AP EAPCET 2024 - 20th May Evening Shift | AP EAPCET Year Wise Previous Years Questions

Chemistry

Mathematics

1. $f: R \rightarrow R$ is defined by $f(x+y)=f(x)+12 y, \forall x, y \in R$. If $f(1)=6$, then $\sum_{r=1}^n f(r)=$ 2. The domain of the real valued function $f(x)=\sqrt{2+x}+\sqrt{3-x}$ is 3. If $2 \cdot 4^{2 n+1}+3^{3 n+1}$ is divisible by $k$ for all $n \in N$, then $k=$ 4. $\left|\begin{array}{ccc}a & b & c \\ a^2 & b^2 & c^2 \\ 1 & 1 & 1\end{array}\right|$ is not equal to 5. Let $A, B, C, D$ and $E$ be $n \times n$ matrices each with non-zero determinant. If $A B C D E=I$, then $C^{-1}=$ 6. If $A=\left[a_{i j}\right], 1 \leq i, j \leq n$ with $n \geq 2$ and $a_{i j}=i+j$ is a matrix, then the rank of $A$ is 7. If $z_1=10+6 i, z_2=4+6 i$ and $z$ is any complex number such that the argument of $\frac{\left(z-z_1\right)}{\left(z-z_ 8. If $\frac{3-2 i \sin \theta}{1+2 i \sin \theta}$ is purely imaginary number, then $\theta=$ 9. If $z=x+i y, x^2+y^2=1$ and $z_1=z e^{i \theta}$, then $\frac{z_1^{2 n}-1}{z_1^{2 n}+1}=$ 10. Let $[r]$ denote the largest integer not exceeditio $r$ and the roots of the equation $3 x^2+6 x+5+\alpha\left(x^2+2 x+2 11. For any real value of $x$. If $\frac{11 x^2+12 x+6}{x^2+4 x+2} \notin(a, b)$, then the value $x$ for which $\frac{11 x^2 12. If the roots of $\sqrt{\frac{1-y}{y}}+\sqrt{\frac{y}{1-y}}=\frac{5}{2}$ are $\alpha$ and $\beta(\beta>\alpha)$ and the e 13. If the roots of the equation $x^3+a x^2+b x+c=0$ are in arithmetic progression. Then, 14. A test containing 3 objective type of questions is conducted in a class. Each question has 4 options and only one option 15. The number of numbers lying between 1000 and 10000 such that every number contains the digit 3 and 7 only once without r 16. The number of ways in which 17 apples can be distributed among four guests such that each guest gets at least 3 apples i 17. If the coefficients of $x^5$ and $x^6$ are equal in the expansion of $\left(a+\frac{x}{5}\right)^{65}$, then the coeffic 18. If $|x| 19. If $\frac{x^2+3}{x^4+2 x^2+9}=\frac{A x+B}{x^2+a x+b}+\frac{C x+D}{x^2+c x+b}$, then $a A+b B+c C+D=$ 20. If $\sec \theta+\tan \theta=\frac{1}{3}$, then the quadrant in which $2 \theta$ lies is 21. If $540^{\circ} 22. If $(\alpha+\beta)$ is not a multiple of $\frac{\pi}{2}$ and $3 \sin (\alpha-\beta)=5 \cos (\alpha+\beta)$, then $\tan \ 23. The general solution of the equation $\sin ^2 \theta+3 \cos ^2 \theta=$ $5 \sin \theta$ is 24. If $\cos ^{-1} 2 x+\cos ^{-1} 3 x=\frac{\pi}{3}$ and $4 x^2=\frac{a}{b}$, then $a+b$ is equal to 25. If $\theta=\sec ^{-1}(\cosh u)$, then $u=$ 26. In $\triangle A B C$, if $4 r_1=5 r_2=6 r_3$, then $\sin ^2 \frac{A}{2}+\sin ^2 \frac{B}{2}+\sin ^2 \frac{C}{2}=$ 27. In $\triangle A B C, r_1 \cot \frac{A}{2}+r_2 \cot \frac{B}{2}+m_3 \cot \frac{C}{2}=$ 28. In $\triangle A B C, b c-r_2 r_3=$ 29. The angle between the diagonals of the parallelogram whose adjacent sides are $2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-5 \ 30. If the points having the position vectors $-i+4 j-4 k_{\text {, }}$, $3 i+2 j-5 k,-3 i+8 j-5 k$ and $-3 i+2 j+\lambda k$ 31. If $|f|=10,|g|=14$ and $|f-g|=15$, then $|f+g|=$ 32. If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are three vectors such that $|\mathbf{a}|=|\mathbf{b}|=|\mathbf{c}|=\sqrt{3}$ an 33. The angle between the line with the direction ratios $(2,5,1)$ and the plane $8 x+2 y-z=14$ is 34. If the mean deviation about the mean is $m$ and variance is $\sigma^2$ for the following data, then $m+\sigma^2=$ .tg 35. If five-digit numbers are formed from the digits $0,1,2,3,4$ using every digit exactly only once. Then, the probability 36. Two natural numbers are chosen at random from 1 to 100 and are multiplied. If $A$ is the event that the product is an ev 37. A box $P$ contains one white ball, three red ball and two black balls. Another box $Q$ contains two white balls, three r 38. A person is known to speak false once out of 4 times, If that person picks a card at random from a pack of 52 cards and 39. For a binomial variate $X \sim B(n, p)$ the difference between the mean and variance is 1 and the difference between the 40. The probability that a man failing to hit a target is $\frac{1}{3}$. If he fires 4 times, then the probability that he h 41. $A(2,3), B(-1,1)$ are two points. If $P$ is a variable point such that $\angle A P B=90^{\circ}$, then locus of $P$ is 42. If the origin is shifted to remove the first degree terms from the equation $2 x^2-3 y^2+4 x y+4 x+4 y-14=0$, then with 43. The circumcentre of the triangle formed by the lines $x+y+2=0,2 x+y+8=0$ and $x-y-2=0$ is 44. If the line $2 x-3 y+5=0$ is the perpendicular bisector of the line segment joining $(1,-2)$ and $(\alpha, \beta)$, then 45. If the area of the triangle formed by the straight lines $-15 x^2+4 x y+4 y^2=0$ and $x=\alpha$ is 200 sq unit, then $|\ 46. The equation for straight line passing through the point of intersection of the lines represented by $x^2+4 x y+3 y^2-4 47. The largest among the distances from the point $P(15,9)$ to the points on the circle $x^2+y^2-6 x-8 y-11=0$ is 48. The circle $x^2+y^2-8 x-12 y+\alpha=0$ lies in the first quadrant without touching the coordinate axes. If $(6,6)$ is an 49. The equation of the circle whose diameter is the common chord of the circles $x^2+y^2-6 x-7=0$ and $x^2+y^2-10 x+16=0$ i 50. If the locus of the mid-point of the chords of the circle $x^2+y^2=25$, which subtend a right angle at the origin is giv 51. The radical centre