Chemistry
1. The difference between the radii of 3rd and 2nd orbit of H -atom is $x \mathrm{pm}$. The difference between the radii of 2. The de-Broglie wavelength of an electron in the third Bohr orbit of H -atom is 3. The correct order of the non-metallic character among the elements $\mathrm{B}, \mathrm{C}, \mathrm{N}, \mathrm{F}$ and 4. How many of the following molecules have two lone pairs of electrons on central atom?
$\mathrm{SF}_6, \mathrm{BF}_3, \ma 5. The pair of molecules / ions with the same bond order value is 6. At what temperature (in K ) the rms velocity of $\mathrm{SO}_2$ molecules is equal to rms velocity of $\mathrm{O}_2$ mol 7. For one mole of an ideal gas an isochore is obtained. The slope of the isochore is $0.082 \mathrm{~atm} \mathrm{~K}^{-1} 8. Consider the following
(A) 0.0025
(B) 500.0
(C) 2.0034
Number of significant figures in $A, B$ and $C$ respectively, are 9. Consider the following reaction
$$ A(g)+3 B(g) \longrightarrow 2 C(g) ; \Delta H^{\ominus}=-24 \mathrm{~kJ} $$
At $25^{\ 10. One mole of $\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}(l)$ was completely burnt in oxygen to form $\mathrm{CO}_2(g)$ and $\m 11. At $25^{\circ} \mathrm{C}, K_a$ of formic acid is $1.8 \times 10^{-4}$. What is the $K_b$ of $\mathrm{HCOO}^{-}$? 12. At $T(\mathrm{~K})$, the following gaseous equilibrium is established.
$$ W+X \rightleftharpoons Y+Z $$
The initial conc 13. 4 mL of ' $X$ volume' $\mathrm{H}_2 \mathrm{O}_2$ on heating gives 80 mL of oxygen at STP. The value of $X$ is 14. Compound ' $X$ ' is prepared commercially by the electrolysis of brine solution.
Which of the following is not the use o 15. Consider the following.
Statement I : $ \mathrm{Al}_2 \mathrm{O}_3$ is amphoteric in nature.
Statement II : Tl2 $\mathrm 16. Identify the incorrect order against the stated property.
17. Among the following compounds, which one is not responsible for the depletion of ozone layer? 18. Which method is used to purify liquids having very high boiling points and liquids which decompose at or below their boi 19. What are $X, Y, Z$ in the following reaction sequence?
But-2-ene $\xrightarrow{X}$ Ethanoic acid $\xrightarrow{Y}$ Etha 20. An element (atomic weight $=250 \mathrm{u}$ ) crystallises in a simple cubic lattice. If the density of the unit cell is 21. 1.95 g of non-volatile and non-electrolyte solute dissolved in 100 g of benzene lowered the freezing point of it by 0.64 22. At $298 \mathrm{~K}, 0.714$ moles of liquid $A$ is dissolved in 5.555 moles of liquid $B$. The vapour pressure of the re 23. The resistance of a conductivity cell filled with 0.1 M KCl solution is $100 \Omega$. If the resistance of the same cell 24. In a first order reaction, the concentration of the reactant is reduced to $1 / 8$ of the initial concentration in 75 mi 25. In a colloidal solution, both the dispersed phase and dispersion medium are in liquid phase. What is the type of colloid 26. The equation which represents Freundlich adsorption isotherm is ( $x=$ amount of gas, $m=$ mass of solid) 27. Which of the following is used as froth stabilizer in froth floatation process? 28. White phosphorus on heating with concentrated NaOH solution in an inert atmosphere of $\mathrm{CO}_2$ gives a salt ' $X$ 29. For which of the following the $E^{\ominus}\left(M^{3+} / M^{2+}\right)$ is negative? 30. In $\mathrm{Fe}_x\left[\mathrm{Fe}_y(\mathrm{CN})_6\right]_3, x, y$ respectively, are 31. The correct statement regarding $X$ and $Y$ in the following set of reactions is 32. Consider the following.
