AP EAPCET 2024 - 22th May Evening Shift | AP EAPCET Year Wise Previous Years Questions

Chemistry

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, 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 5. If $\alpha, \beta$ and $\gamma(\alpha 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{\ 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 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 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 14. There were two women participating with some men in a chess tournament. Each participant played two games with the other 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 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: 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 $ 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 $A B$ exter 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}} 31. Let $|\hat{\mathbf{a}}|=2=|\hat{\mathbf{b}}|=3$ and the angle between $\hat{\mathbf{a}}$ and $\hat{\mathbf{b}}$ be $\fra 32. The values of $x$ for which the angle between the vectors $x^2 \hat{\mathbf{i}}+2 x \hat{\mathbf{j}}+\hat{\mathbf{k}}$ a 33. If $\hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf 34. Based on the following statements, choose the correct option. Statement I The variance of the first $n$ even natural num 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 pro 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 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( 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 ba 39. If a random variable $X$ has the following probability distribution, then its variance is nearly $$ \begin{array}{clllll 40. A radar system can detect an enemy plane in one out of 10 consecutive scans. The probability that it cannot detect an en 41. The locus of a variable point which forms a triangle of fixed area with two fixed points is 42. If the axes are rotated through angle ' $\alpha$ ', then the number of values of a such that the transformed equation of 43. $A$ line $L$ passing through the point $P(-5,-4)$ cuts the lines $x-y-5=0$ and $x+3 y+2=0$ respectively at $Q$ and $R$ s 44. If the reflection of a point $A(2,3)$ in $X$-axis is $B$, reflection of $B$ in the line $x+y=0$ is $C$ and the reflectio 45. The equation of a line which makes an angle of $45^{\circ}$ with each of the pair of lines $x y-x-y+1=0$ is 46. If the slope of one of the lines in the pair of lines $8 x^2+a x y+y^2=0$ is thrice the slope of the second line, then $ 47. The triangle $P Q R$ is inscribed in the circle $x^2+y^2=25$. If $Q=(3,4)$ and $R=(-4,3)$, then $\angle Q P R$ is equal 48. The locus of the point of intersection of perpendicular tangents drawn to the circle $x^2+y^2=10$ is 49. The normal drawn at $(1,1)$ to the circle $x^2+y^2-4 x+6 y-4=0$ is 50. Parametric equations of the circle $2 x^2+2 y^2=9$ are 51. Angle between the circles $x^2+y^2-4 x-6 y-3=0$ and $x^2+y^2+8 x-4 y+11=0$ is 52. Equation of the line touching both parabolas $y^2=4 x$ and $x^2=-32 y$ is 53. The length of the latusrectum of $16 x^2+25 y^2=400$ is 54. The line $21 x+5 y=k$ touches the hyperbola $7 x^2-5 y^2=232$, then $k$ is equal to 55. If the equation $\frac{x^2}{7-k}+\frac{y^2}{5-k}=1$ represents a hyperbola, then 56. If a line $L$ makes angles $\frac{\pi}{3}$ and $\frac{\pi}{4}$ with $Y$-axis and $Z$-axis respectively, then the angle 57. If $l, m$ and $n$ are the direction cosines of a line that is perpendicular to the lines having the direction ratios $(1 58. The foot of the perpendicular drawn from a point $A(1,1,1)$ on to a plane $\pi$ is $P(-3,3,5)$.If the equation of the pl 59. $$\mathop {\lim }\limits_{x \to \infty } \frac{[2 x-3]}{x} \text { is equal to } $$ 60. $\mathop {\lim }\limits_{x \to 0}\frac{\cos 2 x-\cos 3 x}{4 x-\cos 5 x}$ is equal to $\cos 4 x-\cos 5 x$ 61. If a real valued function $f(x)=\left\{\begin{array}{cl}\frac{2 x^2+(k+2) x+9}{3 x^2-7 x-6}, & \text { for } x \neq 3 \\ 62. If $y=\tan ^{-1} \frac{x}{1+2 x^2}+\tan ^{-1} \frac{x}{1+6 x^2}+\tan ^{-1} \frac{x}{1+12 x^2}$, then $\left(\frac{d y}{d 63. If $f(x)=5 \cos ^3 x-3 \sin ^2 x$ and $g(x)=4 \sin ^3 x+\cos ^2 x$, then the derivative of $f(x)$ with respect to $g(x)$ 64. If $y=1+x+x^2+x^3+\ldots \ldots \infty$ and $|x| 65. The semi-vertical angle of a right circular cone is $45^{\circ} \%$ If the radius of the base of the cone is measured as 66. If a man of height 1.8 mt , is walking away from the foot of a light pole of height 6 mt , with a speed of 7 km per hour 67. If the curves $2 x^2+k y^2=30$ and $3 y^2=28 x$ cut each other orthogonally, then $k$ is equal to 68. The interval containing all the real values of $x$ such that the real valued function $f(x)=\sqrt{x}+\frac{1}{\sqrt{x}}$ 69. $\int e^{4 x^2+8 x-4}(x+1) \cos \left(3 x^2+6 x-4\right) d x$ is equal to 70. $\int\left[(\log 2 x)^2+2 \log 2 x\right] d x$ is equal to 71. If $\int \log \left(6 \sin ^2 x+17 \sin x+12\right) \cos x d x=f(x)+c$, then $f\left(\frac{\pi}{2}\right)$ is equal to 72. $\int \frac{1}{\left(1+x^2\right) \sqrt{x^2+2}} d x$ is equal to 73. $\int \sin ^4 x \cos ^4 x d x$ is equal to 74. $\int_0^1 \sqrt{\frac{2+x}{2-x}} d x$ is equal to 75. If $M=\int\limits_0^{\infty} \frac{\log t}{1+t^3} d t$ and $N=\int\limits_{-\infty}^{\infty} \frac{t e^{2 t}}{1+e^{3 t}} 76. $\int\limits_{-2}^2\left(4-x^2\right)^{\frac{5}{2}} d x$ is equal to 77. $$ \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)^ 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 axe 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, $R$ i 2. A particle starts from rest and moves in a straight line. It travels a distance $2 L$ with uniform acceleration and then 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 un 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 bal 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^{ 7. A body of mass 30 kg moving with a velocity $20 \mathrm{~ms}^{-1}$ undergoes one-dimensional elastic collision with anot 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 di 9. Two blocks of equal masses are tied with a light string passing over a massless pulley (assuming frictionless surfaces ) 10. A ring and a disc of same mass and same diameter are rolling without slipping. Their linear velocities are same, then th 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 12. The relation between the force ( $F$ in Newton) acting on a particle executing simple harmonic motion and the displaceme 13. The gravitational potential energy of a body on the surface of the earth is $E$. If the body is taken from the surface o 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 15. Two cylindrical vessels $A$ and $B$ of different areas of cross-section kept on same horizontal plane are filled with wa 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 17. Two ideal gases $A$ and $B$ of same number of moles expand at constant temperatures $T_1$ and $T_2$ respectively such th 18. When 80 J of heat is absorbed by a monoatomic gas, its volume increases by $16 \times 10^{-5} \mathrm{~m}^3$. The pressu 19. The efficiency of a Carnot heat engine is $25 \%$ and the temperature of its source is $127^{\circ} \mathrm{C}$. Without 20. The total internal energy of 2 moles of a monoatomic gas at a temperature $27^{\circ} \mathrm{C}$ is $U$. The total inte 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 i 22. When a convex lens is immersed in a liquid of refractive index equal to $80 \%$ of the refractive index of the material 23. The angle between the axes of a polariser and an analyser is $45^{\circ}$. If the intensity of the unpolarised light inc 24. The magnitude of an electric field which can just suspend a deuteron of mass $3.2 \times 10^{-27} \mathrm{~kg}$ freely i 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 sp 26. The space between the plates of a parallel plate capacitor is halved and a dielectric medium of relative permittivity 10 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 28. Resistance of a wire is $8 \Omega$. It is drawn in such a way that it experiences a longitudinal strain of $400 \%$. The 29. Current flows in a conductor from east to west. The direction of the magnetic field at a point below the conductor is to 30. Two infinite length wires carry currents 8 A and $6^{\mathrm{A}}$ respectively and are placed along $X$ and $Y$-axes res 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 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 u 33. In the circuit shown in the figure, neglecting the source resistance, the voltmeter and ammeter readings respectively ar 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 wavel 36. The principle quantum number $n$ corresponding to the exited state of $\mathrm{He}^{+}$ion. If on transition to the grou 37. Which physical quantity is measured in barn? 38. $$ \text { Truth table for the given circuit is } $$ 39. If $R_C$ and $R_B$ are respectively the resistances of in collector and base sides of the circuit and $\beta$ is the cur 40. Which one of the following is not classified as pulse modulation?

