AP EAPCET 2025 - 21st May Evening Shift | AP EAPCET Year Wise Previous Years Questions

Chemistry

1. The uncertainty in the position of electron $(\Delta x)$ is approximately 100 pm . The uncertainty in momentum (in $\mat 2. Which of the following statements are correct? I. The energy of hydrogen atom in its ground state is -13.6 eV . II. On t 3. Which of the following orders is not correct about the property shown against it? 4. Consider the following changes I and II $$ \mathrm{O}_2^{-} \underset{\text { II }}{\longleftarrow} \mathrm{O}_2 \xright 5. The increasing order of number of lone pair of electrons on the central atom of the following molecules is (I) $\mathrm{ 6. $$ \text { Which of the following is correct for an ideal gas? } $$ 7. At 256 K , rms speed of $\mathrm{SO}_2$ gas molecules is $3.16 \times 10^2 \mathrm{~ms}^{-1}$. What is the most probable 8. 209 g of an element reacts with chlorine to form 315.5 g of its chloride. What is the weight (in g ) of oxygen that reac 9. Consider the following : Statement I : During isothermal expansion of an ideal gas its enthalpy decreases. Statement II 10. The energy required to increase the temperature of 180 g of liquid water from $10^{\circ} \mathrm{C}$ to $15^{\circ} \ma 11. At $25^{\circ} \mathrm{C}$, the percentage of ionisation of $x \mathrm{M}$ acetic acid is 4.242 . What is the pH of the 12. At 298 K , the value of $K_c$ for the following reaction is $x \mathrm{~mol} \mathrm{~L}^{-1}$. What is the approximate 13. $\mathrm{H}_2 \mathrm{O}_2$ with $\mathrm{KMnO}_4$ in acidic medium gives a manganese compound ' $X$ ' and in basic medi 14. Which of the following orders are correct against the stated property? I. $\mathrm{NaO}_2 II. $\mathrm{Mg}(\mathrm{OH})_ 15. In the structure of diborane, the number of 2-centre-2-electron bonds is $X$ and 3-centre-2-electron bonds is $Y$. The v 16. $$ \text { Match the following } $$ $$ \begin{array}{clll} \hline & \text { List-I (Compound) } & & \text { List-II (Use 17. Identify the air pollutant which in high concentration leads to stiffness of flower buds? 18. The number of primary $\left(1^{\circ}\right)$, secondary $\left(2^{\circ}\right)$ and tertiary $\left(3^{\circ}\right)$ 19. The catalyst used for the isomerisation of $n$-alkanes to branched chain alkanes is 20. An element crystallises in bcc lattice. The atomic radius of the element is $2.598 \mathop {\rm{A}}\limits^{\rm{o}}$. Wh 21. A centi molar solution of acetic acid is $50 \%$ dissociated at $27^{\circ} \mathrm{C}$. The osmotic pressure of the sol 22. At 300 K vapour pressure of a pure liquid. ' $A$ ' is 70 mm Hg . It forms an ideal solution with another liquid ' $B$ '. 23. The specific conductance of 0.05 M NaOH solution is $0.0115 \mathrm{~S} \mathrm{~cm}^{-1}$ What is its molar conductance 24. Consider the reaction given below $$ A+2 B \longrightarrow 3 C+2 D $$ If rate of disappearance of $B$ is $x \times 10^{- 25. Identify the catalytic reaction in which both reactants are in different phases. 26. Consider the following. Statement-I : Gold sol is prepared by Bredig's arc method. Statement-II : Bredig's arc method in 27. $$ \text { Which of the following sets are correctly matched? } $$ $$ \begin{array}{cll} \hline & \text { Metal } & \tex 28. The oxides of nitrogen obtained by the reaction of nitric acid with (i) $\mathrm{P}_4 \mathrm{O}_{10'}$ (ii) $\mathrm{P} 29. $$ \text { Match the following } $$ .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-s 30. The ion with $4 f^7$ configuration is 31. Which of the following is the common monomer for the polymers bakelite and melamine? 32. Activation energy for the hydrolysis of sucrose by acid is $X \mathrm{~kJ} \mathrm{~mol}^{-1}$ whereas activation energy 33. The structure of the nitrogen containing heterocyclic base given below represents 34. What is the drug used to control depression and hypertension? 35. What are $X$ and $Y$ respectively, in the following set of reactions? 36. In the following sequence of reactions, what is the end product $(D)$ ? $$ \mathrm{C}_2 \mathrm{H}_5 \mathrm{Br} \xright 37. $$ \text { The most acidic carboxylic acid is } $$ 38. A carbonyl compound $X\left(\mathrm{C}_8 \mathrm{H}_8 \mathrm{O}\right)$ gives yellow precipitate with NaOI . Hemiacetal 39. Which of the following does not involve in Friedel-Craft reaction? 40. Consider the following Statement I : $\mathrm{CH}_3 \mathrm{NH}_2$ is more basic than $\mathrm{NH}_3$ but $\mathrm{C}_6