Statement I : Lactose is composed of $\alpha$ - $D$-glucose and $\beta$-D-glucose.
Statement II 33. $$ \text { Match the following. } $$
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border- 34. $$ \text { The synthetic detergents of the following are } $$
B. $\mathrm{CH}_3\left(\mathrm{CH}_2\right)_{10} \mathrm{C 35. $$ \text { In the given reaction sequence conversion of } Y \text { to } Z \text { is } $$ 36. The preferred reagent for the preparation of pure alkyl chloride from alcohol is 37. What are $X$ and $Y$ respectively in the following set of reactions? 38. $$ \text { Match the following } $$
The correct answer is 39. Consider the reaction sequence
$$ \text { Dimethyl ketone } \xrightarrow[\text { (ii) } \mathrm{H}_2 \mathrm{O}]{\text { 40. What are $X$ and $Y$ respectively in the following reaction sequence?
$$ \mathrm{C}_6 \mathrm{H}_5 \mathrm{~N}_2^{+} X^{
Mathematics
1. The set of all real values of $x$ for which $f(x)=\sqrt{\frac{|x|-2}{|x|-3}}$ is a well defined function is 2. $f(x)$ is a quadratic polynomial satisfying the condition $f(x)+f\left(\frac{1}{x}\right)=f(x) f\left(\frac{1}{x}\right) 3. $$ \sum\limits_{k=1}^n k(k+1)(k+2) \ldots(k+r-1)= $$ 4. If $A=\left[\begin{array}{lll}1 & 2 & 3 \\ 1 & 3 & 5 \\ 2 & 1 & 6\end{array}\right]$ and $|\operatorname{adj}(\operatorn 5. If the values $x=\alpha, y=\beta, z=\gamma$ satisfy all the 3 equations $x+2 y+3 z=4,3 x+y+z=3$ and $x+3 y+3 z=2$, then 6. The number of solutions of the system of equations $2 x+y-z=7, x-3 y+2 z=1, x+4 y-3 z=5$ is 7. The points in the argand plane represented by the complex numbers $4 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k} 8. If $z=x+i y$ and $x^2+y^2=1$, then $\frac{1+x+i y}{1+x-i y}=$ 9. If $x^6=(\sqrt{3}-i)^5$, then the product of all of its roots is 10. If $\alpha \neq 0$ and zero are the roots of the equation $x^2-5 k x+\left(6 k^2-2 k\right)=0$, then $\alpha=$ 11. The set of all real values of $x$ satisfying the inequation $\frac{8 x^2-14 x-9}{3 x^2-7 x-6}>2$ is 12. When the roots of $x^3+\alpha x^2+\beta x+6=0$ are increased by 1 , if one of the resultant values is the least root of 13. Let ' $a$ ' be a non-zero real number. If the equation whose roots are the squares of the roots of the cubic equation $x 14. If ${ }^{27} P_{r+7}=7722{ }^{25} P_{(r+4)}$, then $r=$ 15. If the number of diagonals of a regular polygon is 35 , then the number of sides of the polygon is 16. If four letters are chosen from the letters of the word ASSIGNMENT and are arranged in all possible ways to form 4 lette 17. The terms containing $x^r y^s$ (for certain $r$ and $s$ ) are present in both the expansions of $\left(x+y^2\right)^{13} 18. The coefficient of $x^3$ in the power series expansion of $\frac{1+4 x-3 x^2}{(1+3 x)^3}$ is 19. If $\frac{a x+5}{\left(x^2+b\right)(x+3)}=\frac{x+21}{12\left(x^2+b\right)}+\frac{c}{12(x+3)}$, then $b^2=$ 20. If $\alpha, \beta$ are the acute angles such that $\frac{\sin \alpha}{\sin \beta}=\frac{6}{5}$ and $\frac{\cos \alpha}{\ 21. If $2 \sin x-\cos 2 x=1$, then $\left(3-2 \sin ^2 x\right)=$
