AP EAPCET 2025 - 26th May Evening Shift | AP EAPCET Year Wise Previous Years Questions

Chemistry

Mathematics

1. Let [ $x$ ] represent the greatest integer less than or equal to $x,\{x\}=x-[x] \sqrt{2}=1.414$ and $\sqrt{3}=1.732$. I 2. If the range of the function $f(x)=-3 x-3$ is $\{3,-6,-9,-18\}$, then which one of the following is not in the domain of 3. $\frac{1}{3 \cdot 5}+\frac{1}{5 \cdot 7}+\frac{1}{7 \cdot 9}+\ldots$ to 24 terms $=$ 4. If $B$ is the inverse of a third order matrix $A$ and det $B=k$, then $(\operatorname{adj}(\operatorname{adj} \mathrm{A} 5. If $A=\left[\begin{array}{lll}2 & 2 & 1 \\ 1 & 3 & 1 \\ 1 & 2 & 2\end{array}\right]$ and $\alpha, \beta, \gamma$ are the 6. If the values of $x, y$ and $z$ which satisfy the equations $2 x-3 y+2 z+15=0,3 x+y-z+2=0$ and $x-3 y-3 z+8=0$ simultane 7. If $x=3-2 \sqrt{3} \mathrm{i}$, then $x^4-12 x^3+54 x^2-108 x-54=$ 8. $z_1, z_2, z_3$ represent the vertices $A, B, C$ of a $\triangle A B C$ respectively in the argand plane. If $\left|z_1- 9. The product of the four values of the complex number $(1+i)^{3 / 4}$ is 10. If the difference of the roots of the equation $x^2-7 x+10=0$ is same as the difference of the roots of the equation $x^ 11. The product of all the real roots of the equation $|x|^2-5|x|+6=0$ 12. If $\alpha, \beta$ and $\gamma$ are the roots of the equation $5 x^3-4 x^2+3 x-2=0$, then $\alpha^3+\beta^3+\gamma^3=$ 13. After the roots of the equation $6 x^3+7 x^2-4 x-2=0$ are diminished by $h$, if the transformed equation does not contai 14. The number of integers greater than 6000 that can be formed by using the digits $0,5,6,7,8$ and 9 without repetition is 15. The number of distinct quadratic equations $a x^2+b x+c=0$ with unequal real roots that can be formed by choosing the co 16. The number of ways of dividing 15 persons into 3 groups containing 3,5 and 7 persons so that two particular persons are 17. The coefficient of $x^{10}$ in the expansion of $\left(x+\frac{2}{x}-5\right)^{12}$ is 18. Let $S_1=\sum\limits_{j=1}^{10} j(j-1) \cdot{ }^{10} C_j, S_2=\sum\limits_{j=1}^{10} j \cdot{ }^{10} C_j$ and $$ S_3=\su 19. If $\frac{2 x^4-3 x^2+4}{\left(x^2+1\right)\left(x^2+2\right)}=a+\frac{p x+q}{x^2+1}+\frac{m x+n}{x^2+2}$, then $\frac{n 20. $$ \begin{aligned} & \left(4 \cos ^2 \frac{\pi}{20}-1\right)\left(4 \cos ^2 \frac{3 \pi}{20}-1\right) \\ & \left(4 \cos 21. If $A$ and $B$ are the values such that $(A+B)$ and $(A-B)$ are not odd multiples of $\frac{\pi}{2}$ and $2 \tan (A+B)=3 22. If $\cos ^3 80^{\circ}+\cos ^3 40^{\circ}-\cos ^3 20^{\circ}=k$, then $\frac{4 k}{3}=$ 23. The number of solutions of the equation $4 \cos 2 \theta \cos 3 \theta=\sec \theta$ in the interval $[0,2 \pi]$ is 24. $$ \tan \left(2 \tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{7}\right)\right)= $$ 25. $$ \tanh ^{-1}\left(\frac{1}{3}\right)+\operatorname{coth}^{-1}(3)= $$ 26. In a $\triangle A B C$, if $A=30^{\circ}$ and $\frac{b}{(\sqrt{3}+1)^2+2(\sqrt{2}-1)} =\frac{c}{(\sqrt{3}+1)^2-2(\sqrt{2 