Chemistry
1. The uncertainty in the velocities of two particles $A$ and $B$ are 0.03 and $0.01 \mathrm{~ms}^{-1}$ respectively. The m 2. The total maximum number of electrons possible in $3 d$. $6 d, 5 s$ and $4 f$ orbitals with $m_l$ (magnetic quantum numb 3. The period and group numbers of the element having maximum electronegativity in the long form of periodic table respecti 4. Identify the pair of molecules which have same hybridisation as the hybridisation in xenon (II) fluoride.
5. Identify the set containing isoelectronic species 6. Choose the incorrect statement from the following. 7. An ideal gas mixture of $\mathrm{C}_2 \mathrm{H}_6$ and $\mathrm{C}_2 \mathrm{H}_4$ occupies a volume of 28 L at 1 atm a 8. Complete combustion of ethane gives only gaseous products. In a closed vessel, 15 g of ethane and 112 g of $\mathrm{O}_2 9. Identify the incorrect statements from the following.
I. For adiabatic process, $\Delta U=w_{\text {ad }}$
II. Enthalpy 10. Enthalpy of formation of $\mathrm{CO}_2(\mathrm{~g}), \mathrm{H}_2 \mathrm{O}(\mathrm{l})$ and $\mathrm{C}_6 \mathrm{H}_ 11. The percentage of ionisation of 1 L of $x \mathrm{M}$ acetic acid is 4.242 and is called solution " $A$ ". The percentag 12. At 298 K , the value of $K_p$ for $\mathrm{N}_2 \mathrm{O}_4(g) \rightleftharpoons 2 \mathrm{NO}_2(g)$ is 0.113 atm . Th 13. $\mathrm{H}_2 \mathrm{O}_2$ reduces $\mathrm{KMnO}_4$ in acidic medium to ' $x$ ' and in basic medium to ' $y$ '. What a 14. Which chloride does not exist as hydrate?
15. Identify the incorrect statement about the group 13 elements. 16. Which of the following statements are correct?
(I) $\mathrm{SnF}_4$ is ionic in nature.
(II) Stability of dihalides of g 17. Which of the following when present in excess in drinking water causes the disease methemoglobinemia? 18. $$ \text { IUPAC name of the following compound is } $$ 19. The empirical formula weight of ' $Z$ ' in the given reaction sequence is
$$ n \text {-propyl bromide } \xrightarrow[\te 20. If AgCl is doped with $1 \times 10^{-4}$ mole percent of $\mathrm{CdCl}_2$ the number of cation vacancies (in $\mathrm{m 21. In aqueous glucose solution, the mole fraction of wate is 40 times to mole fraction of glucose. What is the weight perce 22. Benzoic acid molecules undergo dimerisation in benzene. 2.44 g of benzoic acid when dissolved in 30 g of benzene caused 23. When the lead storage battery is in use (during discharge) the reaction that occurs at the anode is 24. The following equation is obtained for a first order reaction at 300 K
$$ \log _{10} \frac{k}{A}=0.00174 $$
What is the 25. $$ \text { Match the following } $$
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;borde 26. Adsorption of a gas on solids follows Freundlich adsorption isotherm. The graph drawn between $\log \frac{x}{m}$ (on $y$ 27. Which of the following reactions is an example of roasting? 28. Nature of two oxides of nitrogen $X$ and $Y$ formed in the reaction of sodium nitrite with hydrochloric acid is 29. $$ \text { Match the following } $$
$$ \begin{array}{cccc} \hline & \begin{array}{c} \text { List-I } \\ \text { (Transi 30. Identify the complex ion with spin only magnetic moment of 4.90 BM .
31. What are $X$ and $Y$ in the following reaction?
$$ n \mathrm{ClCH}=\mathrm{CH}_2 \xrightarrow{x} Y $$ 32. Consider the following
Statement-I : Cane sugar is a disaccharide of $\alpha$-D-glucose and $\beta$-D-fructose.