22. If $\left(\frac{\sin 3 \theta}{\sin \theta}\right)^2-\left(\frac{\cos 3 \theta}{\cos \theta}\right)^2=a \cos b \theta$, 23. If $x \neq(2 n+1) \frac{\pi}{4}$, then the general solutions of $\cos x+\cos 3 x=\sin x+\sin 3 x$ is 24. If $\frac{1}{2} \sin ^{-1}\left(\frac{3 \sin 2 \theta}{5+4 \cos 2 \theta}\right)=\tan ^{-1} x$, then $x=$ 25. If $\operatorname{sech}^{-1} x=\log 2$ and $\operatorname{cosech}^{-1} y=-\log 3$, then $(x+y)=$ 26. If the sides $a, b, c$ of the $\triangle A B C$ are in harmonic progression, then $\operatorname{cosec}^2 A / 2, \operat 27. In $\triangle A B C$, if $r=3$ and $R=5$, then $\frac{1}{a b}+\frac{1}{b c}+\frac{1}{c a}=$ 28. An aeroplane is flying at a constant speed, parallel to the horizontal ground at a height of 5 kms . A person on the gro 29. If the vector $\hat{\mathbf{i}}-7 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ is along the internal bisector of the angle betwe 30. If $\mathbf{a}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+6 \hat{\mathbf{k}} ; \mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+\ha 31. Let $\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and $\mathbf{b}=\hat{\mathbf{i}}+\hat{\mathbf{j} 32. For a positive real number $p$, if the perpendicular distance from a point $-\hat{\mathbf{i}}+p \hat{\mathbf{j}}-3 \hat{ 33. $$ (\mathbf{a}+2 \mathbf{b}-\mathbf{c}) \cdot(\mathbf{a}-\mathbf{b}) \times(\mathbf{a}-\mathbf{b}-\mathbf{c})= $$ 34. Variance of the following discrete frequency distribution is
$$ \begin{array}{llllll} \hline \text { Class Interval } & 35. An unbiased coin is tossed 8 times. The probability that head appears consecutively at least 5 times is 36. A box contains twelve balls of which 4 are red, 5 are green and 3 are white. If three balls are drawn at random simultan 37. There are three families $F_1, F_2, F_3 . F_1$ has 2 boys and 1 girl; $F_2$ has 1 boy and 2 girls; $F_3$ has 1 boy and 1 38. An urn $A$ contains 4 white and 1 black ball; urn $B$ contains 3 white and 2 black balls and urn $C$ contains 2 white an 39. If the probability distribution of a discrete random variable $X$ is given by
$P(X=k)=\frac{2^{-k}(3 k+1)}{2^c}, k=0,1,2 40. In a binomial distribution, if $n=4$ and $P(X=0)=\frac{16}{81}$, then $P(X=4)=$ 41. If $A(1,0), B(0,-2)$ and $C(2,-1)$ are three fixed points, then the equation of the locus of a point $P$ such that area 42. The transformed equation of $3 x^2-4 x y=r^2$ when the coordinate axes are rotated about the origin through an angle of 43. A line $L_1$ passing through the point of intersection of the lines $x-2 y+3=0$ and $2 x-y=0$ is parallel to the line $L 44. If the lines $x+y-2=0,3 x-4 y+1=0$ and $5 x+k y-7=0$ are concurrent at $(\alpha, \beta)$, then equation of the line conc 45. If two sides of a triangle are represented by $3 x^2-5 x y+2 y^2=0$ and its orthocentre is $(2,1)$, then the equation of 46. If $a x^2+2 h x y-2 a y^2+3 x+15 y-9=0$ represents a pair of lines intersecting at $(1,1)$, then $a h=$ 47. A circle passing through the point $(1,0)$ makes an intercept of length 4 units on $X$-axis and an intercept of length $ 48. If $\left(\frac{1}{10}, \frac{-1}{5}\right)$ is the inverse point of a point $(-1,2)$ with respect to the circle $x^2+y^ 49. If the equation of the