of the circles $x^2+y^2+2 x+3 y+1=0$, $x^2+y^2+x-y+3=0, x^2+y^2-3 x+2 y+5=0$ 52. Equation of a tagent line of the parabola $y^2=8 x$, which passes through the point $(1,3)$ is 53. If the chord of the ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1$ having $(1,1)$ as its middle point is $x+\alpha y=\beta$, th 54. If a directrix of a hyperbola centred at the origin and passing through the point $(4,-2 \sqrt{3})$ is $\sqrt{5} x=4$ an 55. If $l_1$ and $l_2$ are the lengths of the perpendiculars drawn from a point on the hyperbola $5 x^2-4 y^2-20=0$ to its a 56. If $O(0,0,0), A(3,0,0)$ and $B(0,4,0)$ form a triangle, then the incentre of $\triangle O A B$ is 57. The direction cosines of the line of intersection of the planes $x+2 y+z-4=0$ and $2 x-y+z-3=0$ are 58. If $L_1$ and $L_2$ are two lines which pass through origin and having direction ratios $(3,1,-5)$ and $(2,3,-1)$ respect 59. $\lim \limits_{x \rightarrow \frac{\pi}{4}} \frac{4 \sqrt{2}-(\cos x+\sin x)^5}{1-\sin 2 x}=$ 60. If $\lim \limits_{x \rightarrow 0} \frac{e^x-a-\log (1+x)}{\sin x}=0$, then $a=$ 61. The values of $a$ and $b$ for which the function$ f(x)=\left\{\begin{array}{cl}1+|\sin x|^{\frac{a}{\sin x \mid}} & \fra 62. If $f(x)=\left\{\begin{array}{cc}2 x+3, & x \leq 1 \\ a x^2+b x, & x>1\end{array}\right.$ is differentiable, $\forall x 63. If $y=t^2+t^3$ and $x=t-t^4$, then $\frac{d^2 y}{d x^2}$ at $t=1$ is 64. In the interval $[0,3]$ The function $f(x)=|x-1|+|x-2|$ is 65. $p_1$ and $p_2$ are the perpendicular distances from the origin to the tangent and normal drawn at any point on the curv 66. The length of the subnormal at any point on the curve $y=\left(\frac{x}{2024}\right)^k$ is constant, if the value of $k$ 67. The acute angle between the curves $x^2+y^2=x+y$ and $x^2+y^2=2 y$ is 68. A' value of $C$ according to the Lagrange's mean value theorem for $f(x)=(x-1)(x-2)(x-3)$ in $[0,4]$ is 69. $\int \frac{d x}{x\left(x^4+1\right)}=$ 70. $\int \frac{d x}{\sqrt{\sin ^3 x \cos (x-a)}}=$ 71. $\int \frac{e^{2 x}}{\sqrt[4]{e^x+1}} d x=$ 72. $\int \frac{2-\sin x}{2 \cos x+3} d x=$ 73. $\int \sin ^{-1} \sqrt{\frac{x}{a+x}} d x=$ 74. $\int\limits_{\frac{-1}{24}}^{\frac{1}{24}} \sec x \log \left(\frac{1-x}{1+x}\right) d x=$ 75. If $[x]$ is the greatest integer function, then $\int_0^5[x] d x=$ 76. $\int_0^{\frac{\pi}{2}} \frac{1}{1+\sqrt{\tan x}} d x=$ 77. $\int_0^\pi \frac{x \sin x}{1+\cos ^2 x} d x=$ 78. Order and degree of the differential equation $\frac{d^3 y}{d x^3}=\left[1+\left(\frac{d y}{d x}\right)^2\right]^{\frac{ 79. Integrating factor of the differential equation $\sin x \frac{d y}{d x}-y \cos x=1$ is 80. The general solution of the differential equation $\left(x \sin \frac{y}{x}\right) d y=\left(y \sin \frac{y}{x}-x\right)