Statemen 33. The deficiency of vitamin $(X)$ causes convulsions. Source of $X$ is $Y$. What are $X$ and $Y$ ? 34. Which of the following is not an example of synthetic detergent?
35. The most reactive compound towards nucleophilic substitution with an aqueous NaOH is 36. An alkyl bromide $X\left(\mathrm{C}_5 \mathrm{H}_{11} \mathrm{Br}\right)$ undergoes hydrolysis in a two step mechanism $ 37. Consider the following sequence of reactions
$$ \mathrm{C}_6 \mathrm{H}_5 \mathrm{COONa} \xrightarrow[\Delta]{\mathrm{Na 38. $$ \text { What is } A \text { in the following reaction? } $$ 39. The correct statement regarding $X$ and $Y$ formed in the following reaction is
$$ \left(\mathrm{CH}_3\right)_3 \mathrm{ 40. Consider the following
Statement-I In the nitration of aniline, more amount of $m$-nitroaniline is formed than expected.
Mathematics
1. $[t]$ denotes the greatest integer function and $[t-m]=[t]-m$ when $m \in Z$.
If $k=2[2 x-1]-1$ and $3[2 x-2]+1=2[2 x-1] 2. If $f(x)=(x+1)^2-1, x \geq-1$, then $\left\{x \mid f(x)=f^{-1}(x)\right\}$ is
3. If $11^{12}-11^2=k\left(5 \times 10^9+6 \times 10^9+33 \times 10^8\right. \left.+110 \times 10^7+\ldots+33\right)$, then 4. If $P=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]$ is the adjoint of a matrix $A$ 5. If $\alpha$ is a real root of the equation $x^3+6 x^2+5 x-42=0$, then the determinant of the matrix
$\left[\begin{array} 6. The rank of the matrix $\left[\begin{array}{cccc}2 & -3 & 4 & 0 \\ 5 & -4 & 2 & 1 \\ 1 & -3 & 5 & -4\end{array}\right]$ 7. If $z$ is a complex number such that $\frac{z-1}{z-i}$ is purely imaginary and locus of $z$ represents a circle with cen 8. If the least positive integer $n$ satisfying the equation $\left(\frac{\sqrt{3}+i}{\sqrt{3}-i}\right)^n=-1$ is $p$ and t 9. Sum of the squares of the imaginary roots of the equation $z^8-20 z^4+64=0$ is 10. Let $(a-3) x^2+12 x+(a+6)>0, \forall x \in R$ and $a \in(\ell, \infty)$. If $a$ is the least positive integral value of 11. If the roots of the equation $x^2+2 a x+b=0$ are real, distinct and differ atmost by 2 m , then $b$ lies in the interval 12. The cubic equation whose roots are the squares of the roots of the equation $x^3-2 x^2+3 x-4=0$ is 13. If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+p x^2+q x+r=0$, then $\alpha^3+\beta^3+\gamma^3=$
14. If all possible 4 -digit numbers are formed by choosing 4 different digits from the given digits $1,2,3,5,8$ then the su 15. The number of ways of forming the ordered pairs $(p, q)$ such that $p>q$ by choosing $p$ and $q$ from the first 50 natur 16. The number of ways in which a committee of 7 members can be formed from 6 teachers, 5 fathers and 4 students in such a w 17. If $C_0, C_2, \ldots, C_n$ are the binomial coefficients in the expansion of $(1+x)^n$, then
