AP EAPCET 2024 - 18th May Morning Shift

List - I (Bond )	List - II (Bond enthalpy (in $\mathrm{kJ} \mathrm{mol}^{-1}$ )
A $\mathrm{Si}-\mathrm{Si}$	I 240
B $\mathrm{C}-\mathrm{C}$	II 297
C $\mathrm{Sn}-\mathrm{Sn}$	III 348
D $\mathrm{Ge}-\mathrm{Ge}$	IV 248

The correct answer is

Arrange the following pestidides in the chronological order of their release into the market.

Organophosphates Organochlorides Sodium chlorate

$\quad \text { (A) } \quad\quad\quad\quad\quad\quad\quad \text { (B) } \quad\quad\quad\quad \text { (C) }$

From the following identify the groups that exhibit negative resonance $(-R)$ effect when attached to conjugated system

$$ \begin{array}{ccccc} \text { Formyl } & \text { Amino } & \text { Alkoxy } & \text { Cyano } & \text { Nitro } \\ A & B & C & D & E \end{array} $$

A dibromide $X\left(\mathrm{C}_4 \mathrm{H}_4 \mathrm{Br}_2\right)$ on dehydrohalogenation gave $Y$ which on reduction with $Z$ gave non-polar isomer of $\mathrm{C}_4 \mathrm{H}_3$. What are $X$ and $Z$ respectively?

The diffraction pattern of crystalline solid gave a peak at $20=60^{\circ}$. What is the distance ( in cm ) between the layers which gave this peak?

( $\lambda$ of $X$-rays is $1.54 \mathring{A}$ ) $\left(\sin 30^{\circ}=0.5, \sin 60^{\circ}=0.866 ; n=1\right)$

(a) $8.89 \times 10^{-8}$

The concentration of 1 L of $\mathrm{CaCO}_3$ solution is 1000 ppm . What is its concentration in mol $\mathrm{L}^{-1}$ ?

$$ (\mathrm{Ca}=40 \mathrm{u}, \mathrm{O}=16 \mathrm{u}, \mathrm{C}=12 \mathrm{u}) $$

At 293 K , methane gas was passed into 1 L . of water. The partial pressure of methane is 1 bar. The number of moles of methane dissolved in 1 L water is ( $K_{\mathrm{H}}$ of methane $=0.4 \mathrm{~K}$ bar)

The $E^{-}$of $M\left|M^{2+} \| \mathrm{Cu}^{2+}\right| \mathrm{Cu}$ is 0.3 V .

At what concentration of $\mathrm{Cu}^{2+}\left(\mathrm{in} \mathrm{mol} \mathrm{L} \mathrm{L}^{-1}\right)$, the $\mathrm{E}_{\mathrm{cel}}$ value becomes zero ? $\left(\frac{2.303 R T}{F}=0.06\right)$

(Conc. of $\mathrm{M}^{2+}=0.1 \mathrm{M}$ )

At 298 K , for a first order resction $(A \rightarrow P)$ the following graph is obtained. The rate constant ( in s ${ }^{-1}$ ) and initial concentration ( in mol $\mathrm{L}^{-1}$ ) of ' $A$ ' are respectively $(Y$-axis $=\ln (a-x): X$-axis $=$ time in sec)

Given below are two statements.

Statements I Easily liqueflable gases are readily adsorbed.

Statements II Adsorption enthalpy for physisorption is less compared to adsorption enthalpy for chemisorption.

The correct answer is

The validity of Freundlich isotherm can be verified by plotting

Which one of the following sets in not correctly matched?

When chlorine reacts with hot and conc. NaOH . The products formed are

Identify the basic oxide from the following.

Which of the following does not show optical isomerism?

A polymer $X$ is biodegradable and is obtained from the monomers $Y, Z$. What are $Y$ and $Z$ ?

Which of the following is an essential amino acid ?

Which of the following hormone is responsible for preparing uterus for implantation of fertilised eggs?

Identify the correct set form the following.

Chlorobenzene ( $X$ ) when reacted with reagent $(A)$ geb converted to phenol $(Y)$. The major product obtained from nitration of $(X)$ gets converted to $p$-nitrophend $(Z)$ by reaction with reagent $(B)$. What are $A$ and $B$ respectively?

Match the following reactions with the prodact obtained from them.

List-I	List-II
A Sandmeyer reaction	I $R-I$
B Finkelstein reaction	II $R-\mathrm{F}$
C Swarts reaction	III $\mathrm{Ar}-\mathrm{Br}$
	IV $R-\mathrm{Br}$

What are $X$ and $Y$ respectively in the following reaction sequence?

