + 2 y + 1 = 0

and

x^{2} + y^{2} - 2 x - 2 y + 1 = 0

Q.51 Correct

Q.51 In-correct

Q.51 Unattempt

If a circle passing through the point

(1, 1)

cuts the circles

x^{2} + y^{2} + 4 x - 5 = 0

and

x^{2} + y^{2} - 4 y + 3 = 0

orthogonally, then the centre of that circle is

If a circle passing through the point

(1, 1)

cuts the circles

x^{2} + y^{2} + 4 x - 5 = 0

and

x^{2} + y^{2} - 4 y + 3 = 0

orthogonally, then the centre of that circle is

Q.52 Correct

Q.52 In-correct

Q.52 Unattempt

Length of the common chord of the circles

x^{2} + y^{2} - 6 x + 5 = 0

and

x^{2} + y^{2} + 4 y - 5 = 0

Length of the common chord of the circles

x^{2} + y^{2} - 6 x + 5 = 0

and

x^{2} + y^{2} + 4 y - 5 = 0

Q.53 Correct

Q.53 In-correct

Q.53 Unattempt

P

and

Q

are the extremities of a focal chord of the parabola

y^{2} = 4 a x

. If

P = (9, 9)

and

Q = (p, q)

, then

p - q =

P

and

Q

are the extremities of a focal chord of the parabola

y^{2} = 4 a x

. If

P = (9, 9)

and

Q = (p, q)

, then

p - q =

Q.54 Correct

Q.54 In-correct

Q.54 Unattempt

The number of normals that can be drawn through the point

(9, 6)

to the parabola

y^{2} = 4 x

The number of normals that can be drawn through the point

(9, 6)

to the parabola

y^{2} = 4 x

Q.55 Correct

Q.55 In-correct

Q.55 Unattempt

The equations of the directrices of the elmpse

9 x^{2} + 4 y^{2} - 18 x - 16 y - 11 = 0

are

The equations of the directrices of the elmpse

9 x^{2} + 4 y^{2} - 18 x - 16 y - 11 = 0

L_{1}^{'}

is the end of a latus rectum of the ellipse

3 x = 2 \pm \frac{\sqrt{5}}{\sqrt{5}}

3 x^{2} + 4 y^{2} = 12

which is lying in the third quadrant. If the normal drawn at

L_{1}^{'}

to this ellipse intersects the ellipse again at the point

P (a, b)

, then

a =

L_{1}^{'}

is the end of a latus rectum of the ellipse

3 x = 2 \pm \frac{\sqrt{5}}{\sqrt{5}}

3 x^{2} + 4 y^{2} = 12

which is lying in the third quadrant. If the normal drawn at

L_{1}^{'}

to this ellipse intersects the ellipse again at the point

P (a, b)

, then

a =

Q.57 Correct

Q.57 In-correct

Q.57 Unattempt

(p, q)

is the point of intersection of a latus rectum and an asymptote of the hyperbola

9 x^{2} - 16 y^{2} = 144

. If

p > 0

and

q > 0

, then

q =

(p, q)

is the point of intersection of a latus rectum and an asymptote of the hyperbola

9 x^{2} - 16 y^{2} = 144

. If

p > 0

and

q > 0

, then

q =

Q.58 Correct

Q.58 In-correct

Q.58 Unattempt

A (3, 2, - 1), B (4, 1, 0), C (2, 1, 4)

are the vertices of a

△ A B C

. If the bisector of

B A C

! intersects the side

B C

D (p, q, r)

, then

\sqrt{2 p + q + r} =

A (3, 2, - 1), B (4, 1, 0), C (2, 1, 4)

are the vertices of a

△ A B C

. If the bisector of

B A C

! intersects the side

B C

D (p, q, r)

, then

\sqrt{2 p + q + r} =

Q.59 Correct

Q.59 In-correct

Q.59 Unattempt

(3, 0, 2)

and

(0, 2, k)

are the direction ratios of two lines and

θ

is the angle between them. If

| \cos θ | = \frac{6}{13}

, then

k =

(3, 0, 2)

and

(0, 2, k)

are the direction ratios of two lines and

θ

is the angle between them. If

| \cos θ | = \frac{6}{13}

, then

k =

(π)

passing through the point

(1, 2, - 3)

is perpendicular to the planes

x + y - z + 4 = 0

and

2 x - y + z + 1 = 0

. If the equation of the plane

(π)

a x + b y + c z + 1 = 0

, then

a^{2} + b^{2} + c^{2} =

A plane

(π)

passing through the point

(1, 2, - 3)

is perpendicular to the planes

x + y - z + 4 = 0

and

2 x - y + z + 1 = 0

. If the equation of the plane

(π)

a x + b y + c z + 1 = 0

, then

a^{2} + b^{2} + c^{2} =

Q.61 Correct

Q.61 In-correct

Q.61 Unattempt

lim_{θ \to \frac{π^{-}}{2}} \frac{8 \tan^{4} θ + 4 \tan^{2} θ + 5}{(3 - 2 \tan θ)^{4}} =

lim_{θ \to \frac{π^{-}}{2}} \frac{8 \tan^{4} θ + 4 \tan^{2} θ + 5}{(3 - 2 \tan θ)^{4}} =

