AP EAPCET (AP EAMCET) 2024 Question Paper May 20 Shift 1 (Available): Download MPC Question Paper with Answer Key PDF

Let \( f(x) = 3 + 2x \) and \( g_n(x) = (f \circ f \circ \dots n times) (x) \). If for all \( n \in \mathbb{N} \), the lines \( y = g_n(x) \) pass through a fixed point \( (a, \beta) \), then \( \alpha + \beta = ? \)

• (1) \( -5 \)
• (2) \( -4 \)
• (3) \( -3 \)
• (4) \( -6 \)

Let \( a > 1 \) and \( 0 < b < 1 \). -∞\( f : \mathbb{R} \to [0, 1] \) is defined by \( f(x) = \begin{cases} a^x & if x < 0
b^x & if 0 \leq x \leq 1 \end{cases} \), then \( f(x) \) is:

• (1) A bijection
• (2) One-one but not onto
• (3) Onto but not one-one
• (4) Neither one-one nor onto

Evaluate the sum: \[ \frac{1}{3 \cdot 7} + \frac{1}{7 \cdot 11} + \frac{1}{11 \cdot 15} + \dots up to 50 terms= \]

• (1) \( \frac{50}{203} \)
• (2) \( \frac{50}{609} \)
• (3) \( \frac{150}{203} \)
• (4) \( \frac{25}{609} \)

If





then evaluate \( A^2 - 5A + 6I \)=

• (1)
• (2)
• (3)
• (4)

Correct Answer: (4)
View Solution

Sum of the positive roots of the equation:

• (1) \( \frac{1 + \sqrt{13}}{2} \)
• (2) \( 1 \)
• (3) \( \frac{\sqrt{13} - 1}{2} \)
• (4) \( 3 \)

If the solution of the system of simultaneous linear equations: \[ x + y - z = 6, \] \[ 3x + 2y - z = 5, \] \[ 2x - y - 2z + 3 = 0 \]
is \( x = \alpha, y = \beta, z = \gamma \), then \( \alpha + \beta = ? \)

• (1) \( -7 \)
• (2) \( 2 \)
• (3) \( 1 \)
• (4) \( -2 \)

If the point \( P \) represents the complex number \( z = x + iy \) in the Argand plane and if \[ \frac{z\bar{z} + 1}{z - 1} \]
is a purely imaginary number, then the locus of \( P \) is:

• (1) \( x^2 + y^2 + x - y = 0 \) and \( (x, y) \neq (1,0) \)
• (2) \( x^2 + y^2 - x + y = 0 \) and \( (x, y) \neq (1,0) \)
• (3) \( x^2 + y^2 - x + y = 0 \) and \( (x, y) = (1,0) \)
• (4) \( x^2 + y^2 + x + y = 0 \)

The set \( S = \{ z \in \mathbb{C} : |z + 1 - i| = 1 \} \) represents:

• (1) the circle with centre at \( (-1, 1) \) and radius 1 unit
• (2) the circle with centre at \( (1, -1) \) and radius 1 unit
• (3) the closed circular disc with centre at \( (-1, -1) \) and radius 1 unit
• (4) the closed circular disc with centre at \( (1, -1) \) and radius 1 unit

If cos \alpha + cos \beta + cos \gamma = sin \alpha + sin \beta + sin \gamma = 0,
then evaluate (\cos^3 \alpha + \cos^3 \beta + \cos^3 \gamma)^2 + (\sin^3 \alpha + \sin^3 \beta + \sin^3 \gamma)^2 =

• (1) \( 1 \)
• (2) \( \frac{3}{4} \)
• (3) \( \frac{9}{16} \)
• (4) \( \frac{9}{8} \)

If \( \alpha \) and \( \beta \) are two double roots of the equation: x^2 + 3(a + 3)x - 9a = 0 for different values of \( a \) (where \( \alpha > \beta \)), then the minimum value of the equation: x^2 + \alpha x - \beta = 0 is:

• (1) \( \frac{69}{4} \)
• (2) \( \frac{69}{4} \)
• (3) \( \frac{35}{4} \)
• (4) \( \frac{35}{4} \)

If \( 2x^2 + 3x - 2 = 0 \) and \( 3x^2 + \alpha x - 2 = 0 \) have one common root, then the sum of all possible values of \( \alpha \) is:

• (1) \( -3.5 \)
• (2) \( 7.5 \)
• (3) \( -7.5 \)
• (4) \( -1.5 \)

If the sum of two roots of \( x^3 + px^2 + qx - 5 = 0 \) is equal to its third root, then \( p(q^2 - 4q) = \) ?

• (1) \( -20 \)
• (2) \( 20 \)
• (3) \( 40 \)
• (4) \( -40 \)

If \( P(x) = x^5 + ax^4 + bx^3 + cx^2 + dx + e \) is a polynomial such that: \[ P(0) = 1, \quad P(1) = 2, \quad P(2) = 5, \] \[ P(3) = 10, \quad P(4) = 17, \]
then find the value of \( P(5) \)=

• (1) \( 26 \)
• (2) \( 146 \)
• (3) \( 126 \)
• (4) \( 76 \)

If a polygon of \( n \) sides has 275 diagonals, then \( n \) is:

• (1) 25
• (2) 35
• (3) 20
• (4) 15

The number of positive divisors of 1080 is:

• (1) 30
• (2) 32
• (3) 23
• (4) 31

If \( a_n = \sum_{r=0}^{n} \frac{1}{\binom{n}{r}} \), then \( \sum_{r=0}^{n} r \binom{n}{r} = \):

• (1) \( (n-1) a_n \)
• (2) \( n a_n \)
• (3) \( \frac{n}{2} a_n \)
• (4) \( a_{n+1} \)

The coefficient of \( x^5 \) in the expansion of \( \left( 2x^3 - \frac{1}{3x^2} \right)^5 \) is:

• (1) 8
• (2) 9
• (3) \( \frac{80}{9} \)
• (4) \( \frac{29}{3} \)

Evaluate the infinite series: \[ 1 + \frac{1}{3} + \frac{1.3}{3.6} + \frac{1.3.5}{3.6.9} + \dots to \infty = \]

• (1) \( \sqrt{5} \)
• (2) \( \sqrt{6} \)
• (3) \( \sqrt{15} \)
• (4) \( \sqrt{3} \)

Given the equation: \[ \frac{A}{x-a} + \frac{Bx + C}{x^2 + b^2} = \frac{1}{(x-a)(x^2 + b^2)} \]
then \( C \)=