$$ \left(C_0+C_1\right)-\le 18. $$ 1+\frac{4}{15}+\frac{4 \cdot 10}{15 \cdot 30}+\frac{4 \cdot 10 \cdot 16}{15 \cdot 30 \cdot 45}+\ldots . .+\infty= $$ 19. If $\frac{3 x+1}{(x-1)\left(x^2+2\right)}=\frac{A}{x-1}+\frac{B x+C}{x^2+2}$, then $5(A-B)=$ 20. $\operatorname{cosec} 48^{\circ}+\operatorname{cosec} 96^{\circ}+\operatorname{cosec} 192^{\circ}+\operatorname{cosec} 3 21. If $\sqrt{3} \cos \theta+\sin \theta>0$, then 22. If $\cos \theta=\frac{-3}{5}$ and $\theta$ does not lie in second quadrant, then $\tan \frac{\theta}{2}=$ 23. The general solution satisfying both the equations $\sin x=-\frac{3}{5}$ and $\cos x=-\frac{4}{5}$ is 24. The number of solution of $\tan ^{-1} 1+\frac{1}{2} \cos ^{-1} x^2-\tan ^{-1} \left(\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sq 25. $$ \tanh ^{-1}(\sin \theta)= $$ 26. In $\triangle A B C$, if $a=8, b=10, c=12$, then $\frac{r}{R}=$ 27. In $\triangle A B C$, if $a=13, b=8, c=7$, then $\cos (B+C)=$ 28. In a $\triangle A B C$, if $\left(r_1-r_3\right)\left(r_1-r_2\right)-2 r_2 r_3=0$, then $a^2-b^2=$ 29. If the median $A D$ of the $\triangle A B C$ is bisected at $E$ and $B E$ meets $A C$ in $E$, then $A F: A C=$ 30. If $\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$ and $\mathbf{b}=-\hat{\mathbf{i}}+3 \hat{\mathb 31. If $\bar{a}$ is a unit vector, then
$$ |\mathbf{a} \times \hat{\mathbf{i}}|^2+|\mathbf{a} \times \hat{\mathbf{j}}|^2+|\m 32. If $\mathbf{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}, \mathbf{b}=-2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}} 33. $3 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+5 \hat{\mat 34. Let $x_1, x_2, \ldots, x_{11}$ be the observations satisfying $\sum\limits_{i=1}^{11}\left(x_i-4\right)=22$ and $\sum\li 35. There are 8 boys and 7 girls in a class room. If the names of all those children are written on paper slips and 3 slips 36. A four member committee is to be formed from a group containing 9 men and 5 women. If a committee is formed randomly, th 37. A die is thrown twice. Let A be the event of getting a prime number when the die is thrown first time and $B$ be the eve 38. A bag contains 5 balls of unknown colours. There are equal chances that out of these five balls, there may be 0 or 12 or 39. If $X \sim B(9, p)$ is a binomial variate satisfying the equation $P(X=3)=P(X=6)$, then $P(X 40. The mean and variance of a binomial distribution are $x$ and 5 respectively. If $x$ is an integer, then the possible val 41. If the locus of a point which is equidistant from the coordinate axes forms a triangle with the line $y=3$, then the are 42. After the coordinate axes are rotated through an angle $\frac{\pi}{4}$ in the anti-clockwise direction without shifting 43. $A(-2,3)$ is a point on the line $4 x+3 y-1=0$. If the points on the line that are 10 units away from the point $A$ are 44. If $\alpha$ is the angle made by the perpendicular drawn from origin to the line $12 x-5 y+13=0$ with the positive $X$-a 45. If the equation of the pair of lines passing through $(1,1)$ and perpendicular to the pair of line $2 x^2+x y-y^2-x+2 y- 46. If the combined equation of the lines joining the origin to the point of intersection of the curve $x^2+y^2-2 x-4 y+2=0$ 47. If the circles $x^2+y^2+5 k x+2 y+k=0$ and $2 x^2+2 y^2+2 k x+3 y-1=0, k \in R$ intersect at points $P$ and $Q$ then the 48. The slope of one of the direct common tangents drawn to the circles $x^2+y^2-2 x+4 y+1=0$ and $x^2+y^2-4 x-2 y+4=0$ is 49. If $(1, a),(b, 2)$ are conjugate points with respect to the circle $x^2+y^2=25$, then $4 a+2 b=$