Q.62 Correct

Q.62 In-correct

Q.62 Unattempt

Define $f : R \to R$ by $f (x) = {\begin{array}{cl} \frac{1 - \cos 4 x}{x^{2}}, & x < 0 \\ a, & x = 0 \\ \frac{\sqrt{x}}{\sqrt{16 + \sqrt{x}} - 4}, & x > 0 \end{array}$

Then, the value of $a$ so that $f$ is continuous at $x = 0$ is

Define $f : R \to R$ by $f (x) = {\begin{array}{cl} \frac{1 - \cos 4 x}{x^{2}}, & x < 0 \\ a, & x = 0 \\ \frac{\sqrt{x}}{\sqrt{16 + \sqrt{x}} - 4}, & x > 0 \end{array}$

Then, the value of $a$ so that $f$ is continuous at $x = 0$ is

Q.63 Correct

Q.63 In-correct

Q.63 Unattempt

y = \frac{\tan x \cos^{- 1} x}{\sqrt{1 - x^{2}}}

, then the value of

\frac{d y}{d x}

, when

x = 0

y = \frac{\tan x \cos^{- 1} x}{\sqrt{1 - x^{2}}}

, then the value of

\frac{d y}{d x}

, when

x = 0

Q.64 Correct

Q.64 In-correct

Q.64 Unattempt

y (\cos x)^{\sin x} = (\sin x)^{\sin x}

, then the value of

\frac{d y}{d x}

x = \frac{π}{4}

y (\cos x)^{\sin x} = (\sin x)^{\sin x}

, then the value of

\frac{d y}{d x}

x = \frac{π}{4}

Q.65 Correct

Q.65 In-correct

Q.65 Unattempt

x = \cos 2 t + \log (\tan t)

and

y = 2 t + \cot 2 t

, then

\frac{d y}{d x} =

x = \cos 2 t + \log (\tan t)

and

y = 2 t + \cot 2 t

, then

\frac{d y}{d x} =

Q.66 Correct

Q.66 In-correct

Q.66 Unattempt

y = 44 x^{45} + 45 x^{- 44}

, then

y^{n} =

y = 44 x^{45} + 45 x^{- 44}

, then

y^{n} =

Q.67 Correct

Q.67 In-correct

Q.67 Unattempt

The approximate value of

\sqrt[3]{730}

obtained by the application of derivatives is

The approximate value of

\sqrt[3]{730}

obtained by the application of derivatives is

Q.68 Correct

Q.68 In-correct

Q.68 Unattempt

θ

is the acute angle between the curves

y^{2} = x

and

x^{2} + y^{2} = 2

, then

\tan θ =

θ

is the acute angle between the curves

y^{2} = x

and

x^{2} + y^{2} = 2

, then

\tan θ =

Q.69 Correct

Q.69 In-correct

Q.69 Unattempt

The vertical angle of a right circular cone is

60^{\circ}

. If water is being poured in to the cone at the rate of

\frac{1}{\sqrt{3}} m^{3} / \min

, then the rate (

m / \min

) at which the radius of the water level is increasing when the height of the water level is 3 m is

The vertical angle of a right circular cone is

60^{\circ}

. If water is being poured in to the cone at the rate of

\frac{1}{\sqrt{3}} m^{3} / \min

, then the rate (

m / \min

) at which the radius of the water level is increasing when the height of the water level is 3 m is

Q.70 Correct

Q.70 In-correct

Q.70 Unattempt

A right circular cone is inscribed in a sphere of radius 3 units. If the volume of the cone is maximum, then semi-vertical angle of the cone is