Arrange the following in decreasing order of their acidity.

What are $X$ and $Y$ in the following set of reactions?

An alkyl halide $\mathrm{C}_3 \mathrm{H}_7 \mathrm{CL}$. on reaction with a reagent $X$ gave the major product $Y\left(\mathrm{C}_4 \mathrm{H}_7 \mathrm{~N}\right) . Y$ on hydrolysis released gas. Which turns red litmus to blue. What are $X$ and $Y$ ?

Mathematics

If a function $ f:R \rightarrow R $ is defined by $ f(x) = x^3 - x $, then $ f $ is

If $ f(x) = \sqrt{x - 1} $ and $ g(f(x)) = x + 2x^2 + 1 $, then $ g(x) $ is

For all positive integers $ n $ if $ 3^{2n+1} + 2^{n+1} $ is divisible by $ k $, then the number of prime numbers less than or equal to $ k $ is

If $ \alpha, \beta, \gamma $ are the roots of $ \begin{bmatrix} 1 & -x & -2 \\ -2 & 4 & -x \\ -2 & 1 & -x \end{bmatrix} = 0 $, then $ \alpha \beta + \beta \gamma + \gamma \alpha = $

If the determinant of a 3rd order matrix $ A $ is $ K $, then the sum of the determinants of the matrices $ A^4 $ and $ (A - A^4) $ is

While solving a system of linear equations $A X=B$ using Cramer's rule with the usual notation if

$$ \Delta=\left|\begin{array}{ccc} 1 & 1 & 1 \\ 2 & -1 & 2 \\ -1 & 1 & 5 \end{array}\right|, \Delta_1=\left|\begin{array}{ccc} 5 & 1 & 1 \\ 4 & -1 & 2 \\ 11 & 1 & 5 \end{array}\right| \text { and } X=\left[\begin{array}{l} \alpha \\ 2 \\ \beta \end{array}\right] \text {, then } \alpha^2+\beta^2= $$

If real parts of $\sqrt{-5-12 i}, \sqrt{5+12 i}$ are positive values, the real part of $\sqrt{-8-6 i}$ is a negative value and $a+i b=\frac{\sqrt{-5-12 i}+\sqrt{5+12 i}}{\sqrt{-8-6 i}}$, then $2 a+b=$

The set of all real values of $ c $ for which the equation $ z\overline{z} + (4 - 3i)z + (4 + 3i)\overline{z} + c = 0 $ represents a circle, is

If $ z = x + iy $ is a complex number, then the number of distinct solutions of the equation $ z^3 + \overline{z} = 0 $ is

If the roots of the quadratic equation $ x^2 - 35x + c = 0 $ are in the ratio 2 : 3 and $ c = 6K $, then $ K = $

For real values of $ x $ and $ a $, if the expression $ \frac{x^3 - 3x^2 - 3x + 1}{2x^2 - 3x + 1} $ assumes all real values, then

If the sum of two roots $\alpha, \beta$ of the equation $x^4-x^3-8 x^2+2 x+12=0$ is zero and $\gamma, \delta(\gamma>\delta)$ are its other roots, then $3 \gamma+2 \delta=$

$f(x+h)=0$ represents the transformed equation of the equation $f(x)=x^4+2 x^3-19 x^2-8 x+60=0$. If this transformation removes the term containing $x^3$ from $f(x)=0$, then $h=$

The number of different ways of preparing a garland using 6 distinct white roses and 6 distinct red roses such that no two red roses come together, is

The number of ways a committee of 8 members can be formed from a group of 10 men and 8 women such that the committee contains at, most 5 men and atleast 5 women, is

If all the letters of the word CRICKET are permuted in all possible ways and the words (with or without meaning), thus formed are arranged in the dictionary order, then the rank of the word CRICKET is

The square root of independent term in the expansion of $ \left( 2x^2 + \frac{5}{x} \right)^5 $ is

The coefficient of $x^5$ in $\left(3+x+x^2\right)^6$ is

The absolute value of the difference of the coefficients of $x^4$ and $x^6$ in the expansion of $x^2 - 2x^2 + (x + 1)^4(x^2 - 1)^2$, is