AP EAPCET 2024 - 22th May Evening Shift

MCQ (Single Correct Answer)

-0

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

$(1, \infty)$

$(0,1)$

$(-\infty, 0) \cup(1, \infty)$

$(-\infty, 0)$

AP EAPCET 2024 - 22th May Evening Shift

MCQ (Single Correct Answer)

-0

$\int e^{4 x^2+8 x-4}(x+1) \cos \left(3 x^2+6 x-4\right) d x$ is equal to

$\frac{e^{4 x^2+8 x-4}}{25}\left[3 \sin \left(3 x^2+6 x-4\right)-4 \cos \left(3 x^2+6 x-4\right)\right]+c$

$\frac{e^{4 x^2+8 x-4}}{50}\left[4 \cos \left(3 x^2+6 x-4\right)+3 \sin \left(3 x^2+6 x-4\right]+c\right.$

$\frac{e^{4 x^2+8 x-4}}{25}\left[3 \cos \left(3 x^2+6 x-4\right)+4 \sin \left(3 x^2+6 x-4\right]+c\right.$

$\frac{e^{4 x^2+8 x-4}}{50}\left[4 \sin \left(3 x^2+6 x-4\right)+3 \cos \left(3 x^2+6 x-4\right]+c\right.$

AP EAPCET 2024 - 22th May Evening Shift

MCQ (Single Correct Answer)

-0

$\int\left[(\log 2 x)^2+2 \log 2 x\right] d x$ is equal to

$(\log 2 x)^2+c$

$2 x \log 2 x+c$

$x(\log 2 x)^2+c$

$2 x(\log x)^2+c$

AP EAPCET 2024 - 22th May Evening Shift

MCQ (Single Correct Answer)

-0

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

$\frac{1}{6}\left[\log 5^5+\log 7^7-12\right]$

$\frac{1}{6}[7 \log 5+5 \log 7+29]$

$\frac{1}{6}[14 \log 5+15 \log 7+12]$

$\frac{1}{6}[15 \log 5+14 \log 7-29]$ $$ $$

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