Q.71 Correct

Q.71 In-correct

Q.71 Unattempt

f (x) = k x^{3} - 3 x^{2} - 12 x + 8

is strictly decreasing for all

x \in R

, then

f (x) = k x^{3} - 3 x^{2} - 12 x + 8

is strictly decreasing for all

x \in R

\int e^{- 2 x} (\tan 2 x - 2 \sec^{2} 2 x \tan 2 x) d x =

\int e^{- 2 x} (\tan 2 x - 2 \sec^{2} 2 x \tan 2 x) d x =

Q.73 Correct

Q.73 In-correct

Q.73 Unattempt

\int x^{3} \sin 3 x d x = f (x) \cos 3 x + g (x) \sin 3 x + C

, then 27

(f (x) + x g (x)) =

\int x^{3} \sin 3 x d x = f (x) \cos 3 x + g (x) \sin 3 x + C

, then 27

(f (x) + x g (x)) =

Q.74 Correct

Q.74 In-correct

Q.74 Unattempt

\int \frac{d x}{9 \cos^{2} 2 x + 16 \sin^{2} 2 x} =

\int \frac{d x}{9 \cos^{2} 2 x + 16 \sin^{2} 2 x} =

Q.75 Correct

Q.75 In-correct

Q.75 Unattempt

\int \frac{2 \cos 3 x - 3 \sin 3 x}{\cos 3 x + 2 \sin 3 x} d x =

\int \frac{2 \cos 3 x - 3 \sin 3 x}{\cos 3 x + 2 \sin 3 x} d x =

Q.76 Correct

Q.76 In-correct

Q.76 Unattempt

$\int_{\frac{- 3}{4}}^{\frac{π - 6}{8}} \log (\sin (4 x + 3)) d x =$

Q.77 Correct

Q.77 In-correct

Q.77 Unattempt

\int_{0}^{16} \frac{\sqrt{x}}{1 + \sqrt{x}} d x =

\int_{0}^{16} \frac{\sqrt{x}}{1 + \sqrt{x}} d x =

Q.78 Correct

Q.78 In-correct

Q.78 Unattempt

\int_{0}^{32 π} \sqrt{1 - \cos 4 x} d x =

\int_{0}^{32 π} \sqrt{1 - \cos 4 x} d x =

Q.79 Correct

Q.79 In-correct

Q.79 Unattempt

The general solution of the differential equation

(9 x - 3 y + 5) d y = (3 x - y + 1) d x

The general solution of the differential equation

(9 x - 3 y + 5) d y = (3 x - y + 1) d x

Q.80 Correct

Q.80 In-correct

Q.80 Unattempt

The general solution of the differential equation

\frac{d y}{d x} = \frac{2 y^{2} + 1}{2 y^{3} - 4 x y + y}

The general solution of the differential equation

\frac{d y}{d x} = \frac{2 y^{2} + 1}{2 y^{3} - 4 x y + y}

Q.1 Correct

Q.1 In-correct

Q.1 Unattempt

The kinetic energy of electrons emitted, when radiation of frequency

1.0 \times 10^{15} Hz

hits a metal, is

2 \times 10^{- 19} J

. What is the threshold frequency of the metal (in Hz )?

(h = 6.6 \times 10^{- 34} Js)

The kinetic energy of electrons emitted, when radiation of frequency

1.0 \times 10^{15} Hz

hits a metal, is

2 \times 10^{- 19} J

. What is the threshold frequency of the metal (in Hz )?

(h = 6.6 \times 10^{- 34} Js)

Q.2 Correct

Q.2 In-correct

Q.2 Unattempt

In which of the following species, the ratio of

s

-electrons to

p

-electrons is same?

In which of the following species, the ratio of

s

-electrons to

p

Identify the pair of elements in which the difference in atomic radii is maximum

List I (Element)	List II (Block)
A Ra	I p - block
B Uuq	II s- block
C Ds	III f - block
D Fm	IV d - block

The correct answer is

Match the following.

List I (Element)	List II (Block)
A Ra	I p - block
B Uuq	II s- block
C Ds	III f - block
D Fm	IV d - block

The correct answer is

Q.5 Correct

Q.5 In-correct

Q.5 Unattempt

Identify the pair in which difference in bond order value is maximum.

Q.6 Correct

Q.6 In-correct

Q.6 Unattempt

The pair of molecules/ions with same geometry but central atoms in them are in different states of hybridisation is

Q.7 Correct

Q.7 In-correct

Q.7 Unattempt

If the density of a mixture of nitrogen and oxygen gases at 400 K and l atm pressure is

0.920 {gL}^{- 1}

, what is the mole fraction of nitrogen in the mixture? (

R = 0.082 L atm {mol}^{- 1} K^{- 1}

; assume ideal gas behaviour for oxygen and nitrogen)

If the density of a mixture of nitrogen and oxygen gases at 400 K and l atm pressure is

0.920 {gL}^{- 1}

, what is the mole fraction of nitrogen in the mixture? (

R = 0.082 L atm {mol}^{- 1} K^{- 1}

; assume ideal gas behaviour for oxygen and nitrogen)

Q.8 Correct

Q.8 In-correct

Q.8 Unattempt

The incorrect rule regarding the determination of significant figures is

Q.9 Correct

Q.9 In-correct

Q.9 Unattempt

At 61 K , one mole of an ideal gas of 1.0 L volume expands isothermally and reversibly to a final volume of 10.0 L . What is the work done in the expansion?

