AP EAPCET 2024 - 22th May Evening Shift
Paper was held on Wed, May 22, 2024 9:30 AM
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Chemistry

1
The de-Broglie wavelength of an electron with kinetic energy of 2.5 eV is (in m$)\left(1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J}\right.$, $m_e=9 \times 10^{-31} \mathrm{~kg}$ )
2
The ratio of ground state energy of $\mathrm{Li}^{2+}, \mathrm{He}^{+}, \mathrm{H}$ is
3

Two statements are given below.

Statement I : Nitrogen has more ionisation enthalpy and electronegativity than beryllium.

Statement II : $\mathrm{CrO}_3, \mathrm{~B}_2 \mathrm{O}_3$ are acidic oxide.

Correct answer is

4
The number of lone pairs of electrons on the central atom of $\mathrm{BrF}_5, \mathrm{XeO}_3, \mathrm{SO}_2$ respectively are
5
The shape of colourless neutral gas formed on thermal decomposition of ammonium nitrate is
6
At $T(\mathrm{~K})$ for one mole of an ideal gas, the graph of $p$ (on $Y$-axis) and $V^{-1}$ (on $X$-axis) gave a straight line with slope of $32.8 \mathrm{~L} \mathrm{~atm} \mathrm{~mol}^{-1}$. What is the temperature (in K$) ?\left(R=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right)$
7

At 290 K , a vessel (I) contains equal moles of three liquids $(A, B, C)$. The boiling points of $A, B$ and $C$ are $350 \mathrm{~K}, 373 \mathrm{~K}$ and 308 K respectively. Vessel (I) is heated to 300 K and vapours were collected into vessel (II). Identify the correct statements. (Assume vessel (I) contains liquids and vapours and vessel (II)contains only vapours)

(I) Vessel - I is rich in liquid $B$

(II) Vessel - II is rich in vapour of $C$

(III) The vapour pressures of $A, B, C$ in vessel (I) at 290 K follows the order $C>A>B$

8
100 mL of $0.1 \mathrm{M} \mathrm{Fe}^{2+}$ solution was titrated with $\frac{1}{60} \mathrm{M}$ $\mathrm{Cr}_2 \mathrm{O}_7^{2-}$ solution in acid medium. What is the volume (in L ) of $\mathrm{Cr}_2 \mathrm{O}_7^{2-}$ solution consumed ?
9

    Observe the following reaction.

    $$ A B \mathrm{O}_3(\mathrm{~s}) \xrightarrow{1000 \mathrm{~K}} A \mathrm{O}(\mathrm{~s})+B \mathrm{O}_2(\mathrm{~g}) $$

    $\Delta_r H$ for this reaction is $x \mathrm{~kJ} \mathrm{~mol}^{-1}$. What is its $\Delta_r U$ (in $\mathrm{kJ} \mathrm{mol}^{-1}$ ) at the same temperature?

    $$ \left(R=8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right) $$

10
A vessel of volume $V \mathrm{~L}$ contains an ideal gas are $T(\mathrm{~K})$. The vessel is partitioned into two equal parts. The volume (in L ) and temperature (in K ) in each part is respectively.
11

At $300 \mathrm{~K}, \Delta_r G^{\Theta}$ for the reaction $A_2(g) \rightleftharpoons B_2(g)$ is $-11.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$. The Equilibrium constant at 300 K is approximately ( $R=8314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ )

12
100 mL of $0.1 \mathrm{M} \mathrm{H} A$ (weak acid) and 100 mL of 0.2 M $\mathrm{Na} A$ are mixed. What is the pH of resultant solution? ( $K_{\mathrm{a}}$ of $\mathrm{H} A$ is $10^{-5}: \log 2=0.3$ )
13

Identify the correct statements from the following.

I. Reaction of hydrogen with fluorine occurs even in dark.

II. Manufacture of ammonia by Haber process is an endothermic reaction.

III. HF is electron rich hydride.

14
Which one of the following alkali metals is the weakes reducing agent as per their $E^{\circ}$ values?
15

In which of the following reactions, hydrogen is oned the products?

I. $\mathrm{NaBH}_4+\mathrm{I}_2 \longrightarrow$

II. $\mathrm{BF}_3+\mathrm{NaH} \xrightarrow{450 \mathrm{~K}}$

III. $\mathrm{BF}_3+\mathrm{LiAlH}_4 \longrightarrow$

IV. $\mathrm{B}_2 \mathrm{H}_6+\mathrm{NH}_3 \xrightarrow{\text { heat }}$

16

Two statements are given below.