Mathematics

1. The set of real values of $x$ such that $f(x)=\sqrt{\frac{[x]-1}{\left.[x]^2-[x]-6\right]}}$ is a real valued function i 2. If a function $f: Z \rightarrow Z$ is defined by $f(x)=x-(-1)^x$, then $f(x)$ is 3. If $2 \cdot 5+5 \cdot 9+8 \cdot 13+11 \cdot 17+\ldots$ to $n$ terms $=a n^3+b n^2+c n+d$, then $a-b+c-d=$ 4. If $A=\left[\begin{array}{ccc}1 & 2 & -2 \\ 2 & -1 & 2 \\ -1 & 1 & -2\end{array}\right]$, then $A+2 A^{-1}=$ 5. If $A=\left[\begin{array}{ccc}a & b & c \\ d & e & f \\ l & m & n\end{array}\right]$ is a matrix such that $|A|>0$ and $ 6. In solving a system of linear equations $A X=B$ by Cramer's rule, in the usual notation, if $\Delta_1=\left|\begin{array 7. If $a=\operatorname{Im}\left(\frac{1+z^2}{2 i z}\right)$ and $z$ is any non-zero complex number such that $|z|=1$, then 8. If $(3+4 i)^{2025}=5^{2023}(x+i y)$, then $\sqrt{x^2+y^2}=$ 9. If $\left(\frac{\cos \theta+i \sin \theta}{\sin \theta+i \cos \theta}\right)^{2024}+\left(\frac{1+\cos \theta+i \sin \th 10. The roots $\alpha, \beta$ of the equation $x^2-6(k-1) x+4(k-2)=0$ are equal in magnitude but opposite in sign, if $\alph 11. If $a x^2+b x+c 12. If $a \pm i b$ and $b \pm a i$ are the roots of $x^4-10 x^3+50 x^2-130 x+169=0$, then $\frac{a}{b}+\frac{b}{a}=$ 13. If $x^2-5 x+6$ is a factor of $f(x)=x^4-17 x^3+k x^2-247 x+210$, then the other quadratic factor of $f(x)$ is 14. If all the letters of the word COMBINATION are arranged in all possible ways to form 11 letter words (with or without me 15. The number of ways of distributing 3 dozen fruits (no two fruits are identical) to 9 persons such that each gets the sam 16. If $\binom{p}{q}={ }^p C_q$ and $\sum\limits_{i=0}^m\binom{10}{i}\binom{20}{m-i}$ is maximum, then $m=$ 17. Coefficient of $x^2$ in the expansion of $\left(x^2+x-2\right)^5$ is 18. If $P_n$ denotes the product of the binomial coefficients in the expansion of $(1+x)^n$, then $\frac{P_{n+1}}{P_n}=$ 19. The coefficient of $x^3$ in the expansion of $\frac{x^4+1}{\left(x^2+1\right)(x-1)}$ when it is expressed in terms of po 20. $$ \begin{aligned} \frac{1}{\sin 1^{\circ} \sin 2^{\circ}}+\frac{1}{\sin 2^{\circ} \sin 3^{\circ}}+\frac{1}{\sin 3^{\cir 21. $$ \cos ^3 \frac{\pi}{8} \cos \frac{3 \pi}{8}+\sin ^3 \frac{\pi}{8} \sin \frac{3 \pi}{8}= $$ 22. If $A+B+C=\frac{\pi}{4}$, then $\sin 4 A+\sin 4 B+\sin 4 C=$ 23. Number of solutions of the equation $\cos \theta+\cos 2 \theta-\sqrt{3}(\sin \theta+\sin 2 \theta)+1=0$ lying in the int 24. If $x$ is a real number, then the number of solutions of $\tan ^{-1}(\sqrt{x(x+1)})+\sin ^{-1}\left(\sqrt{x^2+x+1}\right 25. Domain of the real valued function $f(x)=\log \left(x^2-1\right)+x \operatorname{coth}^{-1} x$ is 26. In a $\triangle A B C$, if $\sin \frac{A}{2}=\frac{1}{4} \sqrt{\frac{3}{5}}, a=2, c=5$ and $b$ is an integer, then the a 27. In a $\triangle A B C$ if $a+c=5 b$, then $\cot \frac{A}{2} \cot \frac{C}{2}=$ 28. In a $\triangle A B C$, if $r_1=3, r_2=4, r_3=6$, then $b=$ 29. Let the position vectors of the vertices of a $\triangle A B C$ be $\mathbf{a , b}, \mathbf{c}$. If on the plane of the 30. The point of intersection of the lines represented by $\mathbf{r}=(\hat{\mathbf{i}}-6 \hat{\mathbf{j}}+2 \hat{\mathbf{k} 31. $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are three vectors such that $|\mathbf{a}|=2,|\mathbf{b}|=3$, $|\mathbf{c}|=5,|\math 32. If the points $A, B, C, D$ with positions vectors $\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, \hat{\mathbf{i}}- 33. $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are unit vectors. If $\mathbf{a}, \mathbf{b}$ are perpendicular vectors, $(\mathbf{ 34. If the variance of the first $n$ natural numbers is 10 and the variance of the first $m$ even natural numbers is 16 , th 35. Given $f(x)=x^2-5 x+4$. Out of first 20 natural numbers, if a number $x$ is chosen at random, then the probability that 36. A problem in Algebra is given to two students $A$ and $B$ whose chances of solving it are $\frac{2}{5}$ and $\frac{3}{4} 37. Three dice are thrown simultaneously and the sum of the numbers appeared on them is noted. If $A$ is the event of gettin 38. A manufacturing company of bulbs has 3 units $A, B$ and $C$ which produce $25 \%, 35 \%$ and $40 \%$ of the bulbs respec 39. The probability distribution of a random variable $X$ is given below$$ \begin{array}{ccccccc} \hline X & 1 & 2 & 3 & 4 & 40. The probability that a student gets distinction in a Mathematics test is $\frac{2}{3}$. If five such tests are conducted 41. If $P$ is a variable point which is at a distance of 2 units. from the line $2 x-3 y+1=0$ and $\sqrt{13}$ units from the 42. If the equation $3 x^2+4 y^2-x y+k=0$ is the transformed equation of $3 x^2+4 y^2-x y-5 x-7 y+2=0$ after shifting the or 43. If the intercept of a straight line $L$ made between the straight lines $5 x-y-4=0$ and $3 x+4 y-4=0$ is bisected at the 44. $A$ line $L$ passes through the point $P(1,2)$ and makes an angle of $60^{\circ}$ with $O X$ in the positive direction. 45. The equation $(2 p-3) x^2+2 p x y-y^2=0$ represents a pair of distinct lines 46. The equation of a chord $A B$ of an ellipse $2 x^2+y^2=1$ is $x-y+1=0$. If $O$ is the origin, then $\sqrt{A O B}=$ 47. If a circle $S$ passes through the origin and makes an intercept of length 4 units on the line $x=2$, then the equation 48. A circle touches the line $2 x+y-10=0$ at $(3,4)$ and passes through the point $(1,-2)$. Then, a point that lies on the 49. If $(a, b)$ is the common point for the circles $x^2+y^2-4 x+4 y-1=0$ and $x^2+y^2+2 x-4 y+1=0$, then $a^2+b^2=$ 50. The angle between the tangents drawn from the point $(2,2)$ to the circle $x^2+y^2+4 x+4 y+c=0$ is $\cos ^{-1}\left(\fra 51. If the circle $S=x^2+y^2+2 g x+4 y+1=0$ bisects the circumference of the circle $x^2+y^2-2 x-3=0$, then the radius of ci 52. The angle between the tangents drawn from