Q.10 Correct

Q.10 In-correct

Q.10 Unattempt

T (K), K_{C}

for the dissociation of

{PCl}_{5}

2 \times 10^{- 2} mol L^{- 1}

. The number of moles of

{PCl}_{5}

that must be taken in 1.0 L flask at the same temperature to get 0.2 mol of chlorine at equilibrium is

T (K), K_{C}

for the dissociation of

{PCl}_{5}

2 \times 10^{- 2} mol L^{- 1}

. The number of moles of

{PCl}_{5}

that must be taken in 1.0 L flask at the same temperature to get 0.2 mol of chlorine at equilibrium is

Q.11 Correct

Q.11 In-correct

Q.11 Unattempt

The dihedral angles in gaseous and solid phases of

H_{2} O_{2}

molecule respectively are

The dihedral angles in gaseous and solid phases of

H_{2} O_{2}

molecule respectively are

Q.12 Correct

Q.12 In-correct

Q.12 Unattempt

Identify the compound which gives

{CO}_{2}

more readily on heating?

Q.13 Correct

Q.13 In-correct

Q.13 Unattempt

The major components of cement are

Q.14 Correct

Q.14 In-correct

Q.14 Unattempt

Consider the following reactions (not balanced).

$\begin{array}{r} {BF}_{3} + NaH \overset{450 K}{\to} X + NaF \\ X + H_{2} O ⟶ Y + H_{2} ↑ \end{array}$

The correct statements about $X$ and $Y$ are

I. $X$ is an electron deficient molecule.

II. in $X, B - B$ bond is present.

III. $Y$ is a weak tribasic acid.

IV. $Y$ acts as a Lewis acid.

Consider the following reactions (not balanced).

$\begin{array}{r} {BF}_{3} + NaH \overset{450 K}{\to} X + NaF \\ X + H_{2} O ⟶ Y + H_{2} ↑ \end{array}$

The correct statements about $X$ and $Y$ are

I. $X$ is an electron deficient molecule.

II. in $X, B - B$ bond is present.

III. $Y$ is a weak tribasic acid.

IV. $Y$ acts as a Lewis acid.

Q.15 Correct

Q.15 In-correct

Q.15 Unattempt

Which of the following does not exist?

Q.16 Correct

Q.16 In-correct

Q.16 Unattempt

Methemoglobinemia is due to

Q.17 Correct

Q.17 In-correct

Q.17 Unattempt

The IUPAC name of the following compound is

Q.18 Correct

Q.18 In-correct

Q.18 Unattempt

The functional groups present in the product ' $X$ ' of the reaction given below are

Q.19 Correct

Q.19 In-correct

Q.19 Unattempt

Identify the major product $(P)$ in the following reaction sequence.

${({CH}_{3})}_{3} CBr \to_{KOH, Δ}^{Alcoholic} X \overset{HBr}{\to} P$

Identify the major product $(P)$ in the following reaction sequence.

${({CH}_{3})}_{3} CBr \to_{KOH, Δ}^{Alcoholic} X \overset{HBr}{\to} P$

Q.20 Correct

Q.20 In-correct

Q.20 Unattempt

What is the percentage of carbon in the product ' $X$ ' formed in the given reaction?

$+ C_{2} H_{5} Cl \to_{{AlCl}_{3}}^{Anhydrous} X$

What is the percentage of carbon in the product ' $X$ ' formed in the given reaction?

$+ C_{2} H_{5} Cl \to_{{AlCl}_{3}}^{Anhydrous} X$

Q.21 Correct

Q.21 In-correct

Q.21 Unattempt

Identify the correct statement about the crystal defects in solids.

79 % N_{2}

and

21 % O_{2}

. At

T (K)

, if Henry's law constants for

N_{2}

and

O_{2}

in water are

857 \times 10^{4} atm

and

4.56 \times 10^{4} atm

, the ratio of mole fraction of

N_{2}

and

O_{2}

dissolved in water at 1 atm is

Dry air contains

79 % N_{2}

and

21 % O_{2}

. At

T (K)

, if Henry's law constants for

N_{2}

and

O_{2}

in water are

857 \times 10^{4} atm

and

4.56 \times 10^{4} atm

, the ratio of mole fraction of

N_{2}

and

O_{2}

dissolved in water at 1 atm is

Q.23 Correct

Q.23 In-correct

Q.23 Unattempt

If the degree of dissociation of formic acid is

11.0 %

, the molar conductivity of 0.02 M solution of it is (Given,

λ^{\circ} (H^{+}) = 349.6 S {cm}^{2} {mol}^{- 1}

λ^{\circ} ({HCOO}^{-}) = 54.6 S {cm}^{2} {mol}^{- 1}

)