• (1) \( \frac{-1}{a^2 + b^2} \)
• (2) \( \frac{1}{a^2 + b^2} \)
• (3) \( \frac{-a}{a^2 + b^2} \)
• (4) \( \frac{a}{a^2 + b^2} \)

If \[ \cos \frac{ \pi }{8} + \cos \frac{3 \pi }{8} + \cos \frac{5 \pi }{8} + \cos \frac{7 \pi }{8} = k, \]
then evaluate \[ \sin^{-1} \left( \frac{k}{\sqrt{2}} \right) + \cos^{-1} \left( \frac{k}{3} \right)= \]

• (1) \( \frac{2\pi}{3} \)
• (2) \( \frac{3\pi}{4} \)
• (3) \( \frac{\pi}{4} \)
• (4) \( \frac{\pi}{2} \)

Evaluate the expression: \[ \frac{\cos 10^\circ + \cos 80^\circ}{\sin 80^\circ - \sin 10^\circ}. \]

• (1) \( \tan 35^\circ \)
• (2) \( \tan 55^\circ \)
• (3) \( \tan 20^\circ \)
• (4) \( \tan 70^\circ \)

Evaluate the expression: \[ \frac{\sin 1^\circ + \sin 2^\circ + \dots + \sin 89^\circ}{2(\cos 1^\circ + \cos 2^\circ + \dots + \cos 44^\circ) + 1} =\]

• (1) \( \sqrt{2} \)
• (2) \( \frac{1}{\sqrt{2}} \)
• (3) \( 2 \)
• (4) \( \frac{1}{2} \)

The number of ordered pairs \( (x, y) \) satisfying the equations: \[ \sin x + \sin y = \sin (x + y) \quad and \quad |x| + |y| = 1. \]

• (1) 2
• (2) 3
• (3) 4
• (4) 6

Evaluate: \[ 4 \tan^{-1} \frac{1}{5} - \tan^{-1} \frac{1}{70} + \tan^{-1} \frac{1}{99}= \]

• (1) \( \frac{\pi}{12} \)
• (2) \( \frac{\pi}{6} \)
• (3) \( \frac{\pi}{4} \)
• (4) \( \frac{\pi}{3} \)

If \( 5 \sinh x - \cosh x = 5 \), then one of the values of \( \tanh x \) is:

• (1) \( \frac{2}{5} \)
• (2) \( \frac{3}{5} \)
• (3) \( \frac{-3}{5} \)
• (4) \( \frac{-1}{5} \)

In \( \triangle ABC \), if \( r_1 = 4 \), \( r_2 = 8 \), \( r_3 = 24 \), then find \( a \)=

• (1) \( 0 \)
• (2) \( \frac{16}{\sqrt{5}} \)
• (3) \( 16\sqrt{5} \)
• (4) \( \sqrt{5} \)

If a circle is inscribed in an equilateral triangle of side \( a \), then the area of any square inscribed in this circle (in square units) is:

• (1) \( \frac{2a^2}{3} \)
• (2) \( \frac{\sqrt{3}a^2}{2} \)
• (3) \( \frac{a^2}{2\sqrt{3}} \)
• (4) \( \frac{a^2}{6} \)

Match the items of List-I with those of List-II (Here \( \Delta \) denotes the area of \( \triangle ABC \)).




Then the correct match is

Let \( O(0) \), \( A(\hat{i} + \hat{j} + \hat{k}) \), \( B(-2\hat{i} + 3\hat{k}) \), \( C(2\hat{i} + \hat{j}) \), and \( D(4\hat{k}) \) be the position vectors of the points \( O, A, B, C, \) and \( D \). If a line passing through \( A \) and \( B \) intersects the plane passing through \( O, C, \) and \( D \) at the point \( R \), then the position vector of \( R \) is:

Let \( \overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c} \) be non-coplanar vectors. If \( \alpha \overrightarrow{d} = \overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c} \), \( \beta \overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c} + \overrightarrow{d} \), then \( | \overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c} + \overrightarrow{d} | = ? \)

• (1) \( 1 \)
• (2) \( 2 \)
• (3) \( |\overrightarrow{a} - \overrightarrow{b} - \overrightarrow{c} | \)
• (4) \( 0 \)

Let \( \overrightarrow{u}, \overrightarrow{v}, \overrightarrow{w} \) be three unit vectors. Let \( \overrightarrow{p} = \overrightarrow{u} + \overrightarrow{v} + \overrightarrow{w} \), \( \overrightarrow{q} = \overrightarrow{u} \times (\overrightarrow{p} \times \overrightarrow{w}) \). If \( \overrightarrow{p} \cdot \overrightarrow{u} = \frac{3}{2} \), \( \overrightarrow{p} \cdot \overrightarrow{v} = \frac{7}{4} \), \( |\overrightarrow{p}| = 2 \), and \( \overrightarrow{v} = K \overrightarrow{q} \), then \( K = ? \)

• (1) \( -1 \)
• (2) \( 2 \)
• (3) \( 3 \)
• (4) \( -2 \)

The distance of the point \( O(0,0,0) \) from the plane \( \overrightarrow{r} \cdot (\hat{i} + \hat{j} + \hat{k}) = 5 \) measured parallel to \( 2\hat{i} + 3\hat{j} - 6\hat{k} \) is?

• (1) \( 35 \)
• (2) \( 30 \)
• (3) \( 25 \)
• (4) \( 42 \)

If \( \overrightarrow{a}, \overrightarrow{b} \) are two non-collinear vectors, then \( |\overrightarrow{b}| \overrightarrow{a} + |\overrightarrow{a}| \overrightarrow{b} \) represents

• (1) a vector parallel to an angle bisector of \( \overrightarrow{a}, \overrightarrow{b} \)
• (2) a vector along the difference of the vectors \( \overrightarrow{a}, \overrightarrow{b} \)
• (3) a vector along \( \overrightarrow{a} + \overrightarrow{b} \)
• (4) a vector outside the triangle having \( \overrightarrow{a}, \overrightarrow{b} \) as adjacent sides

Let \( \overline{X} \) and \( \overline{Y} \) be the arithmetic means of the runs of two batsmen A and B in 10 innings respectively, and \( \sigma_A, \sigma_B \) are the standard deviations of their runs in them. If batsman A is more consistent than B, then he is also a higher run scorer only when

• (1) \( 0 < \frac{\sigma_A}{\sigma_B} < \frac{\overline{X}}{\overline{Y}} < 1 \)
• (2) \( \frac{\overline{X}}{\overline{Y}} \geq \frac{\sigma_A}{\sigma_B} \)
• (3) \( \frac{\overline{X}}{\overline{Y}} < \frac{\sigma_A}{\sigma_B} \)
• (4) \( \frac{\overline{X}}{\overline{Y}} > 1; 1 \leq \frac{\overline{X}}{\overline{Y}} \leq \frac{\sigma_A}{\sigma_B} \)

S is the sample space and A, B are two events of a random experiment. Match the items of List A with the items of List B.