the point $(1,4)$ to the parabola $y^2=4 x$ is 53. The square of the slope of a common tangent drawn to the circle $4 x^2+4 y^2=25$ and the ellipse $4 x^2+9 y^2=36$ is 54. The tangents drawn to the hyperbola $5 x^2-9 y^2=90$ through a variable point $P$ make the angles $\alpha$ and $\beta$ w 55. If $\theta$ is the acute angle between the asymptotes of a hyperbola $7 x^2-9 y^2=63$, then $\cos \theta=$ 56. If $O(0,0,0), A(1,2,1), B(2,1,3)$ and $C(-1,1,2)$ are the vertices of a tetrahedron, then the acute angle between its fa 57. If the angles between the sides of the $\triangle A B C$ formed by $A(2,3,5), B(-1,3,2)$ and $C(3,5,-2)$ are $\alpha, \b 58. If the four points $(6,2,4),(1,3,5),(1,-2,3)$ and $(6, k, 2)$ are coplanar, then $k=$ 59. $$ \mathop {\lim }\limits_{x \to - \infty } \frac{5 x^3-x^2 \sin 5 x}{x \cos 4 x+7|x|^3-4|x|+3}= $$ 60. If $\mathop {\lim }\limits_{x \to {a^ + }} f(x)=p, \mathop {\lim }\limits_{x \to {a^ - }} f(x)=m$ and $f(a)=k$, then whi 61. If a function $f$ defined by $$ f(x)=\left\{\begin{array}{cc} \frac{1-\cos 4 x}{x^2}, & x is continuous at $x=0$, then $ 62. If $y=\tanh ^{-1} \sqrt{\frac{1-x}{1+x}}$, then $\frac{d y}{d x}=$ 63. If $x^2+y^2=t-\frac{1}{t}$ and $x^4+y^4=t^2+\frac{1}{t^2}$, then $\frac{d y}{d x}=$ 64. If $y=(a x+b) \cos x$, then $$ y_2+y_1 \sin 2 x+y\left(1+\sin ^2 x\right)= $$ 65. If the normal drawn at the point $P$ on the curve $y=x \log x$ is parallel to the line $2 x-2 y=3$, then $P=$ 66. If the curves $y^2=16 x$ and $9 x^2+\alpha y^2=25$ intersect at right angles, then $\alpha=$ 67. If the function $y=\sin x(1+\cos x)$ is defined in the interval $[-\pi, \pi]$, then $y$ is strictly increasing in the in 68. If the velocity of a particle moving on a straight line is proportional to the cube root of its displacement, then its a 69. If $\int e^{\sin x}(1+\sec x \tan x) d x=e^{\sin x} f(x)+c$, then in $0 \leq x \leq 2 \pi$, then number of solutions of 70. If $\int \frac{d x}{(x-1)^{\frac{3}{2}}(x-3)^{\frac{1}{2}}}=\sqrt{f(x)}+C$, then $f(-1)-f(0)=$ 71. $$ \int \frac{x}{\left(1-x^2\right) \sqrt{2-x^2}} d x= $$ 72. $\int\left(\frac{1+x+\sqrt{x+x^2}}{\sqrt{x}+\sqrt{1+x}}\right) d x=$ 73. If $\int x^2 \cos ^2 x d x=\frac{1}{6} f(x)+g(x) \sin 2 x +h(x) \cos 2 x+c$, then $f(1)+g(2)+h\left(\frac{1}{2}\right)=$ 74. $$ \int_0^{\frac{\pi}{2}} \log |\tan x+\cot x| d x= $$ 75. $$ \int_0^\pi x \cdot \sin ^5 x \cdot \cos ^6 x d x= $$ 76. $$ \int_{\frac{1}{2}}^{\frac{1}{\sqrt{2}}} \frac{1}{\left(x+\sqrt{1-x^2}\right)\left(1-x^2\right)} d x= $$ 77. The area of the region (in sq. units) enclosed between the curves $y=|x|, y=[x]$ and the ordinates $x=-1$, $x=0, x=1$ is 78. The general solution of the differential equation $\frac{d y}{d x}+x y=4 x-2 y+8$ is 79. The general solution of the differential equation $\left(x+2 y^3\right) \frac{d y}{d x}-y=0, y>0$ is 80. The general solution of the differential equation $\frac{d y}{d x}+\frac{x+y+1}{x-3 y+5}=0$ is