If the degree of dissociation of formic acid is

11.0 %

, the molar conductivity of 0.02 M solution of it is (Given,

λ^{\circ} (H^{+}) = 349.6 S {cm}^{2} {mol}^{- 1}

λ^{\circ} ({HCOO}^{-}) = 54.6 S {cm}^{2} {mol}^{- 1}

Consider the gaseous reaction,

A_{2} + B_{2} ⟶ 2 A B

The following data was obtained for the above reaction.

[A₂]₀	[B₂]₀	Initial rate of formation of AB (mol L⁻¹ s⁻¹)
0.1 M	0.1 M	2.5 × 10⁻⁴
0.2 M	0.1 M	5.0 × 10⁻⁴
0.2 M	0.1 M	1.0 × 10⁻³

The value of rate constant for the above reaction is

Consider the gaseous reaction,

A_{2} + B_{2} ⟶ 2 A B

The following data was obtained for the above reaction.

[A₂]₀	[B₂]₀	Initial rate of formation of AB (mol L⁻¹ s⁻¹)
0.1 M	0.1 M	2.5 × 10⁻⁴
0.2 M	0.1 M	5.0 × 10⁻⁴
0.2 M	0.1 M	1.0 × 10⁻³

The value of rate constant for the above reaction is

Q.25 Correct

Q.25 In-correct

Q.25 Unattempt

Adsorption of a gas a solid adsorbent follows. Freundlich adsorption isotherm. If $x$ is the mass of the gas adsorbed on mass ' $m$ ' of the adsorbent at pressure $p$ . From the graph given extent of adsorption is proportional to

Q.26 Correct

Q.26 In-correct

Q.26 Unattempt

Consider the following reactions.

$X + O_{2} \to {Cu}_{2} O + {SO}_{2}, {Cu}_{2} O + X \to Cu + Y ↑$

The shape of the molecule $Y$ is

Consider the following reactions.

$X + O_{2} \to {Cu}_{2} O + {SO}_{2}, {Cu}_{2} O + X \to Cu + Y ↑$

The shape of the molecule $Y$ is

Q.27 Correct

Q.27 In-correct

Q.27 Unattempt

$Y$ in the given sequence of reactions is

$\begin{matrix} P_{4} + x NaOH + y H_{2} O \overset{{CO}_{2}}{\to} X + z {NaH}_{2} {PO}_{2} \\ X + {CuSO}_{4} ⟶ Y + H_{2} {SO}_{4} \end{matrix}$

$Y$ in the given sequence of reactions is

$\begin{matrix} P_{4} + x NaOH + y H_{2} O \overset{{CO}_{2}}{\to} X + z {NaH}_{2} {PO}_{2} \\ X + {CuSO}_{4} ⟶ Y + H_{2} {SO}_{4} \end{matrix}$

Q.28 Correct

Q.28 In-correct

Q.28 Unattempt

In contact process of manufacture of

H_{2} {SO}_{4}

, the arsenic purifier used in the industrial plant contains

In contact process of manufacture of

H_{2} {SO}_{4}

, the arsenic purifier used in the industrial plant contains

Q.29 Correct

Q.29 In-correct

Q.29 Unattempt

$Pt + 3 : 1$ mixture of $($ Conc. $HCl +$ conc. ${HNO}_{3}) \to [X]^{2 -}$

What is the oxidation state of Pt in $[X]^{2 -}$ complex ion ?

$Pt + 3 : 1$ mixture of $($ Conc. $HCl +$ conc. ${HNO}_{3}) \to [X]^{2 -}$

What is the oxidation state of Pt in $[X]^{2 -}$ complex ion ?

Q.30 Correct

Q.30 In-correct

Q.30 Unattempt

In which of the following, ions are correctly arranged in the increasing order of oxidising power?

Q.31 Correct

Q.31 In-correct

Q.31 Unattempt

Which of the following will have a spin only magnetic moment of 2.86 BM ?

Q.32 Correct

Q.32 In-correct

Q.32 Unattempt

The monomer which is present in both bakelite and melamine polymers is

Q.33 Correct

Q.33 In-correct

Q.33 Unattempt

Cellulose is a polysaccharide and is made of

List I (Type of drug)	List II (Examaple)
A Antacid	I Serotonin
B Antihistamine	II Seldane
C Tranquiliser	III Ranitidine
D Antibiotic	IV Chloramphenicol

The correct answer is

Match the following.