$ \tan 6^\circ + \tan 42^\circ + \tan 66^\circ + \tan 78^\circ = $

The maximum value of $12\sin x - 5\cos x + 3$ is

$\sin^2 16^\circ - \sin^2 76^\circ = $

$1+\sin x+\sin ^2 x+\sin ^3 x+\ldots \ldots+\infty=4+2 \sqrt{3}$ and $0

$\tan^{-1} 2 + \tan^{-1} 3 = $

$\cosh 1 + 2 = $

In $\triangle ABC$, $\cos A + \cos B + \cos C = $

In a $\triangle A B C$, if $a=26, b=30, \cos c=\frac{63}{65}$, then $c=$

If $H$ is orthocentre of $\triangle A B C$ and $A H=x ; B H=y$; $C H=z$, then $\frac{a b c}{x y z}=$

In a regular hexagon $A B C D E F, \mathbf{A B}=\mathbf{a}$ and $\mathbf{B C}=\mathbf{b}$, then $F A=$

If the points with position vectors $(\alpha \hat{\mathbf{i}}+10 \hat{\mathbf{j}}+13 \hat{\mathbf{k}}),(6 \hat{\mathbf{i}}+11 \hat{\mathbf{j}}+11 \hat{\mathbf{k}}),\left(\frac{9}{2} \hat{\mathbf{i}}+\beta \hat{\mathbf{j}}-8 \hat{\mathbf{k}}\right)$ are collinear, then $(19 \alpha-6 \beta)^2=$

If $\mathbf{f}, \mathbf{g}, \mathbf{h}$ be mutually orthogonal vectors of equal magnitudes, then the angle between the vectors $\mathbf{f}+\mathbf{g}+\mathbf{h}$ and $\mathbf{h}$ is

Let $\mathbf{a}, \mathbf{b}$ be two unit vectors. If $\mathbf{c}=\mathbf{a}+2 \mathbf{b}$ and $\mathbf{d}=5 \mathbf{a}-4 \mathbf{b}$ are perpendicular to each other, then the angle between $a$ and $b$ is

If the vectors $\mathbf{a}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$, $\mathbf{c}=3 \hat{\mathbf{i}}+p \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$ are coplanar, then $p=$

For a set of observations, if the coefficient of variation is 25 and mean is 44 , then the variance is

If 5 letters are to be placed in 5 -addressed envelopes, then the probability that atleast one letter is placed in the wrongly addressed envelope, is

A student writes an examination which contains eight true of false questions. If he answers six or more questions correctly, the passes the examination. If the student answers all the questions, then the probability that he fails in the examination, is

The probabilities that a person goes to college by car is $\frac{1}{5}$, by bus is $\frac{2}{5}$ and by train is $\frac{3}{5}$, respectively. The probabilities that he reaches the college late if he takes car, bus and train are $\frac{2}{7}, \frac{4}{7}$ and $\frac{1}{7}$, respectively, If he reaches the college on time, then probability that he travelled by car is

$P, Q$ and $R$ try to hit the same target one after the other. If their probabilities of hitting the target are $\frac{2}{3}, \frac{3}{5}, \frac{5}{7}$ respectively, then the probability that the target is his by $P$ or $Q$ but not by $R$ is

A box contains $20 \%$ defective bulbs. Five bulbs are chosen randomly from this box. Then, the probability that exactly 3 of the chosen bulbs are defective, is

If a random variable $X$ satisfies poisson distribution with a mean value of 5 , then probability that $X<3$ is

The equation $a x y+b y=c y$ represents the locus of the points which lie on

If the axes are rotated through an angle $45^{\circ}$ about the origin in anticlockwise direction, then the transformed equation of $y^2=4 a r$ is

If the lines $3 x+y-4=0, x-\alpha y+10=0, \beta x+2 y+4=0$ and $3 x+y+k=0$ represent the sides of a square, then $\alpha \beta(k+4)^2=$

$A$ is the point of intersection of the lines $3 x+y-4=0$ and $x-y=0$. If a line having negative slope makes an angle of $45^{\circ}$ with the line $x-3 y+5=0$ and passes through $A$, then its equation is

$2 x^2-3 x y-2 y^2=0$ represents two lines $L_1$ and $L_2$. $2 x^2-3 x y-2 y^2-x+7 y-3=0$ represents another two lines $L_3$ and $L_4$. Let $A$ be the point of intersection of lines $L_1, L_3$ and $B$ be the point of intersection of lines $L_2$ and $L_4$. The area of the triangle formed by lines $A B$. $L_3$ and $L_4$ is

The area of the triangle formed by the pair of lines $23 x^2-48 x y+3 y^2=0$ with the line $2 x+3 y+5=0$, is

If $\theta$ is the angle between the tangents drawn from the point $(2,3)$ to the circle $x^2+y^2-6 x+4 y+12=0$ then $\theta=$