Then the correct match is:

• (1) I - e, II - d, III - c, IV - b
• (2) I - a, II - c, III - b, IV - d
• (3) I - d, II - c, III - b, IV - a
• (4) I - b, II - d, III - a, IV - e

If \( P(A \cap B) + P(B \mid A \cap B) = \), then:

• (1) 1
• (2) \( P(A \cup B) \)
• (3) \( P(A \cap B) \)
• (4) 2

Two digits are selected at random from the digits 1 through 9. If their sum is even, then the probability that both are odd is:

• (1) \( \frac{3}{8} \)
• (2) \( \frac{1}{2} \)
• (3) \( \frac{5}{8} \)
• (4) \( \frac{3}{4} \)

A, B, C are mutually exclusive and exhaustive events of a random experiment and E is an event that occurs in conjunction with one of the events A, B, C. The conditional probabilities of E given the happening of A, B, C are respectively 0.6, 0.3 and 0.1. If \( P(A) = 0.30 \) and \( P(B) = 0.50 \), then \( P(C \mid E) = \):

• (1) \( \frac{2}{35} \)
• (2) \( \frac{15}{35} \)
• (3) \( \frac{18}{35} \)
• (4) \( \frac{17}{35} \)

For the probability distribution of a discrete random variable \( X \) as given below, the mean of \( X \) is:

In a random experiment, two dice are thrown and the sum of the numbers appeared on them is recorded. This experiment is repeated 9 times. If the probability that a sum of 6 appears at least once is \( P_1 \) and a sum of 8 appears at least once is \( P_2 \), then \( P_1 : P_2 = \):

• (1) \( 4:3 \)
• (2) \( 3:1 \)
• (3) \( 1:2 \)
• (4) \( 1:1 \)

If the line segment joining the points \( (1,0) \) and \( (0,1) \) subtends an angle of \( 45^\circ \) at a variable point \( P \), then the equation of the locus of \( P \) is:

If the origin is shifted to a point \( P \) by the translation of axes to remove the \( y \)-term from the equation \( x^2 - y^2 + 2y - 1 = 0 \), then the transformed equation of it is:

A line \( L \) intersects the lines \( 3x - 2y - 1 = 0 \) and \( x + 2y + 1 = 0 \) at the points \( A \) and \( B \). If the point \( (1,2) \) bisects the line segment \( AB \) and \( \frac{a}{b} x + \frac{b}{a} y = 1 \) is the equation of the line \( L \), then \( a + 2b + 1 = ? \)

A line \( L \) passing through the point \( (2,0) \) makes an angle \( 60^\circ \) with the line \( 2x - y + 3 = 0 \). If \( L \) makes an acute angle with the positive X-axis in the anticlockwise direction, then the Y-intercept of the line \( L \) is?

If the slope of one line of the pair of lines \( 2x^2 + hxy + 6y^2 = 0 \) is thrice the slope of the other line, then \( h \) = ?

If the equation of the pair of straight lines passing through the point \( (1, 1) \) and perpendicular to the pair of lines \( 3x^2 + 11xy - 4y^2 = 0 \) is \( ax^2 + 2hxy + by^2 + 2gx + 2fy + 12 = 0 \), then find \( 2(a + h - b - g + f - 12) = ? \)

• (1) \( 7 \)
• (2) \( -7 \)
• (3) \( -19 \)
• (4) \( 13 \)

Equation of the circle having its centre on the line \( 2x + y + 3 = 0 \) and having the lines \( 3x + 4y - 18 = 0 \) and \( 3x + 4y + 2 = 0 \) as tangents is:

If power of a point \( (4,2) \) with respect to the circle \( x^2 + y^2 - 2x + 6y + a^2 - 16 = 0 \) is 9, then the sum of the lengths of all possible intercepts made by such circles on the coordinate axes is

Let \( a \) be an integer multiple of 8. If \( S \) is the set of all possible values of \( a \) such that the line \( 6x + 8y + a = 0 \) intersects the circle \( x^2 + y^2 - 4x - 6y + 9 = 0 \) at two distinct points, then the number of elements in \( S \) is:

If the circles \( x^2 + y^2 - 8x - 8y + 28 = 0 \) and \( x^2 + y^2 - 8x - 6y + 25 - a^2 = 0 \) have only one common tangent, then \( a \) is:

If the equation of the circle passing through the points of intersection of the circles \[ x^2 - 2x + y^2 - 4y - 4 = 0, \quad x^2 + y^2 + 4y - 4 = 0 \] and the point \( (3,3) \) is given by \[ x^2 + y^2 + \alpha x + \beta y + \gamma = 0, \] then \( 3(\alpha + \beta + \gamma) \) is:

A common tangent to the circle \( x^2 + y^2 = 9 \) and the parabola \( y^2 = 8x \) is

Let \( F \) and \( F' \) be the foci of the ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) (where \( b < 2 \)), and let \( B \) be one end of the minor axis. If the area of the triangle \( FBF' \) is \( \sqrt{3} \) sq. units, then the eccentricity of the ellipse is:

If a circle of radius 4 cm passes through the foci of the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) and is concentric with the hyperbola, then the eccentricity of the conjugate hyperbola of that hyperbola is:

If a tangent to the hyperbola \( x^2 - \frac{y^2}{3} = 1 \) is also a tangent to the parabola \( y^2 = 8x \), then the equation of such tangent with the positive slope is:

If \( A(1,0,2) \), \( B(2,1,0) \), \( C(2,-5,3) \), and \( D(0,3,2) \) are four points and the point of intersection of the lines \( AB \) and \( CD \) is \( P(a,b,c) \), then \( a + b + c = ? \)

The direction cosines of two lines are connected by the relations \( 1 + m - n = 0 \) and \( lm - 2mn + nl = 0 \). If \( \theta \) is the acute angle between those lines, then \( \cos \theta = \) ?