27. In $\triangle A B C$ is the line joining the circumcentre and the incentre is parallel to $B C$, then $\cos B+\cos C=$ 28. In a $\triangle A B C$, if $r_1: r_2=3: 4$ and $r_2: r_3=2: 3$, then $a:$$b:$$c$= 29. Let $(x, y) \in R \times R$ and $\mathbf{a}=x \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}, \mathbf{b}=6 \hat{\m 30. Line $L_1$ passes through the point $\hat{\mathbf{i}}+\hat{\mathbf{j}}$ and $\hat{\mathbf{k}}-\hat{\mathbf{i}}$. Line $ 31. $\mathbf{a} \cdot \mathbf{b}$ and $\mathbf{c}$ are the position vectors of three non-collinear points on a plane. If $$ 32. If $P=(\mathbf{a} \times \hat{\mathbf{i}})^2+(\mathbf{a} \times \hat{\mathbf{j}})^2+(\mathbf{a} \times \hat{\mathbf{k}}) 33. $\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{ 34. The mean deviation from the median for the following data is $$ \begin{array}{llllll} \hline x_1 & 9 & 3 & 7 & 2 & 5 \\ 35. A company representative is distributing 5 identical samples of a product among 12 houses in a row such that each house 36. $A$ and $B$ are two independent events of a random experiment and $P(A)>P(B)$. If the probability that both $A$ and $B 37. Two dice are thrown and the sum of the numbers appeared on the dice is noted. If $A$ is the event of getting a prime num 38. A family consists of 8 persons. If 4 persons are chosen a random and they are found to be 2 men and 2 women, then the pr 39. The number of trials conducted in a binomial distribution is 6 . If the difference between the mean and variance of this 40. Let $X \sim B(n, p)$ with mean $\mu$ and variance $\sigma^2$. If $\mu=2 \sigma^2$ and $\mu+\sigma^2=3$, then $P(X \leq 3 41. If $A(\cos \alpha, \sin \alpha), B(\sin \alpha,-\cos \alpha), C(1,2)$ are the vertices of a $\triangle A B C$, then the 42. If the axes are translated to the orthocentre of the triangle formed by the points $\mathrm{A}(7,5), \mathrm{B}(-5,-7)$ 43. The angle made by a line $L$ with positive $X$-axis measured in the positive direction is $\frac{\pi}{6}$ and the interc 44. $L_1$ and $L_2$ are two lines having slopes 2 and $-\frac{1}{2}$ respectively. If both $L_1$ and $L_2$ are concurrent wi 45. The lines $L_1: y-x=0$ and $L_2: 2 x+y=0$ intersect the line $L_3: y+2=0$ at $P$ and $Q$ respectively. The bisector of t 46. If $2 x^2+3 x y-2 y^2-5 x+2 f y-3=0$ represents a pair of straight lines, then one of the possible values of $f$ is 47. A circle passing through origin cuts the coordinate axes is $A$ and $B$. If the straight line $A B$ passes through a fix 48. If $(\alpha, \beta)$ is the external centre of similitude of the circles $x^2+y^2=3$ and $x^2+y^2-2 x+4 y+4=0$, then $\f 49. The equation of the circle touching the lines $|x-2|+|y-3|=4$ is 50. If the chord joining the points $(1,2)$ and $(2,-1)$ on a circle subtends an angle of $\frac{\pi}{4}$ at any point on it 51. The equation of the circle which cuts all the three circles $4(x-1)^2+4(y-1)^2=1,4(x+1)^2+4(y-1)^2$ and $4(x+1)^2+4(y+1) 52. If the normal chord drawn at