circle lying in the first quadrant, touching both the coordinate axes and the line $\frac{x}{3}+\ 50. If the point of contact of the circles $x^2+y^2-6 x-4 y+9=0$ and $x^2+y^2+2 x+2 y-7=0$ is $(\alpha, \beta)$, then $7 \be 51. If the circles $x^2+y^2-2 \lambda x-2 y-7=0$ and $3\left(x^2+y^2\right)-8 x+29 y=0$ are orthogonal, then $\lambda=$ 52. If the perpendicular distance from the focus of a parabola $y^2=4 a x$ to its directrix is $\frac{3}{2}$, then the equat 53. Let $A_1$ be the area of the given ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
Let $A_2$ be the area of the region bound 54. If the equation of the tangent of the hyperbola $5 x^2-9 y^2-20 x-18 y-34=0$ which makes an angle $45^{\circ}$ with the 55. If the distance between the foci of a hyperbola $H$ is 26 and distance between its directrices is $\frac{50}{13}$, then 56. If $Q(\alpha, \beta, \gamma)$ is the harmonic conjugate of the point $P(0,-7,1)$ with respect to the line segment joinin 57. On a line with direction cosines $l, m, n, A\left(x_1, y_1, z_1\right)$ is a fixed point. If $B=\left(x_1+4 k l, y_1+4 k 58. If the line of intersection of the planes $2 x+3 y+z=1$ and $x+3 y+2 z=2$ makes an angle $\alpha$ with the positive $X$- 59. $[x]$ denotes the greater integer less than or equal to $x$. If $\{x\}=x-[x]$ and $\lim\limits_{x \rightarrow 0}-\frac{\ 60. $$ \mathop {\lim }\limits_{n \to \infty } \frac{1}{n^3} \sum\limits_{k=1}^n k^2 x= $$ 61. Let $f: R \rightarrow R$ be defined by
$$ f(x)=\left\{\begin{array}{cc} a-\frac{\sin [x-1]}{x-1}, & \text { if } x>1 \\ 62. If $g$ is the inverse of the function $f(x)$ and $g(x)=x+\tan x$, then $f^{\prime}(x)=$ 63. If $\sqrt{x-x y}+\sqrt{y-x y}=1$, then $\frac{d y}{d x}=$ 64. If $y=\tan ^{-1}\left(\frac{x}{1+2 x^2}\right)+\tan ^{-1}\left(\frac{x}{1+6 x^2}\right)$, then $\frac{d y}{d x}=$ 65. If the tangent drawn at the point $\left(x_1, y_1\right), x_1, y_1 \in N$ on the curve $y=x^4-2 x^3+x^2+5 x$ passes thro 66. Which one of the following functions is monotonically increasing in its domain? 67. If $\beta$ is an angle between the normals drawn to the curve $x^2+3 y^2=9$ at the points $(3 \cos \theta, \sqrt{3} \sin 68. If the area of a right-angle triangle with hypotenuse 5 is maximum, then its perimeter is 69. $$ \int\left(\sum_{r=0}^{\infty} \frac{x^r 2^r}{r!}\right) d x= $$ 70. $$ \int \frac{d x}{12 \cos x+5 \sin x}= $$ 71. If $\int \frac{\cos ^3 x}{\sin ^2 x+\sin ^4 x} d x=c-\operatorname{cosec} x-f(x)$, then $f\left(\frac{\pi}{2}\right)=$ 72. $$ \int \frac{13 \cos 2 x-9 \sin 2 x}{3 \cos 2 x-4 \sin 2 x} d x= $$ 73. $$ \int \sqrt{x^2+x+1} d x $$ 74. If $k \in N$, then $\lim\limits_{n \rightarrow \infty}\left[\frac{1}{n+1}+\frac{1}{n+2}+\frac{1}{n+3}+\ldots .+\frac{1}{ 75. $$ \int_{-1}^4 \sqrt{\frac{4-x}{x+1}} d x= $$ 76. $$ \int_0^{\pi / 4} \frac{\cos ^2 x}{\cos ^2 x+4 \sin ^2 x} d x= $$ 77. $$ \int_{5 \pi}^{25 \pi}|\sin 2 x+\cos 2 x| d x= $$ 78. The differential equation of the family of circles passing through the origin and having centre on $X$-axis is 79. The general solution of the differential equation $\frac{d y}{d x}=\frac{x+y}{x-y}$ is 80. The general solution of the differential equation $\frac{d y}{d x}+\frac{\sec x}{\cos x+\sin x} y=\frac{\cos x}{1+\tan x
Physics
1. The number of significant figures in the simplification of $\frac{0.501}{0.05}(0.312-0.03)$ is 2. If the displacement ' $x$ ' of a body in motion in terms of time ' $t$ ' is given by $x=A \sin (\omega t+\theta)$, then 3. If the magnitude of a vector $\mathbf{P}$ is 25 units and its $y$-component is 7 units, then its $x$-component is 4. The height of ceiling in an auditorium is 30 m . A ball is thrown with a speed of $30 \mathrm{~ms}^{-1}$ from the entran 5. A balloon with mass ' $m$ ' is descending vertically with an acceleration ' $a$ ' (where $a 6. A conveyor belt is moving horizontally with a velocity of $2 \mathrm{~ms}^{-1}$. If a body of mass 10 kg is kept on it, 7. Two bodies $A$ and $B$ of masses 20 kg and 5 kg respectively are at rest. Due to the action of a force of 40 N separatel 8. A crane of efficiency $80 \%$ is used to lift 8000 kg of coal from a mine of depth 108 m . If the time taken by the cran 9. Three blocks $A, B$ and $C$ are arranged as shown in the figure such that the distance between two successive blocks is 10. A solid sphere of mass 4 kg and radius 28 cm is on an inclined plane. If the acceleration of the sphere when it rolls do 11. If the maximum velocity and maximum acceleration of a particle executing simple harmonic motion are respectively $5 \mat 12. A body of mass 1 kg is suspended from a spring of force constant $600 \mathrm{Nm}^{-1}$. Another body of mass 0.5 kg mov 13. Two satellites $A$ and $B$ are revolving around the Earth in orbits of heights $1.25 R_E$ and $19.25 R_E$ from the surfa 14. When a wire made of material with Young's modulus $\gamma$ is subjected to a stress $S$, the elastic potential energy pe 15. An aeroplane of mass $4.5 \times 10^4 \mathrm{~kg}$ and total wing area of $600 \mathrm{~m}^2$ is travelling at a consta 16. If the wavelengths of maximum intensity of radiation emitted by two black bodies $A$ and $B$ are $0.5 \mu \mathrm{~m}$ a 17. Water of mass 5 kg in a closed vessel is at a temperature of $20^{\circ} \mathrm{C}$. If the temperature of the water wh 18. A Carnot engine $A$ working between temperatures 600 K and $T(400 \mathrm{~K})$ and 400 K are connected in series. If th 19. When an ideal diatomic gas is heated at constant pressure, the fraction of the heat utilised to increase the internal en 20. If the degrees of freedom of a gas molecule is 6 , then the total internal energy of the gas molecule at a temperature o 21. When a stretched wire of fundamental frequency $f$ is divided into three segments, the fundamental frequencies of these 22. Images of same size are formed by a convex lens when an object is placed either at 20 cm or 10 cm distance from the lens 23. In Young's double slit experiment, the wavelength of monochromatic light is increased by $20 \%$ and the distance betwee 24. Two charged conducting spheres of radii 5 cm and 10 cm have equal surface charge densities. If the electric field on the 25. As shown in the figure, if the values of the electric potential at three points $A, B$ and $C$ in a uniform electric fie 26. As shown in the figure, the work done to move the charge ' $Q$ ' from point $C$ to point $D$ along the semicircle CRD is 27. The length and area of cross-section of a copper wire are respectively 30 m and $6 \times 10^{-7} \mathrm{~m}^2$. If the 28. If current of 80 A is passing through a straight conductor of length 10 m , then the total momentum of electrons in the 29. In a wire of radius 1 mm a steady current of 2 A uniformly distributed across the cross-section of the wire is flowing. 