List I (Type of drug)	List II (Examaple)
A Antacid	I Serotonin
B Antihistamine	II Seldane
C Tranquiliser	III Ranitidine
D Antibiotic	IV Chloramphenicol

The correct answer is

Q.35 Correct

Q.35 In-correct

Q.35 Unattempt

Which of the following is an example of allylic halide?

Q.36 Correct

Q.36 In-correct

Q.36 Unattempt

Identify the correct statements about $Z$ .

$C_{2} H_{5} {NH}_{2} \to_{0^{\circ} C}^{{NaNO}_{2} / HCl} X \overset{H_{2} O}{\to} Y \overset{Cu / 573 K}{\to} Z$

I. $Z$ is an aldehyde.

II. $Z$ undergòes Cannizzaro reaction.

III. $Z$ gives iodoform test.

IV. $Z$ does not give, test with Tollens' reagent.

Identify the correct statements about $Z$ .

$C_{2} H_{5} {NH}_{2} \to_{0^{\circ} C}^{{NaNO}_{2} / HCl} X \overset{H_{2} O}{\to} Y \overset{Cu / 573 K}{\to} Z$

I. $Z$ is an aldehyde.

II. $Z$ undergòes Cannizzaro reaction.

III. $Z$ gives iodoform test.

IV. $Z$ does not give, test with Tollens' reagent.

Q.37 Correct

Q.37 In-correct

Q.37 Unattempt

Assertion (A) : Aldehydes are more reactive than ketones towards nucleophilic addition reactions

Reason (R) : In aldehydes, carbonyl carbon is less electrophilic compared to ketones.

The correct answer is

Assertion (A) : Aldehydes are more reactive than ketones towards nucleophilic addition reactions

Reason (R) : In aldehydes, carbonyl carbon is less electrophilic compared to ketones.

The correct answer is

Q.38 Correct

Q.38 In-correct

Q.38 Unattempt

Arrange the following in the correct order of their boiling points.

Q.39 Correct

Q.39 In-correct

Q.39 Unattempt

What is the major product $Z$ in the given reaction sequence?

${({CH}_{3})}_{2} C = O \to_{(ii) 2 H_{2} O^{+}}^{(i) C_{2} H_{5} MgBr} \to_{Δ}^{\begin{matrix} (i) {OOCl}_{2} \\ (ii) {CH}_{3} ONa \end{matrix}} Y \to_{Peroxide}^{HBr} Z$

What is the major product $Z$ in the given reaction sequence?

${({CH}_{3})}_{2} C = O \to_{(ii) 2 H_{2} O^{+}}^{(i) C_{2} H_{5} MgBr} \to_{Δ}^{\begin{matrix} (i) {OOCl}_{2} \\ (ii) {CH}_{3} ONa \end{matrix}} Y \to_{Peroxide}^{HBr} Z$

List -I (Amine)	List -II (pKb value)
A. N,N-dimethyl aniline	I. 9.30
B. Aniline	II. 8.92
C. N-ethylethanamine	III. 9.38
D. N-methylaniline	IV. 3.00

The correct answer is

Match the following.

List -I (Amine)	List -II (pKb value)
A. N,N-dimethyl aniline	I. 9.30
B. Aniline	II. 8.92
C. N-ethylethanamine	III. 9.38
D. N-methylaniline	IV. 3.00

The correct answer is

The error in the measurement of resistance, when

(10 \pm 05)

A current passing through it produces a potential difference of

(100 \pm 6) V

across it is

The error in the measurement of resistance, when

(10 \pm 05)

A current passing through it produces a potential difference of

(100 \pm 6) V

A stone is thrown vertically up from the top end of a window of height 1.8 m with a velocity of

8 {ms}^{- 1}

. The time taken by the stone to cross the window during its downward journey is (acceleration due to gravity

= 10 {ms}^{- 2}

)

A stone is thrown vertically up from the top end of a window of height 1.8 m with a velocity of

8 {ms}^{- 1}

. The time taken by the stone to cross the window during its downward journey is (acceleration due to gravity

= 10 {ms}^{- 2}

A cannon placed on a cliff at a height of 375 m fires a cannon ball with a velocity of

100 {ms}^{- 1}

at an angle of

30^{\circ}

above the horizontal. The horizontal distance between the cannon and the target is (Acceleration due to gravity

= 10 {ms}^{- 2}

)

A cannon placed on a cliff at a height of 375 m fires a cannon ball with a velocity of

100 {ms}^{- 1}

at an angle of

30^{\circ}

above the horizontal. The horizontal distance between the cannon and the target is (Acceleration due to gravity