the point $\left(\frac{15}{2}, \frac{15}{\sqrt{2}}\right)$ to the parabola $y^2=15 x$ subte 53. If a tangent having slope $\frac{1}{3}$ to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b)$ is a normal to the circl 54. Let $P(a \sec \theta, b \tan \theta)$ and $Q(a \sec \phi, b \tan \phi)$, where $\theta+\phi=\frac{\pi}{2}$ be two points 55. If the angle between the asymptotes of a hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is $2 \tan ^{-1}\left(\frac{2}{3} 56. The point in the $X Y$ - plane which is equidistant from the points $A(2,0,3), B(0,3,2)$ and $C(0,0,1)$ has the coordina 57. If the direction ratio of two lines $L_1$ and $L_2$ are given by $(1,-2,2)$ and $(-2,3,-6)$ respectively, then the direc 58. If the image of the point $A(1,1,1)$ with respect to the plane $4 x+2 y+4 z+1=0$ is $B(\alpha, \beta, \gamma)$, then $\a 59. $$ \mathop {\lim }\limits_{x \to 0} \frac{x+2 \sin x+3 \tan x-\tan ^3 x}{\sqrt{x^2+2 \sin x+\tan x+3}-\sqrt{\sin ^2 x-2 60. $$ \mathop {\lim }\limits_{x \to \infty } \frac{(3-x)^{25}(6+x)^{35}}{(12+x)^{38}(9-x)^{22}}= $$ 61. If a real valued function $$ f(x)=\left\{\begin{array}{cc} \log (1+[x]), & x \geq 0 \\ \sin ^{-1}[x], & -1 \leq x is con 62. If $y=\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)$ and $\left(\frac{d^2 y}{d x^2}\right)_{x=2}=k$, then $25 k=$ 63. If $f(x)=x^{\sec ^{-1} x}$, then $f^{\prime}(2)=$ 64. If $f(x)=\sec ^{-1}\left(\frac{1}{2 x^2-1}\right)$ and $g(x)=\tan ^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right)$, then the 65. If the tangent of the curve $x y+a x+b y=0$ at $(1,1)$ makes an angle $\tan ^{-1} 2$ with $X$-axis, then $\frac{a b}{a+b 66. If the displacement $S$ of a particle travelling along a straight line in $t$ seconds is given by $S=2 t^3+2 t^2-2 t-3$, 67. If the function $f(x)=x^3+b x^2+c x-6$ satisfies all the conditions of Rolle's theorem in $[1,3]$ and $f^{\prime}\left(\ 68. If $P(\alpha, \beta)$ is a point on the curve $9 x^2+4 y^2=144$ in the first quadrant and the minimum area of the triang 69. $$ \int(\log 2 x)^3 d x= $$ 70. $$ \int \frac{x+1}{(x-2) \sqrt{1-x}} d x= $$ 71. $$ \int \frac{1}{1+x+x^2} d x= $$ 72. If $\int \frac{d x}{(x \tan x+1)^2}=f(x)+C$, then $\lim\limits_{x \rightarrow \frac{\pi}{2}} f(x)=$ 73. $$ \int \sin ^3 x \cos ^2 x d x= $$ 74. $$\mathop {\lim }\limits_{n \to \infty } \frac{\pi}{2 n}\left[\sin \frac{\pi}{2 n}+\sin \frac{2 \pi}{2 n}+\sin \frac{3 \ 75. $$ \int_0^\pi\left(\sin ^5 x \cos ^3 x+\sin ^4 x \cos ^4 x+\sin ^3 x \cos ^4 x\right) d x= $$ 76. $$ \int_0^1 \frac{x^4+1}{x^6+1} d x= $$ 77. The area of the region (in sq units) bounded by the curves $x^2+y^2=16$ and $y^2=6 x$ is 78. If $a$ and $b$ are arbitrary constants, then the differential equation corresponding to the family of curves $y=\tan (a 79. The general solution of the differential equation $x y(y+2) d y+\left(y^3-1\right) d x=0$ is 80. The general solution of the differential equation $\left(1+\sin ^2 x\right) \frac{d y}{d x}+y \sin 2 x=\cos x+\sin ^2 x

