Chemistry
1. When a metal surface is irradiated with light of frequency $x \mathrm{~Hz}$, the kinetic energy of emitted photoelectron 2. Identify the correct statements from the following
I. Isotopes of an element show different chemical behaviour.
II. Lyma 3. $$ \text { Match the following } $$$$ \begin{array}{lllc} \hline & \text { List-I (Atomic number; Z) } & & \text { List- 4. In which of the following intramolecular H -bonding is absent? 5. Identify the correct set of molecules with zero dipole moment 6. Consider the following
Statement-I : If the intermolecular forces are stronger than thermal energy, the substance prefer 7. Identify the conditions at which van der Waals' equation of state changes to ideal gas equation. 8. Observe the following
I. 0.0063
II. 132.00
III. 1004
The number of significant figures in I, II and III is respectively. 9. At 273 K the maximum work done when pressure on 10 g of hydrogen is reduced from 10 atm to 1 atm under isothermal, rever 10. At $293 \mathrm{~K}, \Delta_r G^{\circ}$ for the following reaction is $165.469 \mathrm{~kJ} \mathrm{~mol}^{-1}$.
$$ \fr 11. At $T(\mathrm{~K})$, the solubility product of AgBr is $4 \times 10^{-13}$. What is its solubility in 0.1 M KBr solution 12. The following equilibrium is established at STP.
$$ B_2(g) \rightleftharpoons 2 B(g) $$
Atoms of $B$ occupy $20 \%$ of t 13. The volume (in mL ) of 10 volume $\mathrm{H}_2 \mathrm{O}_2$ solution required to completely react with 200 mL of 0.4 M 14. Which of the following statement is incorrect with reference to alkaline earth metals? 15. Consider the following -
Statement I : The order of electronegativity of $\mathrm{B}, \mathrm{Al}$, In Tl is $$ \mathrm{ 16. Which of the following does not exist? 17. Consider the following.
Assertion (A) : CO is poisonous to living beings.
Reason (R) : CO binds to haemoglobin forming c 18. $$ \begin{aligned} &\text { Consider the following reaction sequence }\\ &\text { Vinyl benzene } \xrightarrow[\Delta]{\ 19. $$ \text { The IUPAC name of the following compound is } $$ 20. Gold crystallises in fcc lattice. The edge length of the unit cell is $4 \mathop {\rm{A}}\limits^{\rm{o}}$. The closest 21. 248 g of ethylene glycol $\left(\mathrm{C}_2 \mathrm{H}_6 \mathrm{O}_2\right)$ is added to 200 g of water to prepare ant 22. A solution containing 7.5 g of urea (molar mass $=60 \mathrm{~g} \mathrm{~mol}^{-1}$ ) in 1 kg of water freezes at the s 23. What is $E_{\text {cell }}$ (in V) of the following cell at $298 \mathrm{~K} ?$
$$ \begin{aligned} & \left(E_{\mathrm{Zn 24. $A \rightarrow$ products, is a first order reaction. The following data is obtained for this reaction at $T(\mathrm{~K}) 25. Identify the correct statement from the following
I. Sulphur sol is an example for multi molecular colloid.
II. Starch s 26. Observe the following reactions
I. Sucrose $(a q)+\mathrm{H}_2 \mathrm{O} \xrightarrow{x}$ glucose + fructose
II. Glucos 27. Kaolinite, a form of clay is the ore of metal $x$ and malachite is the ore of metal $y, x$ and $y$ respectively are 28. Gas $X$ is obtained in Deacon's process. X on reacting with iodine and water gives 29. The alloy that contains copper and Zn is $x$ and the one that contains copper and Ni is $y$. What are $x$ and $y$ respec 30. Which of the following complexes exhibit geometrical isomerism?
I. $\left[\mathrm{Co}(\mathrm{en})\left(\mathrm{NH}_3\ri 31. In which polymer preparation, Ziegler- Natta catalyst is used? 32. The incorrect statement about amylose is 33. The improper functioning of ' $X$ ' results in Addison's disease. Hormone ' $Y$ ' is responsible for the development of 34. Which of the following is not an example of antacid? 35. When ethyl bromide and $n$-propyl bromide are allowed to react with Na metal in dry ether, the number of different alkan 36. $$ \text { Observe the following reactions } $$
The order of reactivity of $x, y, z$ towards $\mathrm{S}_{\mathrm{N}} 1$ 37. $$ \text { Consider the following sequence of reactions } $$
The incorrect statement about $z$ is 38. $$ \text { What are } x \text { and } y \text { in the following reaction sequence? } $$ 39. Arrange the products I, II, III from the following reactions in decreasing order of their acid strength. 40. $$ \text { What are } x \text { and } y \text { in the following set of reactions? } $$
Mathematics
1. The domain and range of a real valued function $f(x)=\cos x-3$ are respectively 2. If $f: R \rightarrow R$ and $g: R \rightarrow R$ are two functions defined by $f(x)=2 x-3$ and $g(x)=5 x^2-2$, then the 3. For all $n \in N$, if $1^3+2^3+3^3+\ldots n^3>x$, then a value of $x$ among the following is