Statement I : $\mathrm{SnF}_4, \mathrm{PbF}_4$ are ionic in nature.

Statement II : GeCl ${ }_2$ is more stable than $\mathrm{GeCl}_4$

The correct answer is

17

Match the pollutant is List I with its maximum permissible limit in drinking water given in List II

List I List II
A Lead I 500 ppm
B Sulphate II 50 ppm
C Nitrate III 50 ppb
18
Species $A, B, C, D$ formed in the following bond cleavages respectively are AP EAPCET 2024 - 22th May Evening Shift Chemistry - Chemical Bonding and Molecular Structure Question 4 English
19

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

AP EAPCET 2024 - 22th May Evening Shift Chemistry - Hydrocarbons Question 1 English
20
A compound is formed by atoms of $A, B$ and $C$. Atoms of $C$ form hcp lattice. Atoms of $A$ occupy $50 \%$ of octahedral voids and atoms of $B$ occupy $2 / 3$ rd of tetrahedral voids. What is the molecular formula of the solid?
21

At $300 \mathrm{~K}, 6 \mathrm{~g}$ of urea was dissolved in 500 mL of water. What is the osmotic pressure (in atm) of resultant solution?

$$ \begin{aligned} & \left(R=0.082 \mathrm{~L}^{\operatorname{atm~K}}{ }^{-1} \mathrm{~mol}^{-1}\right) \\ & (\mathrm{C}=12 ; \mathrm{N}=14 ; \mathrm{O}=16 ; \mathrm{H}=1) \end{aligned} $$

22
In water, which of the following gases has the highest Henry's law constant at 293 K ?
23

Consider the cell reaction at 300 K .

$$ A(s)+B^{2+}(a q) \rightleftharpoons A^{2+}(a q)+B(s) $$

Its $E^{\ominus}$ is 1.0 V . The $\Delta_r H^{\ominus}$ of the reaction is $-163 \mathrm{kJmol}^{-1}$.

What is $\Delta_r s^{\ominus}$ (in $\mathrm{JK}^{-1}$ ) of the reaction?

$$ \left(F=96500 \mathrm{C} \mathrm{~mol}^{-1}\right) $$

24
The rate constant of a first order reaction was doubled when the temperature was increased from 300 to 310 K . What is its approximate activation energy (in $\mathrm{kJ} \mathrm{mol}^{-1}$ )? ( $R=8.3 \mathrm{Jmol}^{-1} \mathrm{~K}^{-1}: \log 2=0.3$ )
25
Which of the following solutions is used in the styptic action which prevents bleeding of blood?
26

' $A$ ' is a protecting colloid. The following data is obtained for preventing the coagulation of 10 mL of gold sol to which 1 mL of $10 \% \mathrm{NaCl}$ is added. What is the gold number of ' $A$ '?

Expt. No. Wt (in mg ) of $\boldsymbol{A}$ added to gold sol $$
\text { Coagulation }
$$
1 40 Prevented
2 35 Prevented
3 25 Not prevented
4 32 Not prevented
5 33 Prevented
27

Two statements are given below.

Statement I : The reaction $\mathrm{Cr}_2 \mathrm{O}_3+2 \mathrm{Al} \longrightarrow \mathrm{Al}_2 \mathrm{O}_3+2 \mathrm{Cr}$ $\left(\Delta G^{\ominus}=-421 \mathrm{~kJ}\right)$ is thermodynamically feasible.

Statement II : The above reaction occurs at room temperature.

The correct answer is

28
The basicity of $\mathrm{H}_3 \mathrm{PO}_2, \mathrm{H}_3 \mathrm{PO}_3 \cdot \mathrm{H}_3 \mathrm{PO}_4$ respectively is
29
Which of the following reactions of $\mathrm{KMnO}_4$ occurs in acidic medium ?
30
Which complex among the follwing is most paramagnetic?
31
Polymers that can be softened on heating and hardened on cooling are called
32
The number of -OH groups in open chain and ring structures of D-glucose are respectively
33
Which of the following is correct statement?
34
Which of the following is not correctly matched?
35
AP EAPCET 2024 - 22th May Evening Shift Chemistry - Hydrocarbons Question 2 English Conversion of $X$ to $Y$ is an example of
36
Which of the following is not an example of allylic halide?
37
What is the major product ' $Z$ ' in the following reaction sequence? AP EAPCET 2024 - 22th May Evening Shift Chemistry - Alcohol, Phenols and Ethers Question 1 English
38

Consider the following reactions

AP EAPCET 2024 - 22th May Evening Shift Chemistry - Carboxylic Acids and Its Derivatives Question 2 English

$Y$ can not be obtained from which of the following reaction?