Physics

1. If force $=\frac{\alpha}{\operatorname{density}+\beta^3}$, then the dimensional formulae of $\alpha$ and $\beta$ are res 2. The displacement $(x)$ and time $(t)$ graph of a particle moving along a straight line is shown in the figure. The avera 3. If the horizontal range of a body projected with a velocity ' $u$ ' is 3 times the maximum height reached by it, then th 4. If the velocity at the maximum height of a projectile projected at an angle of $45^{\circ}$ is $20 \mathrm{~ms}^{-1}$, t 5. A body of mass ' $m$ ' moving along a straight line collides with a stationary body of mass ' $2 m^{\prime}$. After coll 6. If a body of mass 2 kg moving with initial velocity of $4 \mathrm{~ms}^{-1}$ is subjected to a force of 3 N for a time o 7. If a constant force of $(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}) \mathrm{N}$ acting on a body of mass 8. A motor can pump 7560 kg of water per hour from a well of depth 100 m . If the efficiency of the pump is $70 \%$, then p 9. A circular dise of diameter 0.8 m and mass 4 kg is rolling on a smooth horizontal plane. If 2.56 N m torque is acting on 10. A solid sphere and a solid cylinder have same mass and same radius. The ratio of the moment of inertia of the solid sphe 11. A particle is executing simple harmonic motion with amplitude $A$. The ratio of the kinetic energies of the particle whe 12. If the potential energy of a particle of mass 0.1 kg moving along $X$-axis is $5 x(x-4) \mathrm{J}$, then the speed of t 13. The potential energy of a satellite of mass ' $m$ ' revolving around the Earth at a height of $R_e$ from the surface of 14. The elastic potential energy stored in a copper rod of length one metre and area of cross-section $1 \mathrm{~mm}^2$ whe 15. When the temperature increases, the viscosity of 16. If a body cools from a temperature of $62^{\circ} \mathrm{C}$ to $50^{\circ} \mathrm{C}$ in 10 minutes and to $42^{\circ 17. If the ratio of universal gas constant and specific heat capacity at constant volume of a gas is given by 0.67 , then th 18. The internal energy of 4 moles of a monoatomic gas at a temperature of $77^{\circ} \mathrm{C}$ is ( $R=$ Universal gas c 19. If 5.6 litres of a monoatomic gas at STP is adiabatically compressed to 0.7 litres, then the work done on the gas is nea 20. If the rms speed of the molecules of a diatomic gas at a temperature of 322 K is $2000 \mathrm{~ms}^{-1}$, then the gas 21. The equation of a transverse wave propagating along a stretched string of length 80 cm is $y=1.5 \sin \left\{\left(5 \ti 22. When an object is placed infront of a convex mirror at a distance ' $u$ ' from the pole of the mirror such that the size 23. A narrow slit of width 2 mm is illuminated with a monochromatic light of wavelength 500 nm . If the distance between the 24. The force between two conducting spheres of same radius having charges $+8 \mu \mathrm{C}$ and $-4 \mu \mathrm{C}$ separ 25. In space the electric potential varies as $V=20|\mathbf{r}|$ volt. where $\mathbf{r}=x \hat{\mathbf{i}}+y \hat{\mathbf{j 26. A capacitor of capacitance $2 \mu \mathrm{~F}$ is charged with the help of a 60 V battery. After disconnecting the batte 27. The readings of the voltmeter and ammeter in the circuit shown in the diagram are respectively 28. When two identical batteries of internal resistance $1 \Omega$ each are connected in series across a resistor $R$, the r 29. The magnetic field at the centre of a long solenoid having 400 turns per unit length and carrying a current ' $i$ ' is $ 30. If a proton of kinetic energy 8.35 MeV enters a uniform magnetic field of 10 T at right angles to the direction of the f 31. A sample of a ferromagnetic iron in the shape of a cube of side $1.0 \mu \mathrm{~m}$ contains $8.7 \times 10^{28}$ atom 32. When current in a coil changes from 2 A to 5 A in time of 0.3 s , if the emf induced in the coil is 40 mv , then the sel 33. In a series LCR circuit, the voltages across the capacitor, resistor and inductor are in the ratio $2: 3: 6,$ if the vol 34. If a 10 W bulb emits electromagnetic waves uniformly in all directions, then the intensity of light at a distance 0.5 m 35. The ratio of de-Broglie wavelengths associated with thermal neutrons at temperatures $127^{\circ} \mathrm{C}$ and $352^{ 36. The ratio of the time periods of the revolution of the electrons in the second and third excited states of hydrogen atom 37. If the surface areas of two nucleii are in the ratio $9: 47$, then the ratio of their mass number is 38. $$ \text { In the given options, the diode that is forward biased is } $$ 39. In a common emitter transistor amplifier the resistance of collector is $3 \mathrm{k} \Omega$. If the current amplificat 40. The layer of the atmosphere that reflects low frequency (LF) electromagnetic waves during day time only is

AP EAPCET 2025 - 26th May Evening Shift

MCQ (Single Correct Answer)

-0

If a real valued function

$$ f(x)=\left\{\begin{array}{cc} \log (1+[x]), & x \geq 0 \\ \sin ^{-1}[x], & -1 \leq x<0 \\ k([x]+|x|), & x<-1 \end{array}\right. $$

is continuous at $x=-1$, then $k=$

$-\pi / 2$

$-\pi$

$\pi$

$\pi / 2$

AP EAPCET 2025 - 26th May Evening Shift

MCQ (Single Correct Answer)

-0

If $y=\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)$ and $\left(\frac{d^2 y}{d x^2}\right)_{x=2}=k$, then $25 k=$

$(-3)^2$

$(-2)^3$

$(-2)^5$

AP EAPCET 2025 - 26th May Evening Shift

MCQ (Single Correct Answer)

-0

If $f(x)=x^{\sec ^{-1} x}$, then $f^{\prime}(2)=$

$\frac{2^{\pi / 3}}{6}(\pi-\sqrt{3} \log 2)$

$\frac{2^{\pi / 6}}{6}(\pi+\sqrt{3} \log 2)$

$\frac{2^{\pi / 3}}{6}(\pi+\sqrt{3} \log 2)$

$\frac{2^{\pi / 6}}{6}(\pi-\sqrt{3} \log 2)$

AP EAPCET 2025 - 26th May Evening Shift

MCQ (Single Correct Answer)

-0

If $f(x)=\sec ^{-1}\left(\frac{1}{2 x^2-1}\right)$ and $g(x)=\tan ^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right)$, then the derivative of $f(x)$ with respect to $g(x)$ is

$\frac{1+x^2}{4 \sqrt{1-x^2}}$

$\frac{\left(1-x^2\right)}{4 \sqrt{1+x^2}}$

$-\frac{4\left(1-x^2\right)}{\sqrt{1+x^2}}$

$-\frac{4\left(1+x^2\right)}{\sqrt{1-x^2}}$

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