4. If $A$ and $B$ are both $3 \times 3$ matrices, then which of the following statements are true?
(i) $A B=0 \Rightarrow A 5. $A=\left[\begin{array}{ccc}1 & -1 & 2 \\ -2 & 3 & -3\end{array}\right]$ is the given matrix and $A^T$ represents the tra 6. If $A=\left[\begin{array}{ccc}x & 2 & 1 \\ -2 & y & 0 \\ 2 & 0 & -1\end{array}\right], x$ and $y$ are non-zero numbers, 7. If $i=\sqrt{-1}$, then $\sum\limits_{n=2}^{30} i^n+\sum\limits_{n=30}^{65} i^{n+3}=$ 8. If $z_1$ and $z_2$ are two of the $n$th roots of unity such that the line segment joining them subtends at a right angle 9. $$ (\sqrt{\sqrt{2}+1}+i \sqrt{\sqrt{2}-1})^8= $$ 10. If the harmonic mean of the roots of the equation $\sqrt{2} x^2-b x+(8-2 \sqrt{5})=0$ is 11. All the values of $k$ such that the quadratic expression $2 k x^2-(4 k+1) x+2$ is negative for exactly three integrals v 12. If $\alpha$ and $\beta(\alpha>\beta)$ are the multiple roots of the equation $4 x^4+4 x^3-23 x^2-12 x+36=0$, then $2 \al 13. If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3-13 x^2+k x+189=0$ such that $\beta-\gamma=2$, then $\ 14. The number of all possible positive integrals solutions of the equation $x y z=30$ is 15. The number of all five letter words (with or without meaning) having atleast one repeated letter than can be formed by u 16. The number of ways of arranging all the letters of the word PERFECTION such that there must be exactly two consonants be 17. If $(1+x)^n=\sum_{r=0}^n C, x^r$, then the value of $C_0+\left(C_0+C_1\right)+\left(C_0+C_1+C_2\right)+\ldots+ \left(C_0 18. If $x$ is so large that terms containing $x^{-3}, x^{-4}, x^{-5}, \ldots$ can be neglected, then the approximate value o 19. Let $H(x)=3 x^4+6 x^3-2 x^2+1$ and $g(x)$ be a linear polynomial. If $\frac{H(x)}{(x-1)(x+1)(x-2)}=f(x) +\frac{g(x)}{(x- 20. If $630^{\circ} 21. For $\theta \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ if $2 \cos \theta+\sin \theta=1$ and $7 \cos \theta+6 \sin \t 22. $$ \sum\limits_{k=0}^{12} \frac{1}{\sin \left((k+1) \frac{\pi}{6}+\frac{\pi}{4}\right) \sin \left(\frac{k \pi}{6}+\frac{ 23. The number of solutions of the equation $2 \sin ^2 \theta-3 \cos ^2 \theta=\sin \theta \cos \theta$ lying in the interva 24. $$ \tan ^{-1} \frac{\sqrt{8-2 \sqrt{15}}}{\sqrt{15}+1}+\tan ^{-1} \frac{1}{\sqrt{5}}= $$ 25. If $\cos \alpha=\sec h \beta$, then $\beta=$ 26. In $\triangle A B C$, the sum of the lengths of two sides is $x$ and the product of those lengths is $y$. If $c$ is the 27. If the area of a $\triangle A B C$ is $4 \sqrt{5}$ sq units. Length of the side $C A$ is 6 units and $\tan \frac{B}{2}=\ 28. In a $\triangle A B C$ if $r_1=2 r_2=3 r_3$, then $a: b$ is 29. Let $2 \hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}}, 5 \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}},-13 \h 30. $\mathbf{a}, \mathbf{b}$ are position vectors of the point $A$ and $B$ respectively, $C$ and $D$ are points on the line 31. If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are three unit vectors such that $|\mathbf{a}-\mathbf{b}|^2+|\mathbf{b}-\mathbf{ 32. If $\mathbf{a}=\hat{\mathbf{i}}+p \hat{\mathbf{j}}-3 \hat{\mathbf{k}}, \mathbf{b}=p \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+ 33. If $\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$, $\mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j} 34. The variance of ungrouped data $2,12,3,11,5,10,6,7$, is 35. If $A$ and $B$ are events of a random experiment such that $P(A \cup B)=\frac{3}{4}, P(A \cap B)=\frac{1}{4}, P(\overlin 36. Two cards are drawn at random from a pack of 52 playing cards. If both the cards drawn are found to be black in colour, 37. A person is known to speak the truth in 3 out of 4 occasions. If he throws a die and reports that it is six, then the pr 38. $70 \%$ of the total employees of a factory are men. Among the employees of that factory 30\% of men and $15 \%$ of wome 39. If a discrete random variable $X$ has the probability distribution $P(X=x)=k \frac{2^{2 x+1}}{(2 x+1)!