39

Assertion (A) : Carboxylic acids are more acidic than phenols

Reason (R) : Resonance structures of carboxylate ion are equivalent, while resonance structures of phenoxide ion are not equivalent.

40

In the reaction sequence $Y$ is

$$ \mathrm{CH}_3 \mathrm{CO}_2 \mathrm{H} \xrightarrow[(2) \Delta]{(1) \mathrm{NH}_3} P \xrightarrow{\mathrm{Br} / \mathrm{NaOH}} Y $$

Mathematics

1
The range of the real valued function $f(x)=\frac{15}{3 \sin x+4 \cos x+10}$ is
2

Define the function, $f, g$ and $h$ from $R$ to $R$ such that $f(x)=x^2-1, g(x)=\sqrt{x^2+1}$ and $h(x)= \begin{cases}0, \text { if } & x \leq 0 \\ x, \text { if } & x \geq 0\end{cases}$ consider the following statements

(i) fog is invertible

(ii) $h$ is an identify function

(iii) $f \circ g$ is not invertible

(iv) $(h \circ f \circ g) x=x^2$

Then, which one of the following is true ?

3
If $P$ is the greatest divisor of $49^n+16 n-1$ for all $n \in N$, then the number of factors of $P$ is
4
$A=\left[\begin{array}{lll}0 & 1 & 2 \\ 2 & 3 & 0 \\ 4 & 0 & 3\end{array}\right]$ and $B$ is a matrix such that $A B=B A$.If $A B$ is not an identity matrix, then the matrix that can be taken as $B$ is
5

If $\alpha, \beta$ and $\gamma(\alpha<\beta<\gamma)$ are the values of $x$ such that $\left[\begin{array}{ccc}x-2 & 0 & 1 \\ 1 & x+3 & 2 \\ 2 & 0 & 2 x-1\end{array}\right]$ is a singular matrix, then $2 \alpha+3 \beta+4 \gamma$ is equal to

6
The system of linear equations $x+2 y+z=-3$, $3 x+3 y-2 z=-1$ and $2 x+7 y+7 z=-4$ has
7
$\arg \left[\frac{(1+i \sqrt{3})(-\sqrt{3}-i)}{(1-i)(-i)}\right]$ is equal to
8

If $P(x, y)$ represents the complex number $z=x+iy$ in the argand plane and $\arg \left(\frac{z-3 i}{z+4}\right)=\frac{\pi}{2}$, then the equation of the locus of $P$ is

9
If $\cos \alpha+4 \cos \beta+9 \cos \gamma=0$ and $\sin \alpha+4 \sin \beta+9 \sin \gamma=0$, then 81 $\cos (2 \gamma-2 \alpha)-16 \cos (2 \beta-2 \alpha)$ is equal to
10
If ' $a$ ' is a rational number, then the roots of the equation $x^2-3 a x+a^2-2 a-4=0$ are
11

The set of all real values ' $a$ ' for which $-1<\frac{2 x^2+a x+2}{x^2+x+1}<3$ holds for all real values of $x$ is

12

The quotient, when $3 x^5-4 x^4+5 x^3-3 x^2+6 x-8$ is divided by $x^2+x-3$ is

13

If $\alpha_1, \alpha_2, \alpha_3, \alpha_4$ and $\alpha_5$ are the roots of $x^5-5 x^4+9 x^3-9 x^2+5 x-1=0$, then $\frac{1}{\alpha_1^2}+\frac{1}{\alpha_2^2}+\frac{1}{\alpha_3^2}+\frac{1}{\alpha_4^2}+\frac{1}{\alpha_5^2}$ is equal to

14

There were two women participating with some men in a chess tournament. Each participant played two games with the other. The number of games that the men played between themselves is 66 more than that of the men played with the women. Then, the total number of participants in the tournament is