30. The magnetic field at the centre of a current carrying circular coil of radius $R$ is $B_c$ and the magnetic field at a 31. A short bar magnet of magnetic moment $10^4 \mathrm{JT}^{-1}$ is free to rotate in a horizontal plane. The work done in 32. A metallic disc of radius 0.3 m is rotating with a constant angular speed of $60 \mathrm{rad} \mathrm{s}^{-1}$ in a plan 33. A resistor of $450 \Omega$ and an inductor are connected in series to an AC source of frequency $\frac{75}{\pi} \mathrm{ 34. If the rms value of the electric field of electromagnetic waves at a distance of 3 m from a point source is $3 \mathrm{N 35. If the threshold wavelength of light for photoelectric emission to take place from a metal surface is $6250 \mathop {\rm 36. The ratio of the wavelengths of the first Lyman line and the second Balmer line of hydrogen atom is 37. Each nuclear fission of ${ }^{235} \mathrm{U}$ releases 200 MeV of energy. If a reactor generates 1 MW power, then the r 38. When three NAND logic gates are connected as shown in the figure, then the logic gate equivalent to the circuit is 39. The device used for voltage regulation is 40. For transmitting a signal of frequency 1000 kHz , the minimum length of the antenna is
1
AP EAPCET 2025 - 22nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $\int \frac{\cos ^3 x}{\sin ^2 x+\sin ^4 x} d x=c-\operatorname{cosec} x-f(x)$, then $f\left(\frac{\pi}{2}\right)=$
A
1
B
0
C
$\pi / 2$
D
$\pi$
2
AP EAPCET 2025 - 22nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$$ \int \frac{13 \cos 2 x-9 \sin 2 x}{3 \cos 2 x-4 \sin 2 x} d x= $$
A
$3 x-\frac{1}{2} \log |3 \cos 2 x-4 \sin 2 x|+C$
B
$\frac{x}{2}-3 \log |3 \cos 2 x-4 \sin 2 x|+C$
C
$3 x+\frac{1}{2} \log |3 \cos 2 x-4 \sin 2 x|+C$
D
$x+\frac{3}{2} \log |3 \cos 2 x-4 \sin 2 x|+C$
3
AP EAPCET 2025 - 22nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$$ \int \sqrt{x^2+x+1} d x $$
A
$\frac{(2 x+1)}{4} \sqrt{x^2+x+1}+\frac{3}{8} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+C$
B
$\frac{x+1}{4} \sqrt{x^2+x+1}+\frac{3}{8} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+C$
C
$\frac{x+1}{4} \sqrt{x^2+x+1}-\frac{3}{8} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+C$
D
$\frac{(2 x+1)}{4} \sqrt{x^2+x+1}-\frac{3}{8} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+C$
4
AP EAPCET 2025 - 22nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $k \in N$, then $\lim\limits_{n \rightarrow \infty}\left[\frac{1}{n+1}+\frac{1}{n+2}+\frac{1}{n+3}+\ldots .+\frac{1}{k n}\right]=$
A
$\log (k+1)$
B
$\log k$
C
$\log (k+5)$
D
$\log (k+1)-\log 6$
Paper Analysis
Total Questions
Chemistry 40
Mathematics 80
Physics 40
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