The distance from a point \( (1,1,1) \) to a variable plane \(\pi\) is 12 units and the points of intersections of the plane with X, Y, Z-axes are \( A, B, C \) respectively. If the point of intersection of the planes through the points \( A, B, C \) and parallel to the coordinate planes is \( P \), then the equation of the locus of \( P \) is:

Evaluate the limit: \[ \lim_{x \to 0} \frac{\sqrt{1 + \sqrt{1 + x^4}} - \sqrt{2 + x^5 + x^6}}{x^4} =\]

Evaluate the limit: \[ \lim_{x \to 1} \frac{\sqrt{x} - 1}{(\cos^{-1} x)^2} =\]

If a function \( f(x) \) is defined as: \[ f(x) = \begin{cases} \frac{\tan(4x) + \tan 2x}{x} & if x > 0
\beta & if x = 0
\frac{\sin 3x - \tan 3x}{x^2} & if x < 0 \end{cases} \]
and is continuous at \( x = 0 \), then find \( |\alpha| + |\beta| \).

If \( y = \tan(\log x) \), then \( \frac{d^2y}{dx^2} \) is given by:

For \( x < 0 \), \( \frac{d}{dx} [|x|^x] \) is given by:

If \( y = x - x^2 \), then the rate of change of \( y^2 \) with respect to \( x^2 \) at \( x = 2 \) is:

If \( T = 2\pi \sqrt{\frac{L}{g}} \), \( g \) is a constant and the relative error in \( T \) is \( k \) times to the percentage error in \( L \), then \( \frac{1}{k} = \) ?

The angle between the curves \( y^2 = 2x \) and \( x^2 + y^2 = 8 \) is

If the function \( f(x) = \sqrt{x^2 - 4} \) satisfies the Lagrange’s Mean Value Theorem on \([2, 4]\), then the value of \( C \) is

If \( x, y \) are two positive integers such that \( x + y = 20 \) and the maximum value of \( x^3 y \) is \( k \) at \( x = a, y = \beta \), then \( \frac{k}{\alpha^2 \beta^2} = ? \)

Evaluate the integral: \[ \int \frac{2x^2 - 3}{(x^2 - 4)(x^2 + 1)} \,dx = A \tan^{-1} x + B \log(x - 2) + C \log(x + 2) \]
Given that, \[ 64A + 7B - 5C = ? \]

Evaluate the integral: \[ \int \frac{3x^9 + 7x^8}{(x^2 + 2x + 5x^9)^2} \,dx= \]

Evaluate the integral: \[ I = \int \frac{\cos x + x \sin x}{x (x + \cos x)} dx =\]

If \[ \int \frac{2}{1+\sin x} dx = 2 \log |A(x) - B(x)| + C \]
and \( 0 \leq x \leq \frac{\pi}{2} \), then \( B(\pi/4) = \) ?

• (1) \( \frac{1}{\sqrt{2} + 3\sqrt{3}} \)
• (2) \( \frac{1}{\sqrt{3} + 2\sqrt{2}} \)
• (3) \( \frac{-1}{\sqrt{3} + 2\sqrt{2}} \)
• (4) \( \frac{2}{\sqrt{2} + \sqrt{2}} \)

If \[ \int \frac{3}{2\cos 3x \sqrt{2} \sin 2x} dx = \frac{3}{2} (\tan x)^{\beta} + \frac{3}{10} (\tan x)^4 + C \]
then \( A = \) ?

• (1) \( \frac{1}{2} \)
• (2) \( 1 \)
• (3) \( 5 \)
• (4) \( \frac{5}{2} \)

Evaluate the integral: \[ I = \int_{-\pi}^{\pi} \frac{x \sin^3 x}{4 - \cos^2 x} dx. \]

• (1) \( 2\pi(1 - \log 3) \)
• (2) \( 2\pi \left(1 - \frac{3}{4} \log 3 \right) \)
• (3) \( \pi \left(1 - \frac{3}{4} \log 3 \right) \)
• (4) \( 4\pi(1 - \log 3) \)

Evaluate the integral: \[ I = \int_{-3}^{3} |2 - x| dx. \]

• (1) \( 12 \)
• (2) \( 16 \)
• (3) \( 13 \)
• (4) \( 25 \)

Evaluate the integral: \[ I = \int_{\frac{1}{\sqrt[5]{32}}}^{\frac{1}{\sqrt[5]{31}}} \frac{1}{\sqrt[5]{x^{30} + x^{25}}} dx. \]

• (1) \( \frac{65}{4} \)
• (2) \( \frac{-75}{4} \)
• (3) \( \frac{75}{4} \)
• (4) \( \frac{-65}{4} \)

Find the area of the region (in square units) enclosed by the curves: \[ y^2 = 8(x+2), \quad y^2 = 4(1-x) \]
and the Y-axis.

• (1) \( \frac{8}{3} (5 - 3\sqrt{2}) \)
• (2) \( \frac{8}{3} (\sqrt{2} -1) \)
• (3) \( \frac{8}{3} (3 - \sqrt{2}) \)
• (4) \( \frac{4}{3} (\sqrt{2} + 1) \)

The sum of the order and degree of the differential equation: \[ \frac{d^y}{dx^t} = c + \left( \frac{d^y}{dx^t} \right)^{\frac{3}{2}} \]
is:

• (1) \( 4 \)
• (2) \( 6 \)
• (3) \( 5 \)
• (4) \( 8 \)

The general solution of the differential equation \[ (x + y)y \,dx + (y - x)x \,dy = 0 \]
is:

• (1) \( x + y \log(cy) = 0 \)
• (2) \( \frac{y}{x} = \log(xy) + c \)
• (3) \( x + y \log(cxy) = 0 \)
• (4) \( \frac{y}{x} = \log(cxy) \)

The general solution of the differential equation \[ (y^2 + x + 1) dy = (y + 1) dx \]
is:

• (1) \( x + 2 + (y+1) \log(y+1)^2 = y + c \)
• (2) \( x + 2 + \log(y+1)^2 = \frac{y}{y+1} + c \)
• (3) \( \frac{x}{y+1} = \log(y+1)^2 + y + c \)
• (4) \( \frac{x+2}{y+1} \log(y+1)^2 = y + c \)

E, m, L, G represent energy, mass, angular momentum and gravitational constant respectively. The dimensions of \[ \frac{EL^2}{mG^2} \]
will be that of