15
The number of ways of arranging 9 men and 5 women around circular table, so that no two women come together are
16

If there are 6 alike fruits, 7 alike vegetables and 8 alike biscuits, then the number of ways of selecting any number of things out of them such that at least one from each category is selected, is

17

If the coefficients of $r$ th, $(r+1)$ th and $(r+2)$ th terms in the expansion of $(1+x)^n$ are in the ratio of $4: 15: 42$, then $n-r$ is equal to

18

If the coefficients of $(2 r+6)$ th and $(r-1)$ th terms in the expansion of $(1+x)^{21}$ are equal, then the value of $r$ is equal to

19

$$ \text { If } \frac{13 x+43}{2 x^2+17 x+30}=\frac{A}{2 x+5}+\frac{B}{x+6} \text {, then } A+B \text { is equal to } $$

20
$\tan \alpha+2 \tan 2 \alpha+4 \tan 4 \alpha+8 \cot 8 \alpha$ is equal to
21
$\tan 9^{\circ}-\tan 27^{\circ}-\tan 63^{\circ}+\tan 81^{\circ}$ is equal to
22
$\cos 6^{\circ} \sin 24^{\circ} \cos 72^{\circ}$ is equal to
23

The values of $x$ in $(-\pi, \pi)$, which satisfy the equation $8^{1+\cos ^2 x+\cos ^4 x+\ldots \ldots}=4^3$ are

24
$\cot \left(\sum\limits_{n=1}^{50} \tan ^{-1}\left(\frac{1}{1+n+n^2}\right)\right)$ is equal to
25

If $\sinh x=\frac{\sqrt{21}}{2}$, then $\cosh 2 x+\sinh 2 x$ is equal to

26
In a $\triangle A B C$, if $a=13, b=14$ and $c=15$, then $r_1=$
27

In $a \triangle A B C$ if $r: R: r_2=1: 3: 7$, then $\sin (A+C)+\sin B$ is equal to

28

In $\triangle A B C,\left(r_1+r_2\right) \operatorname{cosec}^2 \frac{C}{2}$ is equal to

29
If $A=(1,2,3), B=(3,4,7)$ and $C=(-3,-2,-5)$ are three points, then the ratio in which the point $C$ divides $A B$ externally is
30

If the vectors $a \hat{\mathbf{i}}+\mathbf{j}+3 \hat{\mathbf{k}}, 4 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $4 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}$ are coplanar, then $a$ is equal to

31
Let $|\hat{\mathbf{a}}|=2=|\hat{\mathbf{b}}|=3$ and the angle between $\hat{\mathbf{a}}$ and $\hat{\mathbf{b}}$ be $\frac{\pi}{3}$. If a parallelogram is constructed with adjacent sides $2 \hat{\mathbf{a}}+3 \hat{\mathbf{b}}$ and $\hat{\mathbf{a}}-\hat{\mathbf{b}}$, then its shorter diagonal is of length
32

The values of $x$ for which the angle between the vectors $x^2 \hat{\mathbf{i}}+2 x \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+x \hat{\mathbf{k}}$ is obtuse lie in the interval

33

If $\hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and $2 \hat{\mathbf{i}}+\hat{\mathbf{j}}$ are the vertices of a tetrahedron, then its volume is

34

Based on the following statements, choose the correct option.

Statement I The variance of the first $n$ even natural numbers is $\frac{n^2-1}{4}$.

Statement II The difference between the variance of the first 20 even natural numbers and their arithmetic mean is 112 .

35
If each of the coefficients $a, b$ and $c$ in the equation $a x^2+b x+c=0$ is determined by throwing a die, then the probability that the equation will have equal roots, is
36
$A$ and $B$ throw a pair of dice alternately and they note the sum of the numbers appearing on the dice. $A$ wins if he throws 6 before $B$ throws 7 and $B$ wins if he throws 7 before $A$ throws 6 . If $A$ begins then, the probability of his winning is
37

$E_1$ and $E_2$ are two independent events of a random experiment such that $P\left(E_1\right)=\frac{1}{2}$ and $P\left(E_1 \cup E_2\right)=\frac{2}{3}$. Then, match the items of List I with the items of List II.