= 10 {ms}^{- 2}

A 20 ton truck is travelling along a curved path of radius 240 m . If the centre of gravity of the truck above the ground is 2 m and the distance between its wheels is 1.5 m , the maximum speed of the truck with which it can travel without toppling over is (Acceleration due to gravity

= 10 {ms}^{- 2}

)

= 10 {ms}^{- 2}

m

with an initial kinetic energy

E

moves up an inclined plane of inclination

θ

. If

μ

is the coefficient of friction between the plane and the body, the work done against friction before coming to rest is

A block of mass

m

with an initial kinetic energy

E

moves up an inclined plane of inclination

θ

. If

μ

is the coefficient of friction between the plane and the body, the work done against friction before coming to rest is

Q.7 Correct

Q.7 In-correct

Q.7 Unattempt

A man of mass 80 kg goes to the market on a scooter of mass 100 kg with certain speed. On application of brakes, the stopping distance is

s_{1}

. The man returns home on the same scooter, with the same speed with a 60 kg bag of rice. If

s_{2}

is the new stopping distance when the brakes are applied with the same force, then

A man of mass 80 kg goes to the market on a scooter of mass 100 kg with certain speed. On application of brakes, the stopping distance is

s_{1}

. The man returns home on the same scooter, with the same speed with a 60 kg bag of rice. If

s_{2}

is the new stopping distance when the brakes are applied with the same force, then

Q.8 Correct

Q.8 In-correct

Q.8 Unattempt

A thin uniform wire of mass

m

and linear mass density

ρ

is bent in the form of a circular loop. The moment of inertia of the loop about its diameter is

A thin uniform wire of mass

m

and linear mass density

ρ

is bent in the form of a circular loop. The moment of inertia of the loop about its diameter is

A, B

and

C

of masses

m, 2 m

and

3 m

are moving towards north, south and east respectively. If the velocities of the particles

A, B

and

C

are

6 {ms}^{- 1}

12 {ms}^{- 1}

and

8 {ms}^{- 1}

respectively, then the velocity of the centre of mass of the system of particles is

Three particles

A, B

and

C

of masses

m, 2 m

and

3 m

are moving towards north, south and east respectively. If the velocities of the particles

A, B

and

C

are

6 {ms}^{- 1}

12 {ms}^{- 1}

and

8 {ms}^{- 1}

respectively, then the velocity of the centre of mass of the system of particles is

Q.10 Correct

Q.10 In-correct

Q.10 Unattempt

A particle of mass 4 mg is executing simple harmonic motion along

X

-axis with an angular frequency of

40 rad s^{- 1}

. If the potential energy of the particle is

V (x) = a + b x^{2}

, where

V (x)

is in joule and

x

is in metre, then the value of

b

A particle of mass 4 mg is executing simple harmonic motion along

X

-axis with an angular frequency of

40 rad s^{- 1}

. If the potential energy of the particle is

V (x) = a + b x^{2}

, where

V (x)

is in joule and

x

is in metre, then the value of

b

Q.11 Correct

Q.11 In-correct

Q.11 Unattempt

The ratio of the accelerations due to gravity at heights 1280 km and 3200 km above the surface of the earth is (Radius of the earth

= 6400 km

)

The ratio of the accelerations due to gravity at heights 1280 km and 3200 km above the surface of the earth is (Radius of the earth

= 6400 km

If the length of a string is

P

when the tension in it is 6 N and its length is

Q

when the original length of the string is

If the length of a string is

P

when the tension in it is 6 N and its length is

Q

when the original length of the string is

Q.13 Correct

Q.13 In-correct

Q.13 Unattempt

The excess pressure inside a soap bubble of radius 0.5 cm is balanced by the pressure due to an oil column of height 4 mm . If the density of the oil is

900 kg m^{- 3}

, then the surface tension of the soap solution is (Acceleration due to gravity

= 10 {ms}^{- 2}

)

The excess pressure inside a soap bubble of radius 0.5 cm is balanced by the pressure due to an oil column of height 4 mm . If the density of the oil is

900 kg m^{- 3}

, then the surface tension of the soap solution is (Acceleration due to gravity

= 10 {ms}^{- 2}

Water flows through a horizontal pipe of variable cross-section at the rate of

12 π

litre per minute. The velocity of the water at the point, where the diameter of the pipe becomes 2 cm is

Water flows through a horizontal pipe of variable cross-section at the rate of

12 π

litre per minute. The velocity of the water at the point, where the diameter of the pipe becomes 2 cm is