If $2 x-3 y+3=0$ and $x+2 y+k=0$ are conjugate lines with respect to the circle $S=x^2+y^2+8 x-6 y-24=0$, then the length of the tangent drawn from the point $\left(\frac{k}{4}, \frac{k}{3}\right)$ to the circle $S=0$, is

If $Q(h, k)$ is the inverse point of the point $P(1,2)$ with respect to the circle $x^2+y^2-4 x+1=0$, then $2 h+k=$

If $(a, b)$ and ( $c, d)$ are the internal and external centres of similitudes of the circles $x^2+y^2+4 x-5=0$ and $x^2+y^2-6 y+8=0$ respectively, then $(a+d)(b+q)=$

A circle $s$ passes through the points of intersection of the circles $x^2+y^2-2 x+2 y-2=0$ and $x^2+y^2+2 x-2 y+1=0$. If the centre of this circle $S$ lies on the line $x-y+6=0$, then the radius of the circle $S$ is

The line $x-2 y-3=0$ cuts the parabola $y^2=4 \operatorname{ar}$ at the points $P$ and $Q$. If the focus of this parabola is $\left(\frac{1}{4}, k\right)$. then $P Q=$

If $4 x-3 y-5=0$ is a normal to the ellipse $3 x^2+8 y^2=k$, then the equation of the tangent drawn to this ellipse at the point $(-2, m)(m>0)$ is

If the line $5 x-2 y-6=0$ is a tangent to the hyperbola $5 x^2-k y^2=12$, then the equation of the normal to this hyperbola at the point $(\sqrt{6}, p)(p<0)$ is

If the angle between the asymptotes of the hyperbola $x^2-k y^2=3$ is $\frac{\pi}{3}$ and $e$ is its eccentricity, then the pole of the line $x+y-1=0$ with respect to this hyperbola is

Let $P(\alpha, 4,7)$ and $Q(\beta, \beta, 8)$ be two points. If $Y Z$-plane divides the join of the points $P$ and $Q$ in the ratio $2: 3$ and $Z X$-plane divides the join of $P$ and $Q$ in the ratio $4: 5$, then length of line segment $P Q$ is

If $(\alpha, \beta, \gamma)$ are the direction cosines of an angular bisector of two lines whose direction ratios are $(2,2,1)$ and $(2,-1,-2)$, then $(\alpha+\beta+\gamma)^2=$

If the distance between the planes $2 x+y+z+1=0$ and $2 x+y+z+\alpha=0$ is 3 units, then product of all possible values of $\alpha$ is

$\lim \limits_{x \rightarrow 0} \frac{1-\cos x \cdot \cos 2 x}{\sin ^2 x}=$

$\lim \limits_{x \rightarrow-1}\left(\frac{3 x^2-2 x+3}{3 x^2+x-2}\right)^{3 x-2}=$

$f(x)=\left\{\begin{array}{cl}\frac{\left(2 x^2-a x+1\right)-\left(a x^2+3 b x+2\right)}{x+1}, & \text { if } x \neq-1 \\ k_k, & \text { if } x=-1\end{array}\right.$

is a real valued function. If $a, b, k \in R$ and $f$ is continuous on $R$, then $k=$

If $f(x)=\left\{\begin{array}{cl}\frac{2 x e^{1 / 2 x}-3 x e^{-1 / 2 x}}{e^{1 / 2 x}+4 e^{-1 / 2 x}} & \text { if } x \neq 0 \\ 0 & \text { if } x=0\end{array}\right.$ is a real valued function, then

If $y=\tan ^{-1}\left(\frac{2-3 \sin x}{3-2 \sin x}\right)$, then $\frac{d y}{d x}=$

If $x=3\left[\sin t-\log \left(\cot \frac{t}{2}\right)\right]$ and $y=6\left[\cos t+\log \left(\operatorname{tin} \frac{t}{2}\right)\right]$ then $\frac{d y}{d x}=$

By considering $1^{\prime}=0.0175$, he approximate value of $\cot 45^{\circ} 2^{\prime}$ is

A point is moving on the curve $y=x^3-3 x^2+2 x-1$ and the $y$-coordinate of the point is increasing at the rate d 6 units per second. When the point is at $(2,-1)$, the rate of change of $x$-coordinate of the point is

The length of the tangent drawn at the point $P\left(\frac{\pi}{4}\right)$ on the curve $x^{2 / 3}+y^{2 / 3}=2^{2 / 3}$ is

The set of all real values of a such that the real valued function $f(x)=x^3+2 a x^2+3(a+1) x+5$ is strictly increasing in its entire domain is