}, x=0,1,2 \ldots 40. A random variable $X$ follows a binomial distribution in which the difference between its mean and variance is 1. if $2 41. If the distance of a variable point $P$ from a point $A(2,-2)$ is twice the distance of $P$ from $Y$-axis, then the equa 42. If the transformed equation of the equation $2 x^2+3 x y-2 y^2-17 x+6 y+8=0$ after translating the coordinate axes to a 43. $P(6,4)$ is a point on the line $x-y-2=0$. If $A(\alpha, \beta)$ and $B(\gamma, \delta)$ are two points on this line lyi 44. If the straight line $2 x+3 y+1=0$ bisects the angle between two other straight lines one of which is $3 x+2 y+4=0$, the 45. If the slope of both the line given by $x^2+2 h x y+6 y^2=0$ are options and the angle between these lines is $\tan ^{-1 46. If one of the lines represented by $a x^2+2 h x y+b y^2=0$ bisects the angle between the positive coordinates axes, then 47. From a point $P$ on the circle $x^2+y^2=4$, two tangents are drawn to the circle $x^2+y^2-6 x-6 y+14=0$. If $A$ and $B$ 48. If the product of the lengths of the perpendicular drawn from the ends of a diameter of the circle $x^2+y^2=4$ on the li 49. If the intercept made by a variable circle on the X -axis and $Y$-axis are 8 and 6 units respectively, then the locus of 50. The slope of the non-vertical tangent drawn from the point $(3,4)$ to the circle $x^2+y^2=9$ is 51. If the acute angle between the circles $S \equiv x^2+y^2+2 k x+4 y-3=0$ and $S^{\prime} \equiv x^2+y^2-4 x+2 k y+9=0$ is 52. If $L$ is the normal drawn to the parabola $y^2=8 x$ at the point $t=\frac{1}{\sqrt{2}}$, then the foot of the perpendic 53. If the tangents are drawn to the ellipse $x^2+2 y^2=2$, then the locus of the mid-points of the intercepts made by the t 54. One of the latus recta of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ subtends an angle $2 \tan ^{-1}\left(\frac{3 55. If the equation of the hyperbola having $(8,3),(0,3)$ as foci and $\frac{4}{3}$ as eccentricity is $\frac{(x-\alpha)^2}{ 56.
$G(1,0,1)$ is the centroid of the $\triangle A B C$. If $A=(1,-4,2)$ and $B=(3,1,0)$, then $A G^2+C G^2=$
57. If the sum of the distances of the point $(3,4, \alpha), \alpha \in R$ from $X$-axis, $Y$-axis and $Z$-axis is minimum, 58. If the equation of the plane passing through the point $(2,-1,3)$ and perpendicular to each of the planes $3 x-2 y+z=8$ 59. $$ \mathop {\lim }\limits_{x \to \infty } \frac{(\sqrt{2})-\sqrt{1+\cos x}}{\sqrt{15+\cos 2 x-4}}= $$ 60. If a real valued function
$$ f(x)=\left\{\begin{array}{cl} \frac{x^2+(a+3) x+(a+1)}{x+3} & , \text { when } x \neq-3 \\ 61. $$ \mathop {\lim }\limits_{x \to 0} \frac{x \tan 2 x-2 x \tan x}{(1-\cos 3 x)(\operatorname{cosec} x-\cot x)^2}= $$ 62. Match the functions in Column I with their properties in Column II. In the following [ $x$ ] denotes the greatest intege 63. The derivative of $\sec ^{-1}\left(\frac{1}{2 x^2-1}\right)$ with respect to $\sqrt{1-x^2}$ at $x=\frac{1}{2}$ is 64. If $5 f(x)+3 f\left(\frac{1}{x}\right)=x+2$ and $y=x f(x)$, then $\frac{d y}{d x}$ at $x=1$ is equal to 65. The area (in square units) of the triangle formed by the $X$-axis, the tangent and the normal drawn at $(1,1)$ to the cu 66. The value of the Rolle's theorem for the function $f(x)=2 \sin x+\sin 2 x$ in the interval $[0, \pi]$ is 67. If the function $y=g(x)$ representing the slopes of the tangents drawn to the curve $y=3 x^4-5 x^3-12 x^2+18 x+3$ is str 68. Consider the following functions