Physics

1. Find the dimension formula of $\frac{a}{b}$ in the equation $F=a \sqrt{x}+b t^2$, where $F$ is force, $x$ is distance an 2. The relation between time $t$ and displacement $x$ is $t=\alpha x^2+\beta x$, where $\alpha$ and $\beta$ are constants. 3. If two stones are projected at angle $\theta$ and $\left(90^{\circ}-\theta\right)$ respectively with horizontal with a s 4. A particle revolving in a circular path travels the first half of the circumference in 4 s and the next half in 2 s . Wh 5. A block of metal 2 kg is in rest on a smooth plane. It is striked by a jet releasing water of $1 \mathrm{~kg} \mathrm{~s 6. An insect is crawling in a hemi-spherical bowl of radius $R$. If the coefficient of friction between the insect and bowl 7. Two objects having masses $1: 4$ ratio are at rest. When both of them are subjected to same force separately, they achie 8. An object of mas $m$ is projected with an initial velocity $u$ with angle of $\theta$ with the horizontal. The average p 9. A small disc is on the top of a smooth hemisphere of radius $R$. The smallest horizontal velocity $v$ that should be imp 10. A block $P$ is rotating in contact with the vertical wall of a rotor as shown in figures $A, B, C$. The relation between 11. A horizontal board is performing simple harmonic oscillations horizontally with an amplitude 0.3 m and a period of 4 s . 12. A test tube of mass 6 g and uniform area of cross-section $10 \mathrm{~cm}^2$ is floating in water vertically when 10 g 13. What is the height from the surface of earth, where acceleration due to gravity will be $1 / 4$ of that of the earth? $\ 14. Depth of a river is 100 m magnitude of compressibility of the water is $05 \times 10^{-9} \mathrm{~N}^{-1} \mathrm{~m}^2 15. Two mercury drops, each with same radius $r$ merged to form a bigger drop. $T$ is the surface tension of single drop, th 16. The absorption coefficient value of a perfect black body is 17. A certain volume of a gas at 300 K expands adiabatically until its volume is doubled. The resultant fall in temperature 18. The efficiency of a Carnot's engine is $25 \%$. When the temperature of sink is 300 K . The increase in the temperature 19. When 100 J of heat is supplied to a gas, the increase in the internal energy of the gas is 60 J . Then the gas is /can 20. An ideal gas is kept in a cylinder of volume $3 \mathrm{~m}^3$ at a pressure of $3 \times 10^5 \mathrm{~Pa}$. The energy 21. A pipe with 30 cm length is open at both ends. Which harmonic mode of the pipe resonates with the 1.65 kHz source? (Velo 22. An object is placed at a distance of 18 cm in front of a mirror. If the image is formed at a distance of 4 cm on the oth 23. If a microscope is placed in air, the minimum separation of two objects seen as distinct is $6 \mu \mathrm{~m}$. If the 24. Three point charges $+q,+2 q$ and $+4 q$ are placed along a straight line such that the charge $+2 q$ lies at equidistan 25. Three parallel plate capacitors of capacitances $4 \mu \mathrm{~F}$, $6 \mu \mathrm{~F}$ and $12 \mu \mathrm{~F}$ are fi 26. A particle of mass 2 g and charge $6 \mu \mathrm{C}$ is accelerated from rest through a potential difference of 60 V . T 27. A straight wire of resistance $R$ is bent in the shape of $f_d$ square. A cell of emf 12 V is connected between two adja 28. In the given circuit, if the potential at point $B$ is 24 V , the potential at point $A$ is 29. Two long straight parallel conductors $A$ and $B$ carrying currents 4.5 A and 8 A respectively, are separated by 25 cm i 30. Two concentric thin circular rings of radii 50 cm and 40 cm , each carry a current of 3.5 A in opposite directions. If t 31. At a place where the magnitude of the earth's magnetic field is $4 \times 10^{-5} \mathrm{~T}$, a short bar magnet is pl 32. The ratio of the number of turns per unit length of two solenoids $A$ and $B$ are 1:3 and the lengths of $A$ and $B$ are 33. An inductor and a resistor are connected in series to an AC source of voltage $144 \sin \left(100 \pi t+\frac{\pi}{2}\ri 34. Inner shell electrons in atoms moving from one energy level to another lower energy level produce 35. If the kinetic energy of a particle in motion is decreased by $36 \%$, the increase in de-Broglie wavelength of the part 36. The speed of the electron in a hydrogen atom in the $n=3$ level is(Planck's constant $=6.6 \times 10^{-34} \mathrm{Js}$ 37. One mole of radium has an activity of $\frac{1}{3.7}$ kilo curie. Its decay constant is(Avagadro number $=6 \times 10^{2 38. The voltage gain and current gain of a transistor amplifier in common emitter configuration are respectively 150 and 50 39. If the energy gap of a substance is 5.4 eV , then the substance is 40. In amplitude modulation, the amplitude of the carrier wave is 10 V and the amplitude of one of the side bands is 2 V . T

AP EAPCET 2024 - 20th May Evening Shift

MCQ (Single Correct Answer)

-0

The values of $a$ and $b$ for which the function

$ f(x)=\left\{\begin{array}{cl}1+|\sin x|^{\frac{a}{\sin x \mid}} & \frac{-\pi}{6} < x < 0 \\ b, & x=0 \quad \text { is continuous at } x=0 \\ e^{\frac{\tan 2 x}{\tan 3 x},} & 0 < x < \frac{\pi}{6}\end{array}\right. $

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