Chemistry
1. $a, b, c, d$ are electromagnetic radiations. Frequencies of $a, b$ are $3 \times 10^{15} \mathrm{~Hz}, 2 \times 10^{14} 2. The number of electrons with magnetic quantum number, $m_l=0$ in the elements with atomic numbers $Z=24$ and $Z=29$ are 3. Which of the following orders is not correct for the given property?
4. $$ \text { Match the following } $$
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.tg td{border-color:black;borde 5. $$ \text { Which of the following sets are correctly matched? } $$
$$ \begin{array}{llcc} \hline & \text { Molecule } & 6. The correct equation for one mole of a real gas is $a, b$ are constants)
7. $A$ and $B$ are ideal gases. At $T(\mathrm{~K}), 2 \mathrm{~L}$ of ' $A^{\prime}$ 'with a pressure of 1 bar is mixed wit 8. The mass of a mixture containing NaCl and NaBr is 4.0 g . If Na is $30 \%$ of the total mixture, the composition of NaCl 9. The number of extensive and intensive properties in the list given below is respectively, density, enthalpy, mass, tempe 10. One mole of ethanol ( $l$ ) was completely burnt in oxygen to form $\mathrm{CO}_2(\mathrm{~g})$ and $\mathrm{H}_2 \mathr 11. For the following given equilibrium reaction $\frac{K_c}{K_p}$ is equal to 1076 at $T(\mathrm{~K})$. What is the value o 12. The molar solubility of $\mathrm{PbI}_2$ in $0.2 \mathrm{MPb}\left(\mathrm{NO}_3\right)_2$ solution in terms of $K_{s p} 13. Which of the following property is less for $\mathrm{D}_2 \mathrm{O}$ than $\mathrm{H}_2 \mathrm{O}$ ?
14. Identify the correct statement from the following.
A. Among alkali metal ions, $\mathrm{Li}^{+}$has highest hydration en 15. The correct order of electronegativity of group 13 elements is
16. Identify the correct statements.
I. CO reduces the oxygen carrying ability of blood
II. Producer gas contains CO and $\m 17. The incorrect statement from the following is 18. IUPAC names of the given compounds (I) and (II) are respectively
19. $$ \text { Identify the most stable carbocation from the following } $$ 20. A metal crystallises in simple cubic lattice. The volume of one unit cell is $6.4 \times 10^7 \mathrm{pm}^3$. What is th 21. What is the approximate molality of $10 \%(w / w)$ aqueous glucose solution?
(Molar mass of glucose $=180 \mathrm{~g} \m 22. The van't Hoff factor for 0.5 m aqueous $\mathrm{CH}_2 \mathrm{FCOOH}$ solution is 1.075 . What is the experimentally ob 23. $$ \text { Match the following } $$
$$ \begin{array}{llll} \hline & \begin{array}{l} \text { List-I (Symbol of } \\ \tex 24. The following graph is obtained for a first order reaction $(A \rightarrow P)$. The activation energy ( $E_a$ in $\left. 25. $$ \text { Match the following } $$
$$ \begin{array}{llll} \hline & \begin{array}{l} \text { List-I } \\ \text { (Sol) } 26. Which of the following enzymatic reaction is not correctly matched with enzyme shown against it in brackets?
27. Which of the following methods is useful for producing semiconductor grade metals of high purity?
28. Observe the following
$\mathrm{P}_4+\mathrm{SOCl}_2 \rightarrow$ Products
$\mathrm{P}_4+\mathrm{SO}_2 \mathrm{Cl}_2 \rig 29. The IUPAC name of the complex shown below is $\mathrm{K}_3\left[\mathrm{Co}(\mathrm{ox})_3\right]$
30. Identify the ion (hydrated in solution) which is not correctly matched with its spin only magnetic moment (in BM) given 31. Which one of the statements, regarding $X$ is not correct?
3-Hydroxybutanoic acid +3 -Hydroxypentanoic acid $\rightarrow 32. Identify the essential amino acids from the following
I. Leucine
II. Tyrosine
III. Cysteine
IV. Histidine 33. $$ \text { Which of the following represents nucleoside of RNA? } $$ 34. Which of the following is not an antibiotic?
35. What are the major products $X$ and $Y$ respectively in the following set of reactions?
36. Which of the following will undergo methylation with $\mathrm{CH}_3 \mathrm{Cl}$ /anhy. $\mathrm{AlCl}_3$ ?
I. Aniline
I 37. What are $X$ and $Y$ respectively in the following set of reactions?
38. $$ \text { Match the following } $$
$$ \begin{array}{llll} \hline & \text { List-I (Compound) } & & \text { List-II }\le 39. The structures of succinic acid $(x)$ and malonic acid $(y)$ respectively are 40. Benzyl amine can be prepared from which of the following reactions?
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 } $$ 39. In a common emitter transistor amplifier the resistance of collector is $3 \mathrm{k} \Omega$. If the current amplificat 40. The layer of the atmosphere that reflects low frequency (LF) electromagnetic waves during day time only is
1
AP EAPCET 2025 - 26th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$$ \int \frac{x+1}{(x-2) \sqrt{1-x}} d x= $$
A
$\log (x+1)-\log (x-2) \sqrt{1-x}+C$
B
$\log (x-2) \sqrt{1-x}+C$
C
$6 \tan ^{-1} \sqrt{1-x}-2 \sqrt{1-x}+C$
D
$4 \tan ^{-1} \sqrt{1-x}-2 \sqrt{1-x}+C$
2
AP EAPCET 2025 - 26th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$$ \int \frac{1}{1+x+x^2} d x= $$
A
$\frac{2}{\sqrt{3}} \log \left(\frac{2 x+1+\sqrt{3}}{2 x-1-\sqrt{3}}\right)+C$
B
$\frac{1}{\sqrt{3}} \log \left(\frac{2 x+1-\sqrt{3}}{2 x+1+\sqrt{3}}\right)+C$
C
$\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+C$
D
$\frac{2}{\sqrt{5}} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{5}}\right)+C$
3
AP EAPCET 2025 - 26th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $\int \frac{d x}{(x \tan x+1)^2}=f(x)+C$, then $\lim\limits_{x \rightarrow \frac{\pi}{2}} f(x)=$
A
$\frac{\pi}{2}$
B
$\frac{2}{\pi}$
C
$\frac{1}{\pi}$
D
$\infty$
4
AP EAPCET 2025 - 26th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$$ \int \sin ^3 x \cos ^2 x d x= $$
A
$\frac{\sin ^4 x \cos x}{5}-\frac{\sin ^2 x \cos x}{15}-\frac{2 \cos x}{15}+C$
B
$-\frac{\sin ^4 x \cos x}{5}-\frac{\sin ^2 x \cos x}{15}+\frac{2 \cos x}{15}+C$
C
$\frac{\sin ^4 x \cos ^{\prime} x}{5}-\frac{\sin ^2 x \cos x}{15}+\frac{2 x}{15}+C$
D
$\frac{\sin ^4 x \cos x}{5}+\frac{\sin ^2 x \cos x}{3}-\frac{2 x}{15}+C$
Paper Analysis
Total Questions
Chemistry 40
Mathematics 80
Physics 40
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