• (1) Angle (కోణం)
• (2) Length (పొడువు)
• (3) Mass (ద్రవ్యరాశి)
• (4) Time (సమయం)

A body starting from rest with an acceleration of \( \frac{5}{4} \, ms^{-2} \). The distance travelled by the body in the third second is:

• (1) \( \frac{15}{8} \, m \)
• (2) \( \frac{25}{8} \, m \)
• (3) \( \frac{25}{4} \, m \)
• (4) \( \frac{12}{7} \, m \)

A projectile can have the same range \( R \) for two angles of projection. Their initial velocities are the same. If \( T_1 \) and \( T_2 \) are times of flight in two cases, then the product of two times of flight is directly proportional to:

• (1) \( \frac{1}{R} \)
• (2) \( R^3 \)
• (3) \( R^2 \)
• (4) \( R \)

If \[ | \vec{P} + \vec{Q} | = | \vec{P} | = | \vec{Q} |, \]
then the angle between \( \vec{P} \) and \( \vec{Q} \) is:

• (1) \( 0^\circ \)
• (2) \( 120^\circ \)
• (3) \( 60^\circ \)
• (4) \( 90^\circ \)

A 4 kg mass is suspended as shown in the figure. All pulleys are frictionless and spring constant \( K \) is \( 8 \times 10^3 \) Nm\(^{-1}\). The extension in spring is ( \( g = 10 \) ms\(^{-2}\) )

• (1) \( 2 \) mm
• (2) \( 2 \) cm
• (3) \( 4 \) cm
• (4) \( 4 \) mm

A 3 kg block is connected as shown in the figure. Spring constants of two springs \( K_1 \) and \( K_2 \) are 50 Nm\(^{-1}\) and 150 Nm\(^{-1}\) respectively. The block is released from rest with the springs unstretched. The acceleration of the block in its lowest position is ( \( g = 10 \) ms\(^{-2}\) )

• (1) \( 10 \) ms\(^{-2}\)
• (2) \( 12 \) ms\(^{-2}\)
• (3) \( 8 \) ms\(^{-2}\)
• (4) \( 8.8 \) ms\(^{-2}\)

Two bodies A and B of masses \( 2m \) and \( m \) are projected vertically upwards from the ground with velocities \( u \) and \( 2u \) respectively. The ratio of the kinetic energy of body A and the potential energy of body B at a height equal to half of the maximum height reached by body A is:

• (1) 8 : 1
• (2) 1 : 1
• (3) 4 : 1
• (4) 2 : 1

A body of mass 2 kg collides head-on with another body of mass 4 kg. If the relative velocities of the bodies before and after collision are 10 ms\(^{-1}\) and 4 ms\(^{-1}\) respectively, the loss of kinetic energy of the system due to the collision is

• (1) \( 28 \) J
• (2) \( 56 \) J
• (3) \( 84 \) J
• (4) \( 42 \) J

The moment of inertia of a solid sphere of mass 20 kg and diameter 20 cm about the tangent to the sphere is:

• (1) \( 0.24 \, kgm^2 \)
• (2) \( 0.14 \, kgm^2 \)
• (3) \( 0.28 \, kgm^2 \)
• (4) \( 0.08 \, kgm^2 \)

A wooden plank of mass 90 kg and length 3.3 m is floating on still water. A girl of mass 20 kg walks from one end to the other end of the plank. The distance through which the plank moves is

• (1) \(30\) cm
• (2) \(40\) cm
• (3) \(80\) cm
• (4) \(60\) cm

In a time of 2 s, the amplitude of a damped oscillator becomes \( \frac{1}{e} \) times its initial amplitude \( A \). In the next two seconds, the amplitude of the oscillator is:

• (1) \( \frac{1}{2e} \)
• (2) \( \frac{2}{e} \)
• (3) \( \frac{1}{e^2} \)
• (4) \( \frac{2}{e^2} \)

A particle is executing simple harmonic motion with a time period of 3 s. At a position where the displacement of the particle is 60% of its amplitude, the ratio of the kinetic and potential energies of the particle is:

• (1) 5 : 3
• (2) 16 : 9
• (3) 4 : 3
• (4) 25 : 9

The acceleration due to gravity at a height of 6400 km from the surface of the earth is \(2.5 \, ms^{-2}\). The acceleration due to gravity at a height of 12800 km from the surface of the earth is (Radius of the earth = 6400 km)

• (1) \(1.11 \, ms^{-2}\)
• (2) \(1.5 \, ms^{-2}\)
• (3) \(2.22 \, ms^{-2}\)
• (4) \(1.25 \, ms^{-2}\)

When the load applied to a wire is increased from 5 kg wt to 8 kg wt, the elongation of the wire increases from 1 mm to 1.8 mm. The work done during the elongation of the wire is (Acceleration due to gravity = 10 m/s\(^2\)):

• (1) \( 47 \times 10^{-3} \, J \)
• (2) \( 72 \times 10^{-3} \, J \)
• (3) \( 25 \times 10^{-3} \, J \)
• (4) \( 97 \times 10^{-3} \, J \)

The radius of cross-section of the cylindrical tube of a spray pump is 2 cm. One end of the pump has 50 fine holes each of radius 0.4 mm. If the speed of flow of the liquid inside the tube is 0.04 m/s, the speed of ejection of the liquid from the holes is:

• (1) 6 m/s
• (2) 2 m/s
• (3) 4 m/s
• (4) 3 m/s

The temperature difference across two cylindrical rods A and B of same material and same mass are 40°C and 60°C respectively. In steady state, if the rates of flow of heat through the rods A and B are in the ratio 3 : 8, the ratio of the lengths of the rods A and B is:

• (1) 1 : 3
• (2) 5 : 3
• (3) 4 : 3
• (4) 2 : 3

The efficiency of a Carnot cycle is \( \frac{1}{6} \). By lowering the temperature of the sink by 65 K, it increases to \( \frac{1}{3} \). The initial and final temperature of the sink are:

• (1) \( 400 K, 310 K \)
• (2) \( 525 K, 65 K \)
• (3) \( 309 K, 235 K \)
• (4) \( 325 K, 260 K \)

In a cold storage, ice melts at the rate of 2 kg per hour when the external temperature is 20°C. The minimum power output of the motor used to drive the refrigerator which just prevents the ice from melting is (latent heat of fusion of ice = 80 cal g\(^{-1}\))