50. If the pole of the line $x+2 b y-5=0$ with respect to the circle $S \equiv x^2+y^2-4 x-6 y+4=0$ lies on the line $x+b y+ 51. If $P(\alpha, \beta)$ is the radical centre of the circles $S \equiv x^2+y^2+4 x+7=0, S^{\prime}=2 x^2+2 y^2+3 x+5 y+9=0 52. If the tangents of the parabola $y^2=8 x$ passing through the point $P(1,3)$ touches the parabola at $A$ and $B$, then t 53. The equation of the normal drawn at the point $(\sqrt{2}+1,-1)$ to the ellipse $x^2+2 y^2-2 x+8 y+5=0$ is 54. If $3 x+2 \sqrt{2} y+k=0$ is a normal to the hyperbola $4 x^2-9 y^2-36=0$ making positive intercepts on both the axes, t 55. If a hyperbola has asymptotes $3 x-4 y-1=0$ and $4 x-3 y-6=0$, then the transverse and conjugate axes of that hyperbola 56. If $A(0,1,2), B(2,-1,3)$ and $C(1,-3,1)$ are the vertices of a triangle, then the distance between its circumcentre and 57. If the direction cosines of two lines satisfy the equations $l-2 m+n=0, l m+10 m n-2 n l=0$ and $\theta$ is the angle be 58. If $(2,-1,3)$ is the foot of the perpendicular drawn from the origin $(0,0,0)$ to a plane, then the equation of that pla 59. $$\mathop {\lim }\limits_{x \to 0} \frac{x^2 \sin ^2(3 x)+\sin ^4(6 x)}{(1-\cos 3 x)^2}= $$ 60. If a real valued function
$$ f(x)=\left\{\begin{array}{cc} (1+\sin x)^{\cos x}, & -\pi / 2
is continuous at $x=0$, then 61. $$ \mathop {\lim }\limits_{x \to 0} \frac{(\operatorname{cosec} x-\cot x)\left(e^x-e^{-x}\right)}{\sqrt{3}-\sqrt{2+\cos 62. If $y=\sqrt{\cosh x+\sqrt{\cosh x}}$, then $\frac{d y}{d x}=$ 63. If $y=\tan ^{-1} \sqrt{x^2-1}+\sinh ^{-1} \sqrt{x^2-1}, x>1$, then $\frac{d y}{d x}=$
64. If $y=(\log x)^{1 / x}+x^{\log x}$, at $x=e, \frac{d y}{d x}=$ 65. The interval in which the function $f(x)=\tan ^{-1}(\sin x+\cos x)$ is an increasing function is 66. The slope of a tangent drawn at the point $P(\alpha, \beta)$ lying on the curve $y=\frac{1}{2 x-5}$ is -2 . If $P$ lies 67. The function $f(x)=x e^{-x} \forall x \in R$ attains a maximum value at $x=k$, then $k=$
68. If $m$ and $M$ are the absolute minimum and absolute maximum values of the function $f(x)=2 \sqrt{2} \sin x-\tan x$ in t 69. $$ \int \frac{\sec ^2 x}{\sin ^7 x} d x-\int \frac{7}{\sin ^7 x} d x= $$ 70. If $\int\left(x^6+x^4+x^2\right) \sqrt{2 x^4+3 x^2+6} d x=f(x)+c$, then $f(3)=$
71. $$ \int \frac{d x}{(x+1) \sqrt{x^2+1}}= $$ 72. If $\int \frac{d x}{2 \cos x+3 \sin x+4}=\frac{2}{\sqrt{3}} f(x)+C$, then $f\left(\frac{2 \pi}{3}\right)=$ 73. If $\int \frac{1}{\left((x+4)^3(x+1)^5\right)^{1 / 4}} d x=A \cdot\left(\frac{x+4}{x+1}\right)^n+C$ 74. $$ \int_{-\pi / 2}^{\pi / 2} \sin ^2 x \cos ^2 x(\sin x+\cos x) d x= $$ 75. $$ \int_{1 / 5}^{1 / 2} \frac{\sqrt{x-x^2}}{x^3} d x= $$ 76. $$ \int_0^{400 \pi} \sqrt{1-\cos 2 x} d x= $$ 77. Area of the region (in sq. units) bounded by the curve $y=x^2-5 x+4, x=0, x=2$ and the $X$-axis is 78. If the order and degree of the differential equation $x \frac{d^2 y}{d x^2}=\left(1+\left(\frac{d^2 y}{d x^2}\right)^2\r 79. The equation of the curve passing through the point $(0, \pi)$ and satisfying the differential equation $y d x=\left(x+y 80. The general solution of the differential equation $(x-(x+y) \log (x+y)) d x+x d y=0$ is
