AP EAPCET 2024 - 23th May Morning Shift | AP EAPCET Year Wise Previous Years Questions

Chemistry

Mathematics

1. If $A \subseteq Z$ and the function $f: A \rightarrow R$ is defined by $f(x)=\frac{1}{\sqrt{64-(0.5)^{24+x-x^2}}}$, then 2. Which of the following function are odd? I. $f(x)=x\left(\frac{e^x-1}{e^x+1}\right)$ II. $f(x)=k^x+k^{-x}+\cos x$ III. $ 3. The $n$th term of the series $1+(3+5+7)+(9+11+13+15+17)+\ldots$ is 4. 4. If $A=\left[\begin{array}{lll}83 & 74 & 41 \\ 93 & 96 & 31 \\ 24 & 15 & 79\end{array}\right]$, then $\operatorname{de 5. If $\left|\begin{array}{lll}a & 1 & 1 \\ 1 & b & 1 \\ 1 & 1 & c\end{array}\right|>0$, then $a b c>$ 6. If the system of equations $a_1 x+b_1 y+c_1 z=0, a_2 x+b_2 y+c_2 z=0$ and $a_3 x+b_3 y+c_3 z=0$ has only trivial soluti 7. $\omega$ is a complex cube root of unity and if $z$ is a complex number satisfying $|z-1| \leq 2$ and $\left|\omega^2 z- 8. If the roots of the equation $z^3+i z^2+2 i=0$ are the vertices of a $\triangle A B C$, then that $\triangle A B C$ is 9. $(r, \theta)$ denotes $r(\cos \theta+i \sin \theta)$. If $x=(1, \alpha), y=(1, \beta), z=(1, \gamma)$ and $x+y+z=0$, the 10. The set of all real values of $x$ satisfying the inequality $\frac{7 x^2-5 x-18}{2 x^2+x-6} 11. The set of all values of $k$ for which the inequality $x^2-(3 k+1) x+4 k^2+3 k-3>0$ is true for all real values of $x$, 12. The cubic equation whose roots are the square of the roots of the equation is $$ 12 x^3-20 x^2+x+3=0 $$ 13. $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3+3 x^2-10 x-24=0$ If $\alpha(\beta+\gamma), \beta(\gamma+ 14. Among the 4 -digit numbers formed using the digits $0,1,2,3$ and 4 when repetition of digits allowed. Then, the number o 15. The number of ways of arranging 2 red, 3 white and 5 yellow roses of different sizes into a garland such that no two yel 16. The number of ways of selecting- 3 numbers that are in GP from the set $\{1,2,3$, $100\}$ is 17. The independent term in the expansion of $\left(1+x+2 x^2\right)\left(\frac{3 x^2}{2}-\frac{1}{3 x}\right)^9$ is 18. For $|x| 19. $\frac{4 x^2+5}{(x-2)^4}=\frac{A}{(x-2)}+\frac{B}{(x-2)^2}+\frac{C}{(x-2)^3}+\frac{D}{(x-2)^4}$, then $\sqrt{\frac{A}{C} 20. $$ \tan ^2 \frac{\pi}{16}+\tan ^2 \frac{2 \pi}{16}+\tan ^2 \frac{3 \pi}{16}+\tan ^2 \frac{4 \pi}{16} $$ $+\tan ^2 \frac{ 21. $$ \begin{aligned} & \sin ^2 18^{\circ}+\sin ^2 24^{\circ}+\sin ^2 36^{\circ}+\sin ^2 42^{\circ}+\sin ^2 78^{\circ} \\ & 22. If $A B$ and $C$ are the angles of a triangle, then $\frac{\sin A+\sin B+\sin C}{\sin ^2 \frac{A}{2}-\sin ^2 \frac{B}{2} 23. The general solution of $\cot \frac{x}{2}-\cot x=\operatorname{cosec} \frac{x}{2}$ is 24. If $0 25. $\cosh (\log 4)$ is equal to 26. In $\triangle A B C, a^2 \sin 2 B+b^2 \sin 2 A$ is equal to 27. $$ \text { In } \triangle A B C, \frac{r_2\left(r_1+r_3\right)}{\sqrt{r_1 r_2+r_2 r_3+r_3 r_1}} \text { is equal to } $$ 28. In $\triangle A B C,\left(r_2+r_3\right) \operatorname{cosec}^2 \frac{A}{2}$ is equal to 29. If