• (1) \( 28.5 W \)
• (2) \( 13.6 W \)
• (3) \( 9.75 W \)
• (4) \( 16.4 W \)

A Carnot engine has the same efficiency between 800 K and 500 K, and \( x > 600 \) K and 600 K.
The value of \( x \) is:

• (1) \( 1000 K \)
• (2) \( 960 K \)
• (3) \( 846 K \)
• (4) \( 754 K \)

When the temperature of a gas is raised from 27°C to 90°C, the increase in the rms velocity of the gas molecules is:

• (1) \( 10% \)
• (2) \( 15% \)
• (3) \( 20% \)
• (4) \( 17.5% \)

If the frequency of a wave is increased by 25%, then the change in its wavelength is (medium not changed):

• (1) \( 20% \) increase
• (2) \( 20% \) decrease
• (3) \( 25% \) increase
• (4) \( 25% \) decrease

An object lying 100 cm inside water is viewed normally from air. If the refractive index of water is \( \frac{4}{3} \), then the apparent depth of the object is:

• (1) \( 100 cm \)
• (2) \( 50 cm \)
• (3) \( 25 cm \)
• (4) \( 75 cm \)

In Young’s double slit experiment, two slits are placed 2 mm from each other. The interference pattern is observed on a screen placed 2 m from the plane of the slits. Then the fringe width for a light of wavelength 400 nm is:

• (1) \( 0.4 \times 10^{-6} m \)
• (2) \( 4 \times 10^{-6} m \)
• (3) \( 0.4 \times 10^{-3} m \)
• (4) \( 400 m \)

Two spheres A & B of radii 4 cm & 6 cm are given charges of 80 µC & 40 µC respectively. If they are connected by a fine wire, the amount of charge flowing from one to the other is:

• (1) \( 32 \) µC from A to B
• (2) \( 32 \) µC from B to A
• (3) \( 20 \) µC from A to B
• (4) \( 16 \) µC from B to A

The angle between the electric dipole moment of a dipole and the electric field strength due to it on the equatorial line is:

• (1) \( 0^\circ \)
• (2) \( 90^\circ \)
• (3) \( 180^\circ \)
• (4) \( 270^\circ \)

Two condensers \( C_1 \) & \( C_2 \) in a circuit are joined as shown in the figure. The potential of point A is \( V_1 \) and that of point B is \( V_2 \). The potential at point D will be:

• (1) \( \frac{1}{2} (V_1 + V_2) \)
• (2) \( \)
• (3) \( \frac{C_1V_1 + C_2V_2}{C_1 + C_2} \)
• (4) \( \frac{C_2V_1 - C_1V_2}{C_1 + C_2} \)

A block has dimensions 1 cm, 2 cm, and 3 cm. The ratio of the maximum resistance to minimum resistance between any pair of opposite faces of the block is:

• (1) \( 9:1 \)
• (2) \( 1:9 \)
• (3) \( 18:1 \)
• (4) \( 6:1 \)

A current of \(6A\) enters one corner \(P\) of an equilateral triangle \(PQR\) having three wires of resistance \(2 \Omega\) each and leaves by the corner \(R\) as shown in figure. Then the currents \(I_1\) and \(I_2\) are respectively

• (1) \(4A, 2A\)
• (2) \(3A, 3A\)
• (3) \(6A, 0\)
• (4) \(2A, 4A\)

The value of shunt resistance that allows only 10% of the main current through the galvanometer of resistance \( 99 \Omega \) is:

• (1) \( 9 \Omega \)
• (2) \( 4 \Omega \)
• (3) \( 2 \Omega \)
• (4) \( 11 \Omega \)

In a hydrogen atom, an electron is making \( 6.6 \times 10^5 \) revolutions around the nucleus of radius \( 0.47 \) Å. The magnetic field induction produced at the center of the orbit is nearly:

• (1) \( 0.14 \ wb \ m^{-2} \)
• (2) \( 1.4 \ wb \ m^{-2} \)
• (3) \( 14 \ wb \ m^{-2} \)
• (4) \( 140 \ wb \ m^{-2} \)

Any magnetic material loses its magnetic property when it is:

• (1) Dipped in water
• (2) Dipped in sand
• (3) Attached to an iron piece
• (4) Heated to high temperature

When two coaxial coils having the same current in the same direction are brought close to each other, then the value of current in both the coils:

• (1) Increases
• (2) Decreases
• (3)
• (4) Remains same

A resistance of \( 20 \Omega \) is connected to a source of an alternating potential \( V = 200 \sin(10\pi t) \). If \( t \) is the time taken by the current to change from the peak value to the rms value, then \( t \) is (in seconds):

• (1) \( 25 \times 10^{-1} \)
• (2) \( 2.5 \times 10^{-4} \)
• (3) \( 25 \times 10^{-2} \)
• (4) \( 2.5 \times 10^{-2} \)

The average value of electric energy density in an electromagnetic wave is:
[where \( E_0 \) is the peak value]

• (1) \( \frac{\varepsilon_0 E_{rms}^2}{4} \)
• (2) \( \frac{1}{2} \varepsilon_0 E_0^2 \)
• (3) \( \frac{1}{2} \varepsilon_0 E_0 \)
• (4) \( \frac{1}{4} \varepsilon_0 E_0^2 \)

An electron of mass \( m \) with initial velocity \( \vec{v} = v_0 \hat{i} \) (\( v_0 > 0 \)) enters in an electric field \( \vec{E} = -E_0 \hat{i} \) (\( E_0 \) is constant \( > 0 \)) at \( t = 0 \). If \( \lambda \) is its de-Broglie wavelength initially, then the de-Broglie wavelength after time \( t \) is:

• (1) \( \frac{\lambda}{1 + \frac{eE_0 t}{m v_0}} \)
• (2) \( \frac{\lambda}{\left(1 - \frac{eE_0 t}{m v_0}\right)^2} \)
• (3) \( \left(1 + \frac{eE_0 t}{m v_0}\right) \lambda \)
• (4) \( \left(1 + \frac{eE_0 t}{m v_0}\right)^2 \lambda \)

A \( \mu \)-meson of charge \( e \), mass \( 208 \, m_e \) moves in a circular orbit around a heavy nucleus having charge \( +3e \). The quantum state \( n \) for which the radius of the orbit is the same as that of the first Bohr orbit for the hydrogen atom is (approximately):