Physics
1. If the equation for the velocity of a particle at time ' $t$ ' is $v=$ at $+\frac{b}{t+c}$, then the dimensions of $a, b 2. If a stone thrown vertically upwards from a bridge with an initial velocity of $5 \mathrm{~ms}^{-1}$, strikes the water 3. If $\alpha, \beta$ and $\gamma$ are the angles made by a vector with $x, y$ and $z$ axes respectively, then $\sin ^2 \al 4. A particle moving along a straight line covers the first half of the distance with a speed of $3 \mathrm{~ms}^{-1}$, the 5. Water flowing through a pipe of area of cross-section $2 \times 10^{-3} \mathrm{~m}^2$ hits a vertical wall horizontally 6. Two blocks $A$ and $B$ of masses 2 kg and 4 kg respectively are kept on a rough horizontal surface. If same force of 20 7. If a force of $\left(6 x^2-4 x\right) \mathrm{N}$ acts on a body of mass 10 kg , then work to be done by the force in di 8. A circular well of diameter 2 m has water upto the ground level. If the bottom of the well is at a depth of 14 m , the t 9. The co-ordinates of the centre of mass of a uniform $L$ shaped plate of mass 3 kg shown in the figure is 10. A circular disc of mass 20 kg and radius 1 m is rotating about an axis passing through its centre and perpendicular to i 11. The equations for the displacements of two particles in simple harmonic motion are $y_1=0.1 \sin \left(100 \pi t+\frac{\ 12. A spring is stretched by 0.2 m when a mass of 0.5 kg is suspended to it. The time period of the spring when 0.5 kg mass 13. An artificial satellite is revolving around a planet of radius $R$ in a circular orbit of radius ' $a$ '. If the time pe 14. If the longitudinal strain of a stretched wire is $0.2 \%$ and the Poisson's ratio of the material of the wire is 0.3 , 15. If two soap bubbles $A$ and $B$ of radii $r_1$ and $r_2$ respectively are kept in vacuum at constant temperature, then t 16. A small quantity of water of mass ' $m$ ' at temperature $\theta^{\circ} \mathrm{C}$ is mixed with a large mass ' $M$ ' 17. In a Carnot engine, if the absolute temperature of the source is $25 \%$ more than the absolute temperature of the sink, 18. The work done by 6 moles of helium gas when its temperature increases by $20^{\circ} \mathrm{C}$ at constant pressure is 19. If a heat engine and a refrigerator are working between the same two temperatures $T_1$ and $T_2\left(T_1>T_2\right)$, t 20. If the internal energy of 3 moles of a gas at a temperature of $27^{\circ} \mathrm{C}$ is 2250 R , then the number of de 21. If two progressive sound waves represented by $y_1=3 \sin 250 \pi t$ and $y_2=2 \sin 260 \pi t$ (where displacement is i 22. If the least distance of distinct vision for a boy is 35 cm , then the lens to be used by the boy for correcting the def 23. In Young's double slit experiment, if the distance between the slits is increased to 3 times initial distance, then the 24. A solid of mass 1 kg has $6 \times 10^{24}$ atoms. If one electron is removed from every