the vectors $a \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+b \hat{\mathbf{j}}+\hat{\mathbf{k 30. If $\mathbf{A B}=2 \mathbf{i}+3 \mathbf{j}-6 \mathbf{k}, \mathbf{B C}=6 \mathbf{i}-2 \mathbf{j}+3 \mathbf{k}$ are the ve 31. The orthogonal projection vector of $a=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ on $\mathbf{b}=\hat{\ma 32. If $\mathbf{a}=-4 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$ and $\mathbf{b}=\sqrt{2} \hat{\mathbf{i}}-\sqr 33. A unit vector perpendicular to the vectors $a=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$ and $\mathbf{b}= 34. If the mean of the data $7,8,9,7,8,7, \lambda$ and 8 is 8 , then variance of the data is equal to 35. When two dice are thrown the probability of getting the sum of the values on them as 10 or 11 is 36. It is given that in a random experiment events $A$ and $B$ are such that $P(A)=\frac{1}{4}, P(A / B)=\frac{1}{2}$ and $P 37. The probability that $A$ speaks truth is $75 \%$ and the probability that $B$ speaks truth is $80 \%$. The probability t 38. Bag $A$ contains 2 white and 3 red balls and bag $B$ contains 4 white and 5 red balls. If one ball is drawn at random fr 39. If the probability distribution of a random variable $X$ is as follows, then $k$ is equal to $$ \begin{array}{c|l|l|l|l} 40. In a binomial distribution $B(n, p)$ the sum and product of the mean and the variance are 5 and 6 respectively, then $6( 41. The locus of the mid-point of the portion of the line $x \cos \alpha+y \sin \alpha=p$ intercepted by the coordinate axes 42. The origin is shifted to the point $(2,3)$ by translation of axes and then the coordinate axes are rotated about the ori 43. If the straight line passing through $P(3,4)$ makes an angle $\frac{\pi}{6}$ with the positive $X$-axis in anti-clockwis 44. The equation of the perpendicular bisectors of the sides $A B$ and $A C$ of $\triangle A B C$ are $x-y+5=0$ and $x+2 y=0 45. A pair of lines drawn through the origin forms a right angled isosceles triangle with right angle at the origin with the 46. The combined equation of the bisectors of the angles between the lines joining the origin to the points of intersection 47. The circumference of a circle passing through the point $(4,6)$ with two normals represented by $2 x-3 y+4=0$ and $x+y-3 48. If the line through the point $P(5,3)$ meets the circle $x^2+y^2-2 x-4 y+\alpha=0$ at $A(4,2)$ and $B\left(x_1, y_1\righ 49. Consider the point $P(\alpha, \beta)$ on the line $2 x+y=1$. If the $P$ and $(3,2)$ are conjugate points with respect to 50. If $(1,3)$ is the mid-point of a chord of the circle $x^2+y^2-4 x-8 y+16=0$, then the area of the triangle formed by tha 51. If the circles $x^2+y^2+2 \alpha x+2 y-8=0$ and $x^2+y^2-2 x+a y-14=0$ intersect orthogonally, then the distance between 52. If $P$ is a point which divides the line segment joining the focus of the parabola $y^2=12 x$ and a point on the parabol 53. Let $T_1$ be the tangent drawn at a point $P(\sqrt{2}, \sqrt{3})$ on the ellipse $\frac{x^2}{4}+\frac{y^2}{6}=1$. If ( $ 54. If $y=x+\sqrt{2}$ is a tangent to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{2}=1$, then equations of its directrices are 55. The area of the quadrilateral formed with the foci of the hyperbola $\frac{x^2}{16}-\frac{y^2}{9}=1$ and its conjugate h 56. The length of the internal bisector of angle $A$ in $\triangle A B C$ with vertices $A(4,7,8), B(2,3,4)$ and $C(2,5,7)$ 57. If the direction cosines of lines are given by $l+m+n=0$ and $m n-2 l m-2 n l=0$, then the acute angle between those lin 58. If the angle $\theta$ between the line $\frac{x+1}{1}=\frac{y-1}{2}=\frac{z-2}{2}$ and the plane $2 x-y+\sqrt{\lambda} z 59. Let $f(x)=\left\{\begin{array}{cl}1+\frac{2 x}{a}, & 0 \leq x \leq 1 \\ a x, & 1 60. Let $[P]$ denote the greatest integer $\leq P$. If $0 \leq a \leq 2$, then the number of integral values of ' $a$ ' such 61. If $f(x)=\left\{\begin{array}{cl}\frac{\sqrt{a^2-a x+x^2}-\sqrt{x^2+a x+a^2}}{\sqrt{a+x}-\sqrt{a-x}}, & x \neq 0 \text { 62. If $y=\sinh ^{-1}\left(\frac{1-x}{1+x}\right)$, then $\frac{d y}{d x}$ is equal to 63. If $y=(x-1)(x+2)\left(x^2+5\right)\left(x^4+8\right)$, then $\lim _{x \rightarrow-1}\left(\frac{d y}{d x}\right)$ is equ 64. If $f(x)=\left\{\begin{array}{cc}a x^2+b x-\frac{13}{8}, & x \leq 1 \\ 3 x-3, & 1 2\end{array}\right.$ $\forall x \in R 65. $A$ is a point on the circle with radius 8 and centre at $O$. A particle $P$ is moving on the circumference of the circl 66. If the length of the sub-tangent at any $P$ on a curve is proportional to the abscissa of the point $P$, then the equati 67. In each of the following options, a function and an interval are given. Choose the option containing the function and th 68. The function $f(x)=\left\{\begin{array}{cc}\frac{x-|x|}{x}, & x \neq 0 \\ 2, & x=0\end{array}\right.$ 69. If $\int \frac{\sqrt[4]{x}}{\sqrt{x}+\sqrt[4]{x}} d x=$ $\frac{2}{3}\left[A \sqrt[4]{x^3}+B \sqrt[4]{x^2}+C \sqrt[4]{x}+ 70. $\int(\log x)^m x^n d x$ is equal to 71. $\int \sin ^{-1}\left(\sqrt{\frac{x-a}{x}}\right) d x$ is equal to 72. If $\int \frac{\sin x \cos x}{\sqrt{\cos ^4 x-\sin ^4 x}} d x=-\frac{f(x)}{2}+c$, then domain of $f(x)$ is 73. If $y=\left(\tan ^{-1} 2 x\right)^2+\left(\cot ^{-1} 2 x\right)^2$, then $\left(1+4 x^2\right)^2 y^{\prime \prime}-16$ i 74. If $\int_0^{2 \pi}\left(\sin ^4 x+\cos ^4 x\right) d x=K \int_0^\pi \sin ^2 x d x+L \int_0^{\frac{\pi}{2}} \cos ^2 x d x 75. $\int_0^\pi \frac{x \sin x}{4 \cos ^2 x+3 \sin ^2 x} d x$ is equal to 76. If $A=\int_0^{\infty} \frac{1+x^2}{1+x^4} d x, B=\int_0^1 \frac{1+x^2}{1+x^4} d x$, then 77. If $(a, \beta)$ is the stationary point of the curve $y=2 x-x^2$, then the area bounded by the curves $y=2^x, y=2 x-x^2, 78. Among the options given below from which option a differential equation of order two can be formed ? 79. The differential equation for which $a x+b y=1$ is general solution is 80. The solution of the differential equation $e^x y d x+e^x d y+x d x=0$ is