• (1) \( n \approx 20 \)
• (2) \( n \approx 25 \)
• (3) \( n \approx 28 \)
• (4) \( n \approx 29 \)

A nucleus with atomic mass number \( A \) produces another nucleus by losing 2 alpha particles. The volume of the new nucleus is 60 times that of the alpha particle. The atomic mass number \( A \) of the original nucleus is:

• (1) \( 228 \)
• (2) \( 238 \)
• (3) \( 248 \)
• (4) \( 244 \)

A full-wave rectifier circuit is operating from 50 Hz mains, the fundamental frequency in the ripple output will be:

• (1) \( 50 \) Hz
• (2) \( 70.7 \) Hz
• (3) \( 100 \) Hz
• (4) \( 25 \) Hz

A PN junction diode is used as:

• (1) An amplifier
• (2) A rectifier
• (3) An oscillator
• (4) A modulator

A carrier is simultaneously modulated by two sine waves with modulation indices of 0.3 and 0.4; then the total modulation index is:

• (1) \( 1 \)
• (2) \( 0.12 \)
• (3) \( 0.5 \)
• (4) \( 0.7 \)

The angular momentum of an electron in a stationary state of \(Li^{2+}\) (\(Z=3\)) is \( \frac{3h}{\pi} \). The radius and energy of that stationary state are respectively

• (1) \(3.174 Å, -5.45 \times 10^{-19} J\)
• (2) \(6.348 Å, -5.45 \times 10^{-19} J\)
• (3) \(6.348 Å, +5.45 \times 10^{-18} J\)
• (4) \(2.116 Å, -5.45 \times 10^{-19} J\)

Identify the pair of elements in which the number of electrons in the (n-1) shell is the same:

• (1) Fe, Mn
• (2) Zn, Fe
• (3) K, Sc
• (4) Mn, Cr

Match the following:






Options:

(1) A-III, B-IV, C-I, D-II

(2) A-III, B-I, C-IV, D-II

(3) A-IV, B-I, C-I, D-II

(4) A-IV, B-III, C-I, D-II

The correct order of bond angles of the molecules \( SiCl_4 \), \( SO_3 \), \( NH_3 \), \( HgCl_2 \) is:

• (1) \( SO_3 > SiCl_4 > NH_3 > HgCl_2 \)
• (2) \( SiCl_4 > NH_3 > HgCl_2 > SO_3 \)
• (3) \( HgCl_2 > SO_3 > NH_3 > SiCl_4 \)
• (4) \( HgCl_2 > SO_3 > SiCl_4 > NH_3 \)

Observe the following structure:





The formal charges on the atoms 1, 2, 3 respectively are:

• (1) \( +1, 0, -1 \)
• (2) \( 0, 0, -1 \)
• (3) \( -1, 0, +1 \)
• (4) \( 0, 0, 0 \)

Two statements are given below:

Statement-I: The ratio of the molar volume of a gas to that of an ideal gas at constant temperature and pressure is called the compressibility factor.

Statement-II: The RMS velocity of a gas is directly proportional to the square root of \( T(K) \).

The correct answer is:

• (1) Both statement-I and statement-II are correct
  (2) Both statement-I and statement-II are not correct
  (3) Statement-I is correct but statement-II is not correct
  (4) Statement-I is not correct but statement-II is correct

At 133.33 K, the RMS velocity of an ideal gas is \[ (M = 0.083 kg mol^{-1}, R = 8.3 J mol^{-1} K^{-1}) \]

• (1) \( 200 \) m s\(^{-1}\)
• (2) \( 150 \) m s\(^{-1}\)
• (3) \( 2000 \) m s\(^{-1}\)
• (4) \( 400 \) m s\(^{-1}\)

Given below are two statements:

Statement-I: In the decomposition of potassium chlorate, Cl is reduced.

Statement-II: Reaction of Na with \( O_2 \) to form \( Na_2O \) is a redox reaction.

The correct answer is:

• (1) Both statements-I and II are correct
  (2) Both statements-I and II are not correct
  (3) Statement-I is correct but statement-II is not correct
  (4) Statement-I is not correct but statement-II is correct

Observe the following reaction:
\[ 2A_2(g) + B_2(g) \xrightarrow{T(K)} 2A_2B(g) + 600 kJ \]

The standard enthalpy of formation \( (\Delta_f H^\circ) \) of \( A_2B(g) \) is:

• (1) \( 600 kJ mol^{-1} \)
• (2) \( 300 kJ mol^{-1} \)
• (3) \( -300 kJ mol^{-1} \)
• (4) \( -600 kJ mol^{-1} \)

Identify the molecule for which the enthalpy of atomization \( (\Delta_a H^\circ) \) and bond dissociation enthalpy \( (\Delta_{bond} H^\circ) \) are not equal.

• (1) \( H_2 \)
• (2) \( Cl_2 \)
• (3) \( F_2 \)
• (4) \( CH_4 \)

For the reaction:
\[ A_2(g) \rightleftharpoons B_2(g) \]

The equilibrium constant \( K_c \) is given as 99.0. In a 1 L closed flask, two moles of \( B_2(g) \) is heated to T(K). What is the concentration of \( B_2(g) \) (in mol L\(^{-1}\)) at equilibrium?

• (1) \( 0.02 \)
• (2) \( 1.98 \)
• (3) \( 0.198 \)
• (4) \( 1.5 \)

At 27°C, 100 mL of 0.4 M HCl is mixed with 100 mL of 0.5 M NaOH. To the resultant solution, 800 mL of distilled water is added. What is the pH of the final solution?

• (1) \( 12 \)
• (2) \( 2 \)
• (3) \( 1.3 \)
• (4) \( 1.0 \)

‘X’ on hydrolysis gives two products. One of them is solid. What is ‘X’?

• (1) \( P_4O_{10} \)
• (2) \( F_2 \)
• (3) \( SiCl_4 \)
• (4) \( N_3^- \)

Ba, Ca, Sr form halide hydrates. Their formulae are \( BaCl_2 \cdot xH_2O \), \( CaCl_2 \cdot yH_2O \), \( SrCl_2 \cdot zH_2O \). The values of \( x, y, z \) respectively are:

• (1) \( 2, 6, 6 \)
• (2) \( 8, 6, 4 \)
• (3) \( 8, 6, 6 \)
• (4) \( 6, 4, 2 \)

The bond angles \( b_1, b_2, b_3 \) in the above structure are respectively (in \( ^\circ \)):

• (1) \( 79, 101, 118 \)
• (2) \( 118, 101, 79 \)
• (3) \( 79, 118, 101 \)
• (4) \( 118, 79, 101 \)

Which of the following oxides is acidic in nature?