Physics

1. If the maximum and minimum temperatures at a place on a day are measured as $44^{\circ} \mathrm{C} \pm 0.5^{\circ} \math 2. If a ball projected vertically upwards with certain initial velocity from the ground crosses a point at a height of 25 m 3. If a particle of mass ' $m$ ' covers half of the horizontal circle with constant speed ' $v$ ', then the change in its k 4. A car is moving with a velocity of $4 \mathrm{~ms}^{-1}$ towards east. After a time of 4 s , if it is heading north-east 5. A body of mass 5 kg starts from the origin with an initial velocity $(30 \hat{\mathbf{i}}+40 \hat{\mathbf{j}}) \mathrm{m 6. A block of mass 10 kg moving with a speed of $5 \hat{\mathrm{i}} \mathrm{ms}^{-1}$ on a frictionless horizontal surface 7. The bob of a simple pendulum of length 200 cm is released from horizontal position. If $10 \%$ of its initial energy is 8. A steel sphere of radius 1.2 cm collides a second steel sphere at rest. If the collision is elastic and after the collis 9. Ratio of angular velocity of hour hand of a watch and the angular velocity of rotation of Earth is 10. If two bodies of masses 2 kg and 3 kg are moving at right angles with velocities $20 \mathrm{~ms}^{-1}$ and $10 \mathrm{ 11. The kinetic energy of a particle executing simple harmonic motion at a displacement of 3 cm from the mean position is 4 12. A body of mass 1 kg is attached to the lower end of a vertically suspended spring of force constant $600 \mathrm{~N}-\ma 13. If the angular velocity of a planet about its axis is halved, the distance of the stationary satellite of this planet fr 14. When a wire of length ' $L$ ' clamped at one end is pulled by a force ' $F$ ' from the other end, its length increases b 15. A liquid drop of diameter $D$ splits into 3375 small identical drops. If $S$ is the surface tension of the liquid, then 16. When a sphere is taken to the bottom of a sea of depth 1 km , it contracts in volume by $0.01 \%$, then the Bulk modulus 17. If a gas of volume 400 cc at an initial pressure $p$ is suddenly compressed to 100 cc , then its final pressure is (The 18. A Carnot engine having efficiency $60 \%$ receives heat from a source at a temperature 600 K . For the same sink temper 19. A gaseous mixture consists of 2 moles of oxygen and 4 moles of argon at an absolute temperature $T$. Neglecting all vibr 20. The average translational kinetic energy of the oxygen molecules at a temperature of $127^{\circ} \mathrm{C}$ is (Boltzm 21. The speed of a stationary wave represented by the equation $$ y=0.7 \sin \left(\frac{7 \pi}{4} x\right) \cos (350 \pi t) 22. Two thin convex lenses are kept in contact coaxially. If the focal length of the combination of the lenses is 4 cm and s 23. For an observer on the Earth, if a spectral line of wavelength $6600\mathop {\rm{A}}\limits^{\rm{o}}$ emitted by a star 24. Three particles of each charge $q$ are placed at the vertices of an equilateral triangle of side $L$. The work to be don 25. The radii of the inner and outer spheres of a spherical capacitor are 8 cm and 9 cm respectively. The outer sphere is ea 26. If 27 charged water droplets, each of radius $10^{-3} \mathrm{~m}$ and charge $10^{-12} \mathrm{C}$ coalesce to form a s 27. A straight wire of resistance $18 \Omega$ is bent in the form of an equilateral triangular loop. The effective resistanc 28. The power dissipated by a uniform wire of resistance $100 \Omega$ when a potential difference of 120 V is applied across 29. If a straight current carrying wire of linear density $0.12 \mathrm{~kg} \mathrm{~m}^{-1}$ is suspended in mid air by a 30. Two concentric loops $A$ and $B$ of same radius $2 \pi \mathrm{~cm}$ are placed at right angles to each other. If the cu 31. A short bar magnet is placed in a uniform magnetic field of 2 T such that the axis of the magnet makes an angle of $45^{ 32. A horizontal telegraph wire of length 30 m spread east to west fell down freely from a height of 20 m . If the resistanc 33. In an LCR series circuit, if the potential differences across inductor, capacitor and resistor are $60 \mathrm{~V}, 30 \ 34. A plane electromagnetic wave of frequency 25 MHz propagates in vacuum along positive $x$-direction. At a particular poin 35. A particle of mass $8 \mu \mathrm{~g}$ in motion collides with another stationary particle of mass $4 \mu \mathrm{~g}$. 36. The difference between the frequencies of the first and second Lyman lines of hydrogen atom is ( $R=$ Rydberg constant a 37. If the half-life of a radioactive element is 12.5 hours, then the time taken to disintegrate 256 g of the substance into 38. A transistor works as an amplifier when 39. If five logic gates are connected as shown in the figure, then the values of $y_1, y_2$ and $y_3$, are respectively 40. In amplitude modulation of waves, the maximum amplitude is 30 mV and minimum amplitude is 5 mV , then the modulation ind