one atom of $0.005 \%$ of the a 25. One of the two identical capacitors having the same capacitance $C$, is charged to a potential $V_1$ and the other is ch 26. If the energy stored in a spherical conductor having a charge of $12 \mu \mathrm{C}$ is 6 J , then the radius of the sph 27. A part of a circuit is shown in the figure. The ratio of the potential differences between the points $A$ and $C$ and th 28. A DC supply of 160 V is used to charge a battery of emf 10 V and internal resistance $1 \Omega$ by connecting a series r 29. The magnetic moment of an electron moving in a circular orbit of radius $R$ with a time period $T$ is
30. A solenoid of one metre length and 3.55 cm inner diameter carries a current of 5 A . If the solenoid consists of five cl 31. The work done in rotating a bar magnet which is initially in the direction of a uniform magnetic field through $45^{\cir 32. When a current of 4 mA passes through an inductor, if the flux linked with it is $32 \times 10^{-6} \mathrm{Tm}^2$, then 33. In a series resonant LCR circuit, for the power dissipated to become half of the maximum power dissipated, the current a 34. The waves having maximum wavelength among the following electromagnetic waves is
35. If the de-Broglie wavelength of an electron is 2 nm , then its kinetic energy is nearly
(Planck's constant $=6.6 \times 36. The ratio of the wavelengths of the spectral lines emitted due to transitions $3 \rightarrow 2$ and $2 \rightarrow 1$ or 37. The density (in $\mathrm{kg} \mathrm{m}^{-3}$ ) of nuclear matter is of the order of 38. In common emitter amplifier of a transistor, if the ratio of the voltage gain and current amplification factor is 4 , th 39. If three logic gates are connected as shown in the figure, then the correct truth table of the circuit is 40. Ionosphere acts as a reflector for the frequency range of
1
AP EAPCET 2025 - 23rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $\int\left(x^6+x^4+x^2\right) \sqrt{2 x^4+3 x^2+6} d x=f(x)+c$, then $f(3)=$
A
$\frac{3}{2}(95)^{3 / 2}$
B
$\frac{3}{2}(195)^{3 / 2}$
C
$\frac{3}{2}(265)^{3 / 2}$
D
$\frac{3}{2}(175)^{3 / 2}$
2
AP EAPCET 2025 - 23rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$$ \int \frac{d x}{(x+1) \sqrt{x^2+1}}= $$
A
$\frac{1}{\sqrt{2}} \sinh ^{-1}\left(\frac{1+x}{1-x}\right)+C$
B
$\frac{1}{\sqrt{2}} \sinh ^{-1}\left(\frac{1-x}{1+x}\right)+C$
C
$-\frac{1}{\sqrt{2}} \sinh ^{-1}\left(\frac{1-x}{1+x}\right)+C$
D
$-\frac{1}{\sqrt{2}} \sinh ^{-1}\left(\frac{1+x}{1-x}\right)+C$
3
AP EAPCET 2025 - 23rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $\int \frac{d x}{2 \cos x+3 \sin x+4}=\frac{2}{\sqrt{3}} f(x)+C$, then $f\left(\frac{2 \pi}{3}\right)=$
A
$\frac{\pi}{12}$
B
$\frac{\pi}{8}$
C
$\frac{5 \pi}{12}$
D
$\frac{5 \pi}{8}$
4
AP EAPCET 2025 - 23rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $\int \frac{1}{\left((x+4)^3(x+1)^5\right)^{1 / 4}} d x=A \cdot\left(\frac{x+4}{x+1}\right)^n+C$
A
$n$ A=3
B
$n+\frac{1}{A}=-\frac{1}{2}$
C
$A+n=1$
D
$A=n$
Paper Analysis
Total Questions
Chemistry 40
Mathematics 80
Physics 40
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