$$ \begin{array}{lll} \hline & \text { List I } & \text { List II } \\ \hline \text { (A) } & P\left(E_2\right) & \text { (i) }1/2 \\ \hline \text { (B) } & P\left(E_1 / E_2\right) & \text { (ii) } 5 / 6 \\ \hline \text { (C) } & P\left(E_2 / E_1\right) & \text { (iii) } 1 / 3 \\ \hline \text { (D) } & P\left(E_1 \cup E_2\right) & \text { (iv) } 1 / 6 \\ \hline & & \text { (v) } 2 / 3 \\ \hline \end{array} $$

The correct match is
38

A bag contains 4 red and 5 black balls. Another bag contains 3 red and 6 black balls. If one ball is drawn from first bag and two balls from the second bag at random. The probability that out of the three, two are black and one is red, is

39

If a random variable $X$ has the following probability distribution, then its variance is nearly

$$ \begin{array}{clllllll} \hline X=x & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline P(X=x) & 0.05 & 0.1 & 2 K & 0 & 0.3 & K & 0.1 \\ \hline \end{array} $$

40
A radar system can detect an enemy plane in one out of 10 consecutive scans. The probability that it cannot detect an enemy plane at least two times in four consecutive scans, is
41
The locus of a variable point which forms a triangle of fixed area with two fixed points is
42
If the axes are rotated through angle ' $\alpha$ ', then the number of values of a such that the transformed equation of $x^2+y^2+2 x+2 y-5=0$ contains no liner terms is
43
$A$ line $L$ passing through the point $P(-5,-4)$ cuts the lines $x-y-5=0$ and $x+3 y+2=0$ respectively at $Q$ and $R$ such that $\frac{18}{P Q}+\frac{15}{P R}=2$, then slope of line $L$ is
44
If the reflection of a point $A(2,3)$ in $X$-axis is $B$, reflection of $B$ in the line $x+y=0$ is $C$ and the reflection of $C$ in $x-y=0$ is $D$, then the point of intersection of the lines $C D, A B$ is
45
The equation of a line which makes an angle of $45^{\circ}$ with each of the pair of lines $x y-x-y+1=0$ is
46
If the slope of one of the lines in the pair of lines $8 x^2+a x y+y^2=0$ is thrice the slope of the second line, then $a$ is equal to
47
The triangle $P Q R$ is inscribed in the circle $x^2+y^2=25$. If $Q=(3,4)$ and $R=(-4,3)$, then $\angle Q P R$ is equal to
48
The locus of the point of intersection of perpendicular tangents drawn to the circle $x^2+y^2=10$ is
49
The normal drawn at $(1,1)$ to the circle $x^2+y^2-4 x+6 y-4=0$ is
50
Parametric equations of the circle $2 x^2+2 y^2=9$ are
51
Angle between the circles $x^2+y^2-4 x-6 y-3=0$ and $x^2+y^2+8 x-4 y+11=0$ is
52
Equation of the line touching both parabolas $y^2=4 x$ and $x^2=-32 y$ is
53
The length of the latusrectum of $16 x^2+25 y^2=400$ is
54
The line $21 x+5 y=k$ touches the hyperbola $7 x^2-5 y^2=232$, then $k$ is equal to
55
If the equation $\frac{x^2}{7-k}+\frac{y^2}{5-k}=1$ represents a hyperbola, then
56

    If a line $L$ makes angles $\frac{\pi}{3}$ and $\frac{\pi}{4}$ with $Y$-axis and $Z$-axis respectively, then the angle between $L$ and another line having direction ratio $1,1,1$ is

57
If $l, m$ and $n$ are the direction cosines of a line that is perpendicular to the lines having the direction ratios $(1,2,-1)$ and $(1,-2,1)$, then $(l+m+n)^2$ is equal to
58
The foot of the perpendicular drawn from a point $A(1,1,1)$ on to a plane $\pi$ is $P(-3,3,5)$.If the equation of the plane parallel to the plane of $\pi$ and passing through the mid-point of $A P$ is $a x-y+c z+d=0$, then $a+c-d$ is equal to
59

$$\mathop {\lim }\limits_{x \to \infty } \frac{[2 x-3]}{x} \text { is equal to } $$

60
$\mathop {\lim }\limits_{x \to 0}\frac{\cos 2 x-\cos 3 x}{4 x-\cos 5 x}$ is equal to $\cos 4 x-\cos 5 x$
61