- 20^{\circ} C

is mixed with 25 g of steam at

100^{\circ} C

, then the final mixture at thermal equilibrium contains

When 54 g of ice at

- 20^{\circ} C

is mixed with 25 g of steam at

100^{\circ} C

, then the final mixture at thermal equilibrium contains

Q.16 Correct

Q.16 In-correct

Q.16 Unattempt

A solid sphere at a temperature

T K

is cut in to two hemisphere. The ratio of energies radiated by one hemisphere to the whole sphere per second is

A solid sphere at a temperature

T K

is cut in to two hemisphere. The ratio of energies radiated by one hemisphere to the whole sphere per second is

Q.17 Correct

Q.17 In-correct

Q.17 Unattempt

d Q, d U

and

d W

are heat energy absorbed, change in internal energy and external work done respectively by a diatomic gas at constant pressure, then

d W : d U : d Q

d Q, d U

and

d W

are heat energy absorbed, change in internal energy and external work done respectively by a diatomic gas at constant pressure, then

d W : d U : d Q

Q.18 Correct

Q.18 In-correct

Q.18 Unattempt

If the temperature of a gas increased from

27^{\circ} C

159^{\circ} C

, the increase in the rms speed of the gas molecules is

If the temperature of a gas increased from

27^{\circ} C

159^{\circ} C

, the increase in the rms speed of the gas molecules is

Q.19 Correct

Q.19 In-correct

Q.19 Unattempt

A boy standing on a platform observes the frequency of a train horn as it passes by. The change in the frequency noticed as the train approaches and recedes him with a velocity of 108 kmph is (speed of sound in air

= 330 {ms}^{- 1}

)

= 330 {ms}^{- 1}

If three sources of sound of frequencies

(n - 1), n

and

(n + 1)

are vibrated together, the number of beats produced and heard per second respectively are

If three sources of sound of frequencies

(n - 1), n

and

(n + 1)

are vibrated together, the number of beats produced and heard per second respectively are

Q.21 Correct

Q.21 In-correct

Q.21 Unattempt

A small angled prism is made of a material of refractive index

\frac{3}{2}

. The ratio of the angles of minimum deviations when the prism is placed in air and in water of refractive index

\frac{4}{3}

A small angled prism is made of a material of refractive index

\frac{3}{2}

. The ratio of the angles of minimum deviations when the prism is placed in air and in water of refractive index

\frac{4}{3}

Q.22 Correct

Q.22 In-correct

Q.22 Unattempt

If you are using eye glasses of power 2 D, your near point is

Q.23 Correct

Q.23 In-correct

Q.23 Unattempt

The diameter of the objective of a telescope is 3.6 m . The limit of resolution of the telescope for a light of wavelength 540 nm is

Q.24 Correct

Q.24 In-correct

Q.24 Unattempt

Two point charges of magnitudes

- 8 μ C

and

+ 32 μ C

are separated by a distance of 15 cm in air. The position of the point from

- 8 μ C

charge at which the resultant electric field becomes zero is

Two point charges of magnitudes

- 8 μ C

and

+ 32 μ C

are separated by a distance of 15 cm in air. The position of the point from

- 8 μ C

charge at which the resultant electric field becomes zero is

Q.25 Correct

Q.25 In-correct

Q.25 Unattempt

If half of the space between the plates of a parallel plate capacitor is filled with a medium of dielectric constant 4 , the capacitance is

C_{1}

. If one-third of the space between the plates of the capacitor is filled with the medium of dielectric constant 4 , the capacitance is

C_{2}

. If in both cases, the dielectric is placed parallel to the plated of the capacitor, then

C_{1} : C_{2} =

If half of the space between the plates of a parallel plate capacitor is filled with a medium of dielectric constant 4 , the capacitance is

C_{1}

. If one-third of the space between the plates of the capacitor is filled with the medium of dielectric constant 4 , the capacitance is

C_{2}

. If in both cases, the dielectric is placed parallel to the plated of the capacitor, then

C_{1} : C_{2} =

Q.26 Correct

Q.26 In-correct

Q.26 Unattempt

The potential difference between the ends of a straight conductor of length 20 cm is 16 V . If the drift speed of the electrons is

2.4 \times 10^{- 4} {ms}^{- 1}

, the electron mobility in

m^{2} V^{- 1} s^{- 1}

The potential difference between the ends of a straight conductor of length 20 cm is 16 V . If the drift speed of the electrons is

2.4 \times 10^{- 4} {ms}^{- 1}

, the electron mobility in

m^{2} V^{- 1} s^{- 1}

Q.27 Correct

Q.27 In-correct

Q.27 Unattempt

The potential difference $V$ across the filament of the bulb shown in the given Wheatstone bridge varies as $V = i (2 i + 1)$ , where $i$ is the current in ampere through the filament of the bulb. The emf of the battery $V_{a}$ , so that the bridge become balanced is