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 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

$(-7,5)$

$(5, \infty)$

$(1,5)$

$(-\infty, 1)$

AP EAPCET 2024 - 22th May Evening Shift

MCQ (Single Correct Answer)

-0

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

$3 x^2-7 x-21$

$3 x^3-7 x^2+21 x-45$

$3 x^4-7 x^3+21 x^2-45+114$

$114 x-143$

AP EAPCET 2024 - 22th May Evening Shift

MCQ (Single Correct Answer)

-0

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

$\frac{1}{7}$

AP EAPCET 2024 - 22th May Evening Shift

MCQ (Single Correct Answer)

-0

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

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