Physics

1. Which of the following is not a unit of permeability? 2. A diving board is at at height of $h$ from the water surface. A swimmer standing on this board thrown a stone vertically 3. Path of projectile is given by the equation $Y=P x-Q x^2$, match the following accordingly (acceleration due to gravity 4. A bowling machine placed at a height $h$ above the earth surface releases different balls with different angles but with 5. A balloon carrying some sand of mass $M$ is moving down with a constant acceleration $a_0$. The mass $m$ of sand to be r 6. A person walks up a stalled escalator in 90 s. When standing on the same moving escalator, he reached in 60s. The time i 7. A particle of mass $m$ at rest on a rough horizontal surface with a coefficient of friction $\mu$ is given a velocity $u 8. A soccer ball of mass 250 g is moving horizontally to the left with a speed $22 \mathrm{~ms}^{-1}$. This ball is kicked 9. The moment of inertia of a solid sphere about its diameter is $20 \mathrm{~kg}-\mathrm{m}^2$. The moment of inertia of a 10. One ring, one solid sphere and one solid cylinder are rolling down on same inclined plane starting from rest The radius 11. As shown in the figure, two blocks of masses $m_1$ and $m_2$ are connected to spring of force constant $k$. The blocks a 12. A mass $M$, attached to a horizontal spring executes simple harmonic motion with amplitude $A_1$. When mass $M$ passes m 13. The time period of revolution of a satellite close to planet's surfaces is 80 min . The time period of another satellite 14. The work done on a wire of volume of $2 \mathrm{~cm}^3$ is $16 \times 10^2 \mathrm{~J}$. If the Young's modulus of the m 15. Water flows from a tap of diameter 1.5 cm with $75 \times 10^{-5} \mathrm{~m}^3 \mathrm{~s}^{-1}$. Coefficient of viscos 16. A uniform metal solid sphere is rotating with angular speed $\omega_0$ about diameter. If the temperature is raised by $ 17. When 2 moles of a monoatomic gas expands adiabatically from a temperature of $80^{\circ} \mathrm{C}$ to $50^{\circ} \mat 18. A gas absorbs 18 J of heat and work done on the gas is 12 J . Then, the change in internal energy of the gas 19. If the ratio of the absolute temperature of the sink and source of a Carnot engine is changed from $2: 3$ to $3: 4$, the 20. The ratio of the molar specific heat capacities of monoatomic and diatomic gases at constant pressure is 21. The frequency of fifth harmonic of a closed organ pipe is equal to the frequency of third harmonic of an open organ pipe 22. When a convex lens is immersed in two different liquids of refractive indices 1.25 and 1.5 , the ratio of the focal leng 23. Two light waves of intensities $I$ and $2 I$ superimpose on each other. If the path difference between the light waves r 24. A particle of mass 0.5 g and charge $10 \mu \mathrm{C}$ is subjected to a uniform electric field of $8 \mathrm{NC}^{-1}$ 25. 125 identical charged small spheres coalesce to form a big charged sphere. If the electric potential on each small spher 26. Two particles of charges 4 nC and $Q$ are kept in air with a separation of 10 cm between them. If the electrostatic pote 27. The emf of a cell of internal resistance $2 \Omega$ is measured using a voltmeter of resistance $998 \Omega$. The error 28. In a meter bridge experiment, a resistance of $9 \Omega$ is connected in the left gap and an unknown resistance greater 29. A charge $q$ is spread uniformly over an isolated ring $R$. The ring is rotated about its natural axis with angular spee 30. Current sensitivities of two galvanometers $G_1$ and $G_2$ of resistances $100 \Omega$ and $50 \Omega$ are $10^8 \mathrm 31. The relation between $\mu$ and $H$ for a specimen of iron is $\mu=\left[\frac{1.4}{H}+12 \times 10^{-4}\right] \mathrm{H 32. In a circuit the current falls from a 14 A to 4 A in a time 0.2 ms . If the induced emf is 150 V , then the self-inducta 33. An alternating current is given by $i=(3 \sin \omega t+4 \cos \omega t) \mathrm{A}$. The rms current will be 34. For plane electromagnetic waves propagating in the positive $z$-direction. The combination which gives the correct possi 35. A photon incident on a metal of work function 2 eV produced photoelectron of maximum kinetic energy of 2 eV . The wavele 36. Energy levels $A, B$ and $C$ of a certain atom corresponding to increasing values of energy i.e $E_A < E_B < E_C$. 37. In a nuclear reactor, the fuel is consumed at the rate of $1 \times 10^{-3} \mathrm{gs}^{-1}$. The power generated in kW 38. In the diodes show in the diagrams, which one is reverse biased? 39. $$ \text { The following configuration of gates is equivalent to } $$ 40. Size of the antenna for a carrier wave of frequency 3 MHz is

AP EAPCET 2024 - 23th May Morning Shift

MCQ (Single Correct Answer)

-0

If $0 < x < \frac{1}{2}$ and $\alpha=\sin ^{-1} x+\cos ^{-1}\left(\frac{x}{2}+\frac{\sqrt{3-3 x^2}}{2}\right)$, then $\tan \alpha+\cot \alpha$ is equal to

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