• (1) \( GeO_2 \)
• (2) \( CO \)
• (3) \( PbO_2 \)
• (4) \( SnO \)

Match the following:

• (1) \( A - III, B - II, C - I \)
  (2) \( A - III, B - I, C - II \)
  (3) \( A - II, B - I, C - III \)
  (4) \( A - II, B - III, C - I \)

The number of nucleophiles in the following list is:
\[ CH_3NH_2, \quad CH_3CHO, \quad C_2H_4, \quad CH_3SH \]

• (1) \( 1 \)
• (2) \( 2 \)
• (3) \( 4 \)
• (4) \( 3 \)

An alkene X (\( C_4H_8 \)) on reaction with HBr gave Y (\( C_4H_9Br \)). Reaction of Y with benzene in the presence of anhydrous \( AlCl_3 \) gave Z which is resistant to oxidation with \( KMnO_4 + KOH \). What are X, Y, Z respectively?

Correct Answer: (1)
View Solution

A solid compound is formed by atoms of A (cations), B (cations), and O (anions). Atoms of O form an hcp lattice. Atoms of A occupy 25% of tetrahedral holes and atoms of B occupy 50% of octahedral holes. What is the molecular formula of the solid?

• (1) \( AB_2O_4 \)
• (2) \( ABO_3 \)
• (3) \( ABO_2 \)
• (4) \( A_2BO_4 \)

The density of nitric acid solution is 1.5 g mL\(^{-1}\). Its weight percentage is 68. What is the approximate concentration (in mol L\(^{-1}\)) of nitric acid? (N = 14 u; O = 16 u; H = 1 u)

• (1) \( 14.2 \)
• (2) \( 11.6 \)
• (3) \( 18.2 \)
• (4) \( 16.2 \)

The osmotic pressure of seawater is 1.05 atm. Four experiments were carried out as shown in the table. In which of the following experiments, pure water can be obtained in part-II of the vessel?

• (1) \( I, III \) only
  (2) \( II, IV \) only
  (3) \( I, II, III, IV \)
  (4) \( IV \) only

Evaluate the integral: \[ \int_0^{\frac{\pi}{4}} \left( \tan^3 x + \tan^5 x \right) dx \]

• (A) \( \frac{5}{12} \)
• (B) \( \frac{1}{3} \)
• (C) \( \frac{1}{4} \)
• (D) \( \frac{1}{6} \)
• (E) \( \frac{1}{12} \)

For a first-order reaction, the concentration of reactant was reduced from 0.03 mol L\(^{-1}\) to 0.02 mol L\(^{-1}\) in 25 min. What is its rate (in mol L\(^{-1}\) s\(^{-1}\))?

• (1) \( 6.667 \times 10^{-6} \)
  (2) \( 4 \times 10^{-4} \)
  (3) \( 6.667 \times 10^{-4} \)
  (4) \( 4 \times 10^{-6} \)

‘X’ is a protecting colloid. The following data is obtained for preventing the coagulation of 10 mL of gold sol to which 1 mL of 10% NaCl is added. What is the gold number of ‘X’?

• (1) \( 24 \)
  (2) \( 26 \)
  (3) \( 27 \)
  (4) \( 25 \)

Which sol is used as an intramuscular injection?

• (1) Antimony Sol
  (2) Silver Sol
  (3) Emulsion of Milk of Magnesia
  (4) Gold Sol

The reactions which occur in blast furnace at 500 – 800 K during extraction of iron from haematite are


i. \(3Fe_2O_3 + CO \rightarrow 2Fe_3O_4 + CO_2\)

ii. \(Fe_2O_3 + 3C \rightarrow 2Fe + 3CO\)

iii. \(FeO + 4CO \rightarrow 3Fe + 4CO_2\)

iv. \(FeO + CO \rightarrow 2FeO + CO_2\)

• (1) \( i, ii, iii, iv \)
• (2) \( i, iii only \)
• (3) \( i, iv only \)
• (4) \( i, iii, iv \)

Which of the following reactions give phosphine?


i. Reaction of calcium phosphide with water

ii. Heating white phosphorus with concentrated NaOH solution in an inert atmosphere

iii. Heating red phosphorus with alkali

• (1) \( i, ii only \)
• (2) \( i, ii, iii \)
• (3) \( ii, iii only \)
• (4) \( i, iii only \)

Which transition metal does not form ‘MO’ type oxide? (M = transition metal)

• (1) \( V \)
• (2) \( Cr \)
• (3) \( Mn \)
• (4) \( Sc \)

The paramagnetic complex ion which has no unpaired electrons in \( t_{2g} \) orbitals is

• (1) \( [Fe(CN)_6]^{4-} \)
• (2) \( [Fe(CN)_6]^{3-} \)
• (3) \( [Zn(NH_3)_6]^{2+} \)
• (4) \( [Ni(NH_3)_6]^{2+} \)

Which of the following is an example for fibre?

When glucose is oxidized with nitric acid, the compound formed is

• (1) Gluconic acid
• (2) n-Hexanoic acid
• (3) Saccharic acid
• (4) Cyanohydrin

The number of essential and non-essential amino acids from the following list respectively is

Given amino acids: Val, Gly, Leu, Lys, Pro, Ser

• (1) \( 5, 1 \)
• (2) \( 4, 2 \)
• (3) \( 2, 4 \)
• (4) \( 3, 3 \)

Which of the following pair is not correctly matched?

• (1) Salvarsan – to treat syphilis
• (2) Luminal – Antidepressant
• (3) Morphine – to treat cardiac pain
• (4) Acetylsalicylic acid – Antipyretic

An alkene X (\( C_4H_8 \)) does not exhibit cis-trans isomerism. Reaction of X with \( Br_2 \) in the presence of UV light gave Y. What is Y?

• (1)
• (2)
• (3)
• (4)

The two reactions involved in the conversion of benzene diazonium chloride to biphenyl are respectively

• (1) Swarts, Fittig
• (2) Gattermann, Swarts
• (3) Sandmeyer, Wurtz
• (4) Sandmeyer, Fittig

Consider the reactions:

Consider the following reactions:






Y and Z respectively are:

The incorrect statement about 'B' is:

The conversion of X to Y is: