Chemistry
1. The wavenumber of the first line $\left(n_2=3\right)$ in the Balmer series of hydrogen is overline $\bar{v}_1 \mathrm{~c 2. Which of the following sets of quantum numbers is not possible for the electron? 3. The correct order of atomic radii of $\mathrm{C}, \mathrm{Al}$ and S is 4. How many of the following molecules / ions have trigonal planar structure?
$$ \mathrm{BO}_3^{3-}, \mathrm{NH}_3, \mathrm 5. Consider the following
Assertion (A) Dipole moment of $\mathrm{NF}_3$ is lesser than $\mathrm{NH}_3$.
Reason (R) In $\ma 6. At $\mathrm{T}(\mathrm{K})$, a gaseous mixture contains $\mathrm{H}_2$ and $\mathrm{O}_2$. The total pressure of the mix 7. The most probable speed $\left(U_{\text {mp }}\right)$ of 8 g of $\mathrm{H}_2$ is $2 \times 10^2 \mathrm{~ms}^{-1}$. Th 8. 1.84 g of a mixture of $\mathrm{CaCO}_3$ and $\mathrm{MgCO}_3$ is strongly heated to get a residue of 0.96 g . The perce 9. Identify the correct statements from the following.
I. Work is a path function.
II. Enthalpy is an extensive property.
I 10. Which of the following processes entropy change $(\Delta S)$ is negative?
I. Sublimation of dry ice
II. Freezing of wate 11. At $25^{\circ} \mathrm{C}$, the percentage of ionisation of ' $x$ ' M acetic acid is 4.242 . What is the value of $x$ ? 12. At $T(\mathrm{~K}), K_C$ value for
$\mathrm{AO}_2(\mathrm{~g})+\mathrm{BO}_2(\mathrm{~g}) \rightleftharpoons \mathrm{AO} 13. The incorrect statement in the following is 14. Which of the following statements are correct regarding lithium and magnesium?
I. They react slowly with water.
II. Thei 15. The incorrect statement from the following is 16. In Buckminster fullerene, the number of six membered carbon rings is ' $x$ ' and five membered carbon rings is ' $y$ '. 17. $$ \text { Match the following } $$
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;borde 18. Consider the following
Statement I Kolbe's electrolysis of sodium propionate gives $n$-hexane as product.
Statement II I 19. The correct decreasing order of priority for the functional group of organic compounds in the IUPAC method of nomenclatu 20. A compound is formed by two elements $A$ and $B$. Atoms of the element $B$ (as anion) make ccp lattice and those of elem 21. The mole fractions of glucose and water in aqueous glucose solution are 0.0244 and 0.9756 respectively. What is the weig 22. At $T(\mathrm{~K})$, the vapour pressure of an aqueous solution of a non-volatile solute, whose mole fraction is 0.02 is 23. If $E_{\mathrm{Fe}^{2+} / \mathrm{Fe}}^{\circ}=-0.441 \mathrm{~V}$ and $E_{\mathrm{Fe}^{3+} / \mathrm{Fe}^{2+}}^{\circ}= 24. At $T(\mathrm{~K})$ the following equation is obtained for a first order reaction $\log \frac{k}{A}=-\frac{x}{T}$. The a 25. Which one of the following is not the correct characteristic property of physical adsorption? 26. In each of four separate beakers (I, II, III, IV), $X \mathrm{~mL}$ of $y \mathrm{M} \mathrm{Fe}_2 \mathrm{O}_3 x \mathr 27. In the extraction of iron from haematite, the impurity $(x)$ of the ore is removed in the form of ' $y$ ', what are $x$ 28. Which of the following is not correct? 29. How many of the following lanthanide elements exhibit +4 oxidation state?
Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy 30. In which of the following, complex ions are not in correct order with respect to their magnitude of crystal field splitt 31. Novolac is formed by the polymerisation of monomer ' $x$ ' in the presence of $\mathrm{OH}^{-}$ions. What is ' $x$ '? 32. Which of the following contain $\alpha$-D-glucose units?
I. Cane sugar
II. Milk sugar
III. Cellulose
IV. Amylose 33. Identify the set containing purine and pyrimidine base of DNA respectively. 34. Bithionol is added to soaps to impart antiseptic properties. The number of -OH and -Cl groups in its structure are respe 35. Which of the following is the product of Fittig reaction? 36. $$ \text { Match the following } $$
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-s 37. Which of the following represents Etard reaction? 38. The correct order of boiling points of the compounds given below is
(A) methoxy ethane
(B) propan-1-ol
(C) propanal
(D) 39. The correct statement about the product of the following reaction is
$$ \mathrm{CH}_3 \mathrm{CHO} \xrightarrow[\text { 40. How many amines with molecular formula $\mathrm{C}_3 \mathrm{H}_9 \mathrm{~N}$ can react with benzenE sulphonyl chloride
Mathematics
1. Let $f: N \rightarrow N$ be a function such that $f(x+y)=f(x)+f(y)+x y$ for every $x, y \in N$. If $f(\mathbb{l})=2$, th 2. If a real valued function $f:[-1,2] \rightarrow B$ defined by
$$ f(x)= \begin{cases}1-x, & \text { when }-1 \leq x \leq 3. For all $n \in N, \frac{3^n-1}{2} \geq$ 4. The value of $p$ and $q$ is that system of equations $2 x+p y+6 z=8, x+2 y+q z=5$ and $x+y+3 z=4$ may have no solution a 5. $A$ is the set of all matrices of order 3 with entries 0 or 1 only. $B$ is the subset of $A$ consisting of all matrices 6. Consider the matrices $A=\left[\begin{array}{ccc}x & y & 0 \\ -3 & 1 & 2 \\ 1 & -2 & z\end{array}\right]$ and $B=\left[\ 7. The minimum value of $|z-1|+|z-5|$ is
8. If $z=x+i y$ and if the point $P$ in the argand diagram represents $z$, then the locus of the point $P$ satisfying the e 9. If $z$ is a non-real root of $x^7=1$, then $1+3 z+5 z^2+7 z^3+9 z^4+11 z^5+13 z^6=$ 10. If $(2 k-1) x^2-2(3 k-2) x+4 k>0$ for every $x \in R$, then the sum of all possible integral values of $k$ is 11. The sum of the least positive integer and the greatest negative integer in the range of the function $f(x)=\frac{x^2-5 x 12. If $\alpha$ is a repeated root of multiplicity 2 of the equation $18 x^3-33 x^2+20 x-4=0$, then 13. The equation $6 x^4-5 x^3+13 x^2-5 x+6=0$ will have 14. All the letters of the word LETTER are arranged in all possible ways and the words (with or without meaning) thus formed 15. 5-digit numbers are formed by using the digits $0,1,2$, $3,5,7$ without repetetion and all of them are arranged in ascen 16. The number of divisors of 7 ! is 17. If $k$ is a positive integer and $10^k$ is a divisor of the number $9^{11}+11^9$, then the greatest value of $k$ is 18. The number of all possible values of $k$ for which the expansion $(\sqrt{x}+\sqrt[k]{y})^{10}$ will have exactly nine ir 19. If $\frac{x+1}{(x-1)^2\left(x^2+1\right)}=\frac{A}{x-1}+\frac{B}{(x-1)^2}+\frac{C x+D}{x^2+1}$, then $\sqrt{3 A^2+4 D^2+ 20. If $A+B=\frac{\pi}{4}$, then $\frac{\cos B-\sin B}{\cos B+\sin B}=$ 21. If $7 \cos \theta-\sin \theta=5$ and $\tan \theta>0$, then $\tan \theta=$ 22. $$ \sin ^3 10^{\circ}+\sin ^3 50^{\circ}-\sin ^3 70^{\circ}= $$ 23. The number of solutions of $\sin 2 x+\cos 4 x=2$ in the interval $[-\pi, \pi]$ is 24. The range of the real valued function $f(x)=\cos ^{-1}(-x)+\sin ^{-1}(-x)+\operatorname{cosec}^{-1}(x)$ is 25. If $\cosh 2 x=199$, then $\cot h x=$ 26. The horizontal distance between a tower and a building is $10 \sqrt{3}$ units. If the angle of depression of the foot of 27. In a $\triangle A B C, A-B=120^{\circ}, R=8 r$, then $\frac{1+\cos C}{1-\cos C}=$ 28. In $\triangle A B C, \sqrt{\frac{r \cdot r_2}{r_3 r_1}}=$ 29. $\hat{\mathbf{i}}-2 \hat{\mathbf{j}}$ is a point on the line parallel to the vector $2 \hat{\mathbf{i}}+\hat{\mathbf{k}} 30. Points $P$ and $Q$ are given by $\mathbf{O P}=\hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}}$ and $\mathbf{O Q}=-\ha 31. Angle between a diagonal of a cube and a diagonal of its face which are coterminus is 32. For $a \in R$, if the vectors $\mathbf{p}=(a+1) \hat{\mathbf{i}}+a \hat{\mathbf{j}}+a \hat{\mathbf{k}}$, $\mathbf{q}=a \ 33. If $\mathbf{a}=\hat{\mathbf{i}}+4 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}, \mathbf{b}=-2 \hat{\mathbf{i}}+5 \hat{\mathbf{j}} 34. The following data represents the frequency distribution of 20 observations
$$ \begin{array}{ccccccc} \hline x_i & 3 & 4 35. The probability that a person $A$ completes a work in a given time is $\frac{2}{3}$ and the probability that another per 36. If $l, m$ represent any two elements (identical or different) of the set $\{1,2,3,4,5,6,7\}$, then the probability that 37. $A$ and $B$ are playing chess game with each other. The probability that $A$ wins the game is 0.6 . the probability that 38. $U_1, U_2, U_3$ are three urns. $U_1$ contains 5 red, 3 white, 2 back balls: $U_2$ contains 4 red 4 white, 2 black balls 39. If the probability distribution of a random variable $X$ is as follows, then $P(X \leq 2)=$
$$ \begin{array}{cccccc}\hli 40. If $X$ follows poisson distribution with variance 2 , then $P(X \geq 3)=$ 41. A straight line passing through a fixed point $(2,3)$ intersects the coordinate axes at points $P$ and $Q$. If $O$ is th 42. By rotating the axes about the origin in anti-clockwise direction with certain angle, if the equation $x^2+4 x y+y^2=1$ 43. If the lines $x+2 a y+a=0, x+3 b y+b=0$, $x+4 c y+c=0$ are concurrent, then $a, b, c$ are in 44. If $M$ is the foot of the perpendicular drawn from the origin to the line $x-2 y+3=0$ which meets the $X$ and $Y$-axes a 45. One line of the pair of lines $x^2+x y-2 y^2=0$ is perpendicular to one line of the pair of lines $3 y^2-5 x y-2 x^2=0$ 46. If the angle between the lines joining the origin to the points of intersection of $x+2 y+\lambda=0$ and $2 x^2-2 x y+3 47. If $Q$ is the inverse point of $P(-1,1)$ with respect to the circle $x^2+y^2-2 x+2 y=0$, then the line containing $Q$ is 48. If the circle passing through $(3,5),(5,5)$ and $(3,-3)$ cuts the circle $x^2+y^2+2 x+2 f y=0$ orthogonally, then $f=$ 49. Length of the common chord of two circles of same radius is $2 \sqrt{17}$. If one of the two circles is $x^2+y^2+6 x+4 y 50. A circle $S \equiv x^2+y^2-16=0$ intersects another circle $S^{\prime}=0$ of radius 5 units such that their common chord 51. Let $\theta$ be the angle between the circles $S \equiv x^2+y^2+2 x-2 y+c=0$ and $S^{\prime} \equiv x^2+y^2-6 x-8 y+9=0$ 52. $P Q$ is a focal chord of the parabola $y^2=4 x$ with focus $S$. If $P=(4,4)$, then $S Q=$ 53. The angle between the tangents drawn from a point $(-3,2)$ to the ellipse $4 x^2+9 y^2-36=0$ is 54. If a tangent to the hyperbola $x y=-1$ is also a tangent to the parabola $y^2=8 x$, then the equation of that tangent is 55. The distance between the tangents of the hyperbola $2 x^2-3 y^2=6$ which are perpendicular to the line $x-2 y+5=0$ is 56. If $A(0,0,0) B(3,4,0)$ and $C(0,12,5)$ are the vertices of a $\triangle A B C$, then the $x$-coordinate of its incentre 57. If $A=(0,4,-3), B=(5,0,12)$ and $C=(7,24,0)$, then $\sqrt{B A C}=$ 58. A plane $\pi$ is passing through the points $A(1,-2,3)$ and $B(6,4,5)$. If the plane $\pi$ is perpendicular the plane $3 59. $$ \mathop {\lim }\limits_{y \to 0} \frac{\sqrt{1+\sqrt{1+y^4}}-\sqrt{2}}{y^4}= $$ 60. If $\mathop {\lim }\limits_{x \to 0} \frac{\cos 2 x-\cos 4 x}{1-\cos 2 x}=k$, then $\lim\limits_{x \rightarrow k} \frac{ 61. If the function $f(x)=\left\{\begin{array}{l}1+\cos x, x \leq 0 \\ a-x, 02\end{array}\right.$ everywhere, then $a^2+b^2= 62. If $x=2 \cos ^3 \theta$ and $y=3 \sin ^2 \theta$, then $\frac{d y}{d x}=$ 63. Assertion (A) If $y=f(x)=(|x|-|x-1|)^2$, then $\left(\frac{d y}{d x}\right)_{x=1}=1$
Reason (R) $\mathop {\lim }\limits_ 64.
If $y=|\cos x-\sin x|+|\tan x-\cot x|$, then
$$ \left(\frac{d y}{d x}\right)_{x=\frac{\pi}{3}}+\left(\frac{d y}{d x}\r 65.
If the tangent drawn at the point $(\alpha, \beta)$ on the curve $x^{\frac{2}{3}}+y^{\frac{2}{3}}=4$ is parallel to the 66. The displacement $S$ of a particle measured from a fixed point $O$ on a line is given by $S=t^3-16 t^2+64 t-16$. Then, t 67. If the extreme value of the function $f(x)=\frac{4}{\sin x}+\frac{1}{1-\sin x}$ in $\left[0, \frac{\pi}{2}\right]$ is $m 68. The interval in which the curve represented by $f(x)=2 x+\log \left(\frac{x}{2+x}\right)$ is 69. $$ \int \frac{1}{9 \cos ^2 x-24 \sin x \cos x+16 \sin ^2 x} d x= $$ 70. If $\int \frac{1}{\cot \frac{x}{2} \cot \frac{x}{3} \cot \frac{x}{6}} d x=A \log \left|\cos \frac{x}{2}\right| +B \log \ 71. $$ \int \frac{\sin x+\cos x}{\sin x-\cos x} d x= $$ 72. $$ \int \frac{x^4-1}{x^2 \sqrt{x^4+x^2+1}} d x= $$ 73. $$ \int \frac{(3 x-2) \tan \left(\sqrt{9 x^2-12 x+1}\right)}{\sqrt{9 x^2-12 x+1}} d x= $$ 74. $\int_{\frac{-\pi}{4}}^{\frac{\pi}{3}}\left|\tan \left(x-\frac{\pi}{6}\right)\right| d x=$ 75. $$ \int_0^\pi \frac{x \sin x}{\sin ^2 x+2 \cos ^2 x} d x= $$ 76. The area of the region lying between the curves $y=\sqrt{4-x^2}, y^2=3 x$ and the $Y$-axis is 77. $$ \mathop {\lim }\limits_{n \to \infty }\left(\frac{1}{1^2+n^2}+\frac{2}{2^2+n^2}+\frac{3}{3^2+n^2}+\ldots+\frac{n}{n^2 78. The general solution of the differential equation $\frac{d y}{d x}=\frac{2 x^2-x y-y^2}{x^2-y^2}$ is 79. If the degree of the differential equation corresponding to the family of curves $y=a x+\frac{1}{a}$ (where $a \neq 0$ i 80. The general solution of the differential equation $y+\cos x\left(\frac{d y}{d x}\right)-\cos ^2 x=0$ is
Physics
1. The dimensional formula of Planck's constant is 2. The ratio of the displacements of a freely falling body during second and fifth seconds of its motion is 3. The magnitudes of two vectors are $A$ and $B(A>B)$. If the maximum resultant magnitude of the two vectors is ' $n$ ' tim 4. A particle crossing the origin at time $t=0$ moves in the $X Y$-plane with a constant acceleration ' $a$ ' in $y$-direct 5. A train of mass $10^6 \mathrm{~kg}$ is moving at a constant speed of $108 \mathrm{~km} / \mathrm{h}$. If the frictional 6. Two balls each of mass 250 g moving in opposite directions each with a speed $16 \mathrm{~ms}^{-1}$ collide and rebound 7. A body is moving along a straight line under the influence of a constant power source. If the relation between the displ 8. A body is projected at an angle of $60^{\circ}$ with the horizontal. If the initial kinetic energy of the body is $X$, t 9. A thin uniform circular disc rolls with a constant velocity without slipping on a horizontal surface. Its total kinetic 10. Three thin uniform rods each of mass $M$ and length $L$ are placed along the three axes of a cartesian co-ordinate syste 11. For a particle executing simple harmonic motion, the ratio of kinetic and potential energies at a point where displaceme 12. When the mass attached to a spring is increased from 4 kg to 9 kg , the time period of oscillation increases by $0.2 \pi 13. Two solid spheres each of radius ' $R$ ' made of same material are placed in contact with each other. If the gravitation 14. The force required to stretch a steel wire of area of cross-section $1 \mathrm{~mm}^2$ to double its length is
(Young's 15. In a hydraulic lift, if the radius of the smaller piston is 5 cm and the radius of the larger piston is 50 cm , then the 16. If the values of the temperature of a body in Fahrenheit and Celsius scales are in the ratio of $13: 5$, then the temper 17. A Carnot heat engine absorbs 600 J of heat from a source at a temperature of $127^{\circ} \mathrm{C}$ and rejects 400 J 18. During adiabatic expansion, if the temperature of 3 moles of a diatomic gas decreases by $50^{\circ} \mathrm{C}$, then t 19. The fundamental limitation to the coefficient of performance of a refrigerator is given by 20. If the ratio of specific heats of a gas at constant pressure and at constant volume is $\gamma$, then the number of degr 21. A steel wire of length 81 cm has a mass of $5 \times 10^{-3} \mathrm{~kg}$.
If the wire is under a tension of 50 N , the 22. A light ray incidents on an equilateral prism made of material of refractive index $\sqrt{3}$. Inside the prism, if the 23. An unpolarised beam of light incidents on a group of three polarising sheets arranged such that the angle between the ax 24. In a region, the electric field is given by $\mathbf{E}=(3 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}+7 \hat{\mathbf{k}}) \math 25. The energy stored in a capacitor is $W$. To double the charge on the plates of the capacitor, the additional work to be 26. The velocity acquired by an electron at rest when subjected to a uniform electric field of potential difference 180 V is 27. Charge ' $Q$ ' (in coulomb) flowing through a conductor in terms of time ' $t$ ' (in second) is given by the equation $Q 28. In a metal, the charge carrier density is $9.1 \times 10^{28} \mathrm{~m}^{-3}$ and its electrical conductivity is $6.4 29. The force per unit length on a straight wire carrying current of 8 A making an angle of $30^{\circ}$ with a uniform magn 30. A wire of length 10 m carrying current of 1 A is bent in to a circular loop. If a magnetic field of $2 \pi \times 10^{-4 31. A short bar magnet has a magnetic moment of $0.48 \mathrm{JT}^{-1}$. The magnitude of magnetic field at a point at 10 cm 32. A coil of 45 turns and radius 4 cm is placed in a uniform magnetic field such that its plane is perpendicular to the dir 33. For better tuning of a series $L C R$ circuit in a communication system, the preferred combination is 34. The magnitude of the electric field of a plane electromagnetic wave travelling in free space is $E$. If $\mu_0$ and $\va 35. An alpha particle moves along a circular path of radius 0.5 mm in a magnetic field of $2 \times 10^{-2} \mathrm{~T}$. Th 36. The difference between the frequencies of second and first Paschen lines of hydrogen atom is ( $R=$ Rydberg constant and 37. If the time taken for a radioactive substance to decay $8 \%$ to $77 \%$ is 12 minutes, then the half life of the substa 38. A transistor has 3 impurity regions of different doping levels. In the order of increasing doping level, the regions are 39. A camera is fabricated using a semiconducting material having a band gap of 3 eV . The wavelength of light if can detect 40. If in an amplitude modulated wave, the maximum amplitude is 14 V and the modulation index is 0.4 , then the amplitude of
1
AP EAPCET 2025 - 22nd May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$$ \int_0^\pi \frac{x \sin x}{\sin ^2 x+2 \cos ^2 x} d x= $$
A
$\frac{\pi}{2}$
B
$\frac{\pi^2}{2}$
C
$\frac{\pi^2}{4}$
D
$\frac{\pi}{4}$
2
AP EAPCET 2025 - 22nd May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The area of the region lying between the curves $y=\sqrt{4-x^2}, y^2=3 x$ and the $Y$-axis is
A
$\frac{\pi}{3}-\frac{1}{2 \sqrt{3}}$
B
$\frac{\pi}{6}+\frac{1}{2 \sqrt{3}}$
C
$\frac{\pi}{3}+\frac{1}{2 \sqrt{3}}$
D
$\frac{\pi}{6}-\frac{1}{2 \sqrt{3}}$
3
AP EAPCET 2025 - 22nd May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$$ \mathop {\lim }\limits_{n \to \infty }\left(\frac{1}{1^2+n^2}+\frac{2}{2^2+n^2}+\frac{3}{3^2+n^2}+\ldots+\frac{n}{n^2+n^2}\right)= $$
A
1
B
$\frac{1}{2} \log 2$
C
$2 \log 2$
D
0
4
AP EAPCET 2025 - 22nd May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The general solution of the differential equation $\frac{d y}{d x}=\frac{2 x^2-x y-y^2}{x^2-y^2}$ is
A
$\log \left|\frac{y^2-2 x^2}{x^2}\right|+\sqrt{2} \log \left|\frac{y-\sqrt{2} x}{y+\sqrt{2} x}\right| +2 \sqrt{2} \log |x|=C $
B
$\sqrt{2} \log \left|\frac{y^2-2 x^2}{x^2}\right|+\log \left|\frac{y-\sqrt{2} x}{y+\sqrt{2} x}\right| +2 \sqrt{2} \log |x|=C $
C
$\sqrt{2} \log \left|\frac{y^2+2 x^2}{x^2}\right|+\log \left|\frac{y+\sqrt{2} x}{y-\sqrt{2} x}\right| +2 \sqrt{2} \log |x|=C $
D
$\log \left|\frac{2 x^2-y^2}{x^2}\right|+\sqrt{2} \log \left|\frac{y+\sqrt{2} x}{y-\sqrt{2} x}\right| +\log |x|=C $
Paper Analysis
Total Questions
Chemistry 40
Mathematics 80
Physics 40
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