If a real valued function $f(x)=\left\{\begin{array}{cl}\frac{2 x^2+(k+2) x+9}{3 x^2-7 x-6}, & \text { for } x \neq 3 \\ 1, & \text { for } x=3\end{array}\right.$ is continuous at $x=3$ and $l$ is a finite value, then $l-k$ is equal to

62
If $y=\tan ^{-1} \frac{x}{1+2 x^2}+\tan ^{-1} \frac{x}{1+6 x^2}+\tan ^{-1} \frac{x}{1+12 x^2}$, then $\left(\frac{d y}{d x}\right)_{x=\frac{1}{2}}$ is equal to
63

If $f(x)=5 \cos ^3 x-3 \sin ^2 x$ and $g(x)=4 \sin ^3 x+\cos ^2 x$, then the derivative of $f(x)$ with respect to $g(x)$ is

64
If $y=1+x+x^2+x^3+\ldots \ldots \infty$ and $|x|<1$, then $y^{\prime \prime}$ is equal to
65

The semi-vertical angle of a right circular cone is $45^{\circ} \%$ If the radius of the base of the cone is measured as 14 cm with an error of $\left(\frac{\sqrt{2}-1}{11}\right) \mathrm{cm}$, then the approximate error in measuring its total surface area is (in sq cm)

66

If a man of height 1.8 mt , is walking away from the foot of a light pole of height 6 mt , with a speed of 7 km per hour on a straight horizontal road opposite to the pole, then the rate of change of the length of his shadow is (in kmph )

67

If the curves $2 x^2+k y^2=30$ and $3 y^2=28 x$ cut each other orthogonally, then $k$ is equal to

68
The interval containing all the real values of $x$ such that the real valued function $f(x)=\sqrt{x}+\frac{1}{\sqrt{x}}$ is strictly increasing is
69
$\int e^{4 x^2+8 x-4}(x+1) \cos \left(3 x^2+6 x-4\right) d x$ is equal to
70
$\int\left[(\log 2 x)^2+2 \log 2 x\right] d x$ is equal to
71

If $\int \log \left(6 \sin ^2 x+17 \sin x+12\right) \cos x d x=f(x)+c$, then $f\left(\frac{\pi}{2}\right)$ is equal to

72
$\int \frac{1}{\left(1+x^2\right) \sqrt{x^2+2}} d x$ is equal to
73
$\int \sin ^4 x \cos ^4 x d x$ is equal to
74
$\int_0^1 \sqrt{\frac{2+x}{2-x}} d x$ is equal to
75
If $M=\int\limits_0^{\infty} \frac{\log t}{1+t^3} d t$ and $N=\int\limits_{-\infty}^{\infty} \frac{t e^{2 t}}{1+e^{3 t}} d t$, then
76
$\int\limits_{-2}^2\left(4-x^2\right)^{\frac{5}{2}} d x$ is equal to
77

$$ \mathop {\lim }\limits_{x \to \infty }\left[\left(1+\frac{1}{n^3}\right)^{\frac{1}{n^3}}\left(1+\frac{8}{n^3}\right)^{\frac{4}{n^3}}\left(1+\frac{27}{n^3}\right)^{\frac{9}{n^3}} \ldots . .(2)^{\frac{1}{n}}\right] \text { is equaln } $$

78
$\int\limits_{-5 \pi}^{5 \pi}(1-\cos 2 x)^{\frac{5}{2}} d x$ is equal to
79
The differential equation of the family of hyperbols having their centres at origin and their axes along coordinates axes is
80

The general solution of the differential equation $\left(x y+y^2\right) d x-\left(x^2-2 x y\right) d y=0$ is

Physics

1

In the equation $\left(p+\frac{a}{V^2}\right)(V-b)=R T$, where $p$ is pressure, $V$ is volume, $T$ is temperature, $R$ is universal gas constant, $a$ and $b$ are constants. The dimensions of $a$ are

2

A particle starts from rest and moves in a straight line. It travels a distance $2 L$ with uniform acceleration and then moves with a constant velocity a further distance of $L$. Finally, it comes to rest after moving a distance of $3 L$ under uniform retardation. Then, the ratio of average speed to the maximum speed $\left(\frac{v}{v_m}\right)$ of the particle is

3
A boy throws a ball with a velocity $v_0$ at an angle $\alpha$ to the ground. At the same time he starts running with uniform velocity to catch the ball before it hits the ground. To achieve this, he should run with a velocity of
4
A ball at point $O$ is at a horizontal distance of 7 m from a wall. On the wall a target is set at point $C$. If the ball is throw from $O$ at an angle $37^{\circ}$ with horizontal aiming the target $C$. But it hits the wall at point $D$ which is at a vertical distance $y_0$ below $C$. If the initial velocity of the ball is $15 \mathrm{~ms}^{-1}$. Find $y_0\left(\right.$ given, $\left.\cos 37^{\circ}=\frac{4}{5}\right)$ AP EAPCET 2024 - 22th May Evening Shift Physics - Motion in a Plane Question 1 English
5
The acceleration of a body sliding down the inclined plane, having coefficient of friction $\mu$ is
6

A body of 2 kg mass slides down with an acceleration of $4 \mathrm{~ms}^{-2}$ on an inclined plane having slope of $30^{\circ}$. The external force required to take the same body up the plane with same acceleration will be (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

7

A body of mass 30 kg moving with a velocity $20 \mathrm{~ms}^{-1}$ undergoes one-dimensional elastic collision with another ball of same mass moving in the opposite direction with a velocity of $30 \mathrm{~ms}^{-1}$. After collision the velocity of first and second bodies respectively are

8
A force of $(4 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}) \mathrm{N}$ is action on a particle of mass 2 kg displaces the particle from a position of $(2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}})$ $m$ to a position of $(4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}) \mathrm{m}$. The work done by the force on the particle in joules is
9

Two blocks of equal masses are tied with a light string passing over a massless pulley (assuming frictionless surfaces ) acceleration of centre of mass of the two blocks is $\left(g=10 \mathrm{~ms}^{-2}\right)$

AP EAPCET 2024 - 22th May Evening Shift Physics - Center of Mass and Collision Question 1 English

10
A ring and a disc of same mass and same diameter are rolling without slipping. Their linear velocities are same, then the ratio of their kinetic energy is
11

The displacement of a particle of mass 2 g executing simple harmonic motion is $x=8 \cos \left(50 t+\frac{\pi}{12}\right) \mathrm{m}$, where $t$ is time in second. The maximum kinetic energy of the particle is

12
The relation between the force ( $F$ in Newton) acting on a particle executing simple harmonic motion and the displacement of the particle ( $y$ in metre) is $500 F+\pi^2 y=0$. If the mass of the particle is 2 g . The time period of oscillation of the particle is
13
The gravitational potential energy of a body on the surface of the earth is $E$. If the body is taken from the surface of the earth to a height equal to $150 \%$ of the radius of the earth. Its gravitational potential energy is
14

A wire of length 100 cm and area of cross-section $2 \mathrm{~mm}^2$ is stretched by two forces of each 440 N applied at the ends of the wire in opposite directions along the length of the wire. If the elongation of the wire is 2 mm , the Young's modulus of the material of the wire is

15
Two cylindrical vessels $A$ and $B$ of different areas of cross-section kept on same horizontal plane are filled with water to the same height. If the volume of water in vessel $A$ is 3 times the volume of water in vessel $B$, then the ratio of the pressures at the bottom of the vessels $A$ and $B$ is
16

Water of mass $m$ at $30^{\circ} \mathrm{C}$ is mixed with with 5 g of ice at $-20^{\circ} \mathrm{C}$. If the resultant temperature of the mixture is $6^{\circ} \mathrm{C}$, then the value of $m$ is (specific heat capacity of ice $=0.5 \mathrm{cal} \mathrm{g}^{-10} \mathrm{C}^{-1}$, specific heat capacity of water $=1$ calg ${ }^{-1}{ }^{\circ} \mathrm{C}^{-1}$ and latent heat of fusion of ice $=80 \mathrm{cal} \mathrm{g}^{-1}$ )

17
Two ideal gases $A$ and $B$ of same number of moles expand at constant temperatures $T_1$ and $T_2$ respectively such that the pressure of gas $A$ decreases by $50 \%$ and the pressure of gas $B$ decreases by $75 \%$. If the work done by both the gases is same, then $T_1: T_2$
18
When 80 J of heat is absorbed by a monoatomic gas, its volume increases by $16 \times 10^{-5} \mathrm{~m}^3$. The pressure of the gas is
19
The efficiency of a Carnot heat engine is $25 \%$ and the temperature of its source is $127^{\circ} \mathrm{C}$. Without changing the temperature of the source, if absolute temperature of the sink is decreased by $10 \%$, the efficiency of the engine is
20