$\int \frac{1}{x^5 \sqrt[3]{x^3+1}} d x=$

$\int \frac{x+1}{\sqrt{x^2+x+1}} d x=$

$\int\left(\tan ^9 x+\tan x\right) d x=0$

$\int \frac{\operatorname{cosec} x}{3 \cos x+4 \sin x} d x=$

$\int e^{2 x+3} \sin 6 x d x=$

$\lim \limits_{n \rightarrow+\infty}\left[{\frac{1}{n^4}+\frac{1}{\left(n^2+1\right)^{\frac{3}{2}}}+\frac{1}{\left(n^2+4\right)^{\frac{3}{2}}}+\frac{1}{\left(n^2+9\right)^{\frac{3}{2}}}}{+\ldots \ldots+\frac{1}{4 \sqrt{2} n^5}}\right]=$

$\int_{\log 4}^{\log 4} \frac{e^{2 x}+e^x}{e^{2 r}-5 e^x+6} d x=$

$\int_1^2 \frac{x^4-1}{x^6-1} d x=$

The area of the region ( in sq units) enclosed by the curve $y=x^3-19 x+30$ and the $X$-axis, is

The differential equation representing the family of circles having their centres of Y -axis is $\left(y_1=\frac{d y}{d x}\right.$ and $\left.y_2=\frac{d^2 y}{d x^2}\right)$

The general solution of the differential equation $\left(\sin y \cos ^2 y-x \sec ^2 y\right) d y=(\tan y) d r$, is

The general solution of the differential equation $(x-y-1) d y=(x+y+1) d x$ is

Physics

Match the following．

(a) Thermal conductivity	(i) $\left[\mathrm{MLT}^{-3} \mathrm{~K}^{-1}\right]$
(b) Boltzmann constant	(ii) $\left[M^0 L^2 T^{-2} K^{-1}\right]$
(c) Latent heat	(iii) $\left[M L^2 T^{-2} K^{-1}\right]$
(d) Specific heat	(iv) $\left[M^0 L^2 T^{-2}\right]$

Object is projected such that it has to attain maximum range. Another body is projected to reach maximum heigh. If both the objects reached the same maximum height, then the ratio of initial velocities

Ball is projected at an angle of $45^{\circ}$ with the horizontal．It passes through a wall of height $h$ at a horizontal distance $d_1$ from the point of profection and strikes the ground at a distance $d_1+d_2$ from the point of projection, then $h$ is :

second after projection，a projectile is travelling in a direction inclined at $45^{\circ}$ to horizontal．After two more seconds，it is travelling horizontally．Then，the magnitude of velocity of the projectile is $\left(g=10 \mathrm{~ms}^{-2}\right)$

Three blocks of masses $2 \mathrm{~m}, 4 \mathrm{~m}$ and 6 m are placed as shown in figure. If $\sin 37^{\circ}=\frac{3}{5}, \sin 53^{\circ}=\frac{4}{5}$, the acceleration of the system is

Two masses $m_1$ and $m_2$ are connected by a light string passing over smooth pulley. When set free $m_1$ moves downwards by 3 m in 3 s . The ratio of $\frac{m_l}{m_2}$ is $\left(g=10 \mathrm{~ms}^{-2}\right)$

In an inclastic collision, after collision the kinetic energy

A spring of $5 \times 10^3 \mathrm{Nm}^{-1}$ spring constant is stretched initially by 10 cm from unstretched position. The work required to stretch it further by another 10 cm is

The moment of inertia of a solid cylinder and a hollow cylinder of same mass and same radius about the axes of the cylinders are $I_1$ and $I_2$. The relation between $I_1$ and $I_2$ is

A wheel of angular speed $600 \mathrm{rev} / \mathrm{min}$ in is made to slow down at a rate of $2 \mathrm{rad} \mathrm{s}^{-2}$. The number of revolutions made by the wheel before coming to rest is

Time period of a simple pendulum in air is $T$. If the pendulum is in water and executes SHM. Its time period is $t$. The value of $\frac{T}{t}$ is. (density of bob is $\frac{5000}{3} \mathrm{~kg} \mathrm{~m}^{-3}$ )

For a particle executing simple harmonic motion, Match the following statements ( conditions) from Column I to statements (shapes of graph) in Columinit

Column I	Column II
a Velocity-displacement graph $(\omega=1)$	i Straight line
b Acceleration-displacement graph	ii Sinusoidal
c Acceleration - time graph	iii Circle
d Acceleration - velocity $(\omega \neq 1)$	iv Ellipse