AP EAPCET 2025 - 21st May Evening Shift

MCQ (Single Correct Answer)

-0

If the velocity of a particle moving on a straight line is proportional to the cube root of its displacement, then its acceleration is

constant

inversely proportional to its velocity

proportional to its velocity

proportional to its displacement

AP EAPCET 2025 - 21st May Evening Shift

MCQ (Single Correct Answer)

-0

If $\int e^{\sin x}(1+\sec x \tan x) d x=e^{\sin x} f(x)+c$, then in $0 \leq x \leq 2 \pi$, then number of solutions of $f(x)=1$ is

AP EAPCET 2025 - 21st May Evening Shift

MCQ (Single Correct Answer)

-0

If $\int \frac{d x}{(x-1)^{\frac{3}{2}}(x-3)^{\frac{1}{2}}}=\sqrt{f(x)}+C$, then $f(-1)-f(0)=$

-3

-4

-2

-1

AP EAPCET 2025 - 21st May Evening Shift

MCQ (Single Correct Answer)

-0

$$ \int \frac{x}{\left(1-x^2\right) \sqrt{2-x^2}} d x= $$

$\log \left|\frac{\sqrt{2-x^2}+1}{\sqrt{2-x^2}-1}\right|+C$

$\frac{1}{2} \log \left|\frac{\sqrt{2-x^2}}{1-x^2}\right|+C$

$\frac{1}{2} \log \left|\frac{1+\sqrt{2-x^2}}{1-\sqrt{2-x^2}}\right|+C$

$\log \left|\frac{1-x^2}{\sqrt{2-x^2}}\right|+C$

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