The total internal energy of 2 moles of a monoatomic gas at a temperature $27^{\circ} \mathrm{C}$ is $U$. The total internal energy of 3 moles of a diatomic gas at a temperature $127^{\circ} \mathrm{C}$ is

21

The fundamental frequency of an open pipe is 100 hz If the bottom end of the pipe is closed and $1 / 3$ rd of the pipe is filled with water, then the fundamental frequency of the pipe is

22

When a convex lens is immersed in a liquid of refractive index equal to $80 \%$ of the refractive index of the material of the lens. The focal length of the lens increases by $100 \%$. The refractive index of the liquid is

23
The angle between the axes of a polariser and an analyser is $45^{\circ}$. If the intensity of the unpolarised light incident on the polariser is $I$, then the intensity of light emerged from the analyser is
24

The magnitude of an electric field which can just suspend a deuteron of mass $3.2 \times 10^{-27} \mathrm{~kg}$ freely in ari is

25
Two charges 5 nC and -2 nC are placed at points $( 5 cm\mathrm{~}$ $0,0)$ and $(23 \mathrm{~cm}, 0,0)$ in a region of space where there is no other external field. The electrostatic potential energy of this charge system is
26
The space between the plates of a parallel plate capacitor is halved and a dielectric medium of relative permittivity 10 is introduced between the plates. The ratio of the final and initial capacitances of the capacitor is
27
A battery of emf 8 V and internal resistance $0.5 \Omega$ is being charged by a 120 V DC supply using a series resister of $15.5 \Omega$. The terminal voltage of 8 V batter) during charging is
28
Resistance of a wire is $8 \Omega$. It is drawn in such a way that it experiences a longitudinal strain of $400 \%$. The final resistance of the wire is
29
Current flows in a conductor from east to west. The direction of the magnetic field at a point below the conductor is towards
30
Two infinite length wires carry currents 8 A and $6^{\mathrm{A}}$ respectively and are placed along $X$ and $Y$-axes respectively. Magnetic field at a point $P(0,0, C)$ will
31
A short magnet oscillates with a time period 0.1 s at a place where horizontal magnetic field is $24 \mu \mathrm{~T}$. A downward current of 18 A is established in a vertical wire kept at a distance of 20 cm east of the magnet. The new time period of oscillations of the magnet is
32

A metallic wire loop of side $(l) 0.1 \mathrm{~m}$ and resistance of $1 \Omega$ is moved with a constant velocity in a uniform magnetic field of $2 \mathrm{Wm}^{-2}$ as shown in the figure. The magnetic field is perpendicular to the plane of the loop. The loop is connected to a network of resistors. The velocity of loop, so as to have a steady current of 1 mA in loop is

AP EAPCET 2024 - 22th May Evening Shift Physics - Electromagnetic Induction Question 1 English
33

In the circuit shown in the figure, neglecting the source resistance, the voltmeter and ammeter readings respectively are

AP EAPCET 2024 - 22th May Evening Shift Physics - Current Electricity Question 1 English
34
The radiation of energy $E$ falls normally on a perfectly reflecting surface. The momentum transferred to the surface is
35

Light of wavelength $4000\mathop {\rm{A}}\limits^{\rm{o}}$ is incident on a sodium surface for which the threshold wavelength of photoelectrons is $5420 \mathop {\rm{A}}\limits^{\rm{o}}$. The work function of sodium is

36

The principle quantum number $n$ corresponding to the exited state of $\mathrm{He}^{+}$ion. If on transition to the ground state two photons in succession with wavelength $1026 \mathop {\rm{A}}\limits^{\rm{o}}$ and $304 \mathop {\rm{A}}\limits^{\rm{o}}$ are emitted $\left(R=1.097 \times 10^{-7} \mathrm{~m}^{-1}\right)$

37
Which physical quantity is measured in barn?
38

$$ \text { Truth table for the given circuit is } $$

AP EAPCET 2024 - 22th May Evening Shift Physics - Semiconductor Devices and Logic Gates Question 1 English
39

If $R_C$ and $R_B$ are respectively the resistances of in collector and base sides of the circuit and $\beta$ is the current amplification factor, then the voltage gain of a transistor amplifier in common emitter configuration is

40
Which one of the following is not classified as pulse modulation?
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