I. $f(x)= \begin{cases}\frac{1}{2}-x & , x
II. $f(x)=|3 x-1|$
III. $f(x)=x|x|$
IV. $f(x 69. $$ \int \frac{e^{\sin x}(\sin 2 x-8 \cos x)}{2(\sin x-3)^2} d x= $$ 70. If $\int\left(3 t^2 \sin \frac{1}{t}-t \cos \frac{1}{t}\right) d t=f(t) \sin \left(\frac{1}{t}\right)+C$ then $f(2)=$ 71. $$ \int(\log x)^3 x^4 d x= $$ 72. $$ \int \frac{\sin 2 x}{\sin ^2 x+3 \cos x-3} d x $$ 73. If $\int \frac{d x}{\sin ^3 x+\cos ^3 x}=A \log \left|\frac{\sqrt{2}+t}{\sqrt{2}-t}\right|+B \tan ^{-1}(t)+C$, then $\le 74. $$ \int_{\pi / 4}^{\pi / 3} \frac{\cos x-\sin x}{\sin 2 x} d x= $$ 75. $$ \int_0^{\pi / 2} \frac{\sin x}{1+\cos x+\sin x} d x= $$ 76. $$ \mathop {\lim }\limits_{x \to \infty }\left[\frac{n+1}{n^2+1^2}+\frac{n+2}{n^2+2^2}+\frac{n+3}{n^2+3^2}+\ldots+\frac{ 77. $$ \int_0^\pi \frac{x \sin x}{1+\cos ^2 x} d x= $$ 78. The differential equation corresponding to the family of parabolas whose axis is along $x=1$ is 79. The general solution of the equation $\frac{d y}{d x}+\frac{1}{x} y=\frac{1}{x} e^x$ 80. The general solution of the differential equation
$$ \left(x \sin \frac{y}{x}\right) d y=\left(y \sin \frac{y}{x}-x\righ
Physics
1. Among the following, the physical quantity having the dimensions of Young's modulus is 2. If a car travels $40 \%$ of the total distance with a speed $v_1$ and the remaining distance with a speed $v_2$, then av 3. If bullets are fired in all possible directions from same point with equal velocity of $10 \mathrm{~ms}^{-1}$ and with a 4. A ball is projected from a point with a speed $V_0$ at certain angle with the horizontal. From the same point and at the 5. The power required for an engine to maintain a constant speed of $50 \mathrm{~ms}^{-1}$ for a train of mass $3 \times 10 6. As shown in the figure, a force $F$ is applied on a block of mass $\sqrt{3} \mathrm{~kg}$ placed on a rough horizontal s 7. The linear momentum of a body of mass 8 kg is $24 \mathrm{~kg} \mathrm{~ms}^{-1}$. If a constant force of 24 N acts on t 8. A person holds a ball of mass 0.25 kg in his hand and throws it, so that it leaves his hand with a speed of $12 \mathrm{ 9. If the radius of gyration of a thin circular ring about an axis passing through its centre and perpendicular to its plan 10. If a wheel starting from rest is rotating with an angular acceleration of $\pi \mathrm{rad} \mathrm{s}^{-2}$, then the n 11. If the displacement $y$ (in cm ) of a particle executing simple harmonic motion is given by the equation $y=5 \sin (3 \p 12. The angular frequency of a block of mass 0.1 kg oscillating with the help of a spring of force constant $2.5 \mathrm{~N} 13. An infinite number of objects each 1 kg mass are placed on the $X$-axis on both sides of $x=0$ at $\pm 1 \mathrm{~m}$, $ 14. As shown in the figure, a light uniform rod $P Q$ of length 150 cm is suspended from the ceiling horizontally using two 15. If water flows with a velocity of $20 \mathrm{cms}^{-1}$ in a pipe of radius 2 cm , then the flow is (The coefficient of 16. An electric kettle takes 4 A current at 220 V . If the entire electric energy is converted into heat energy, then the ti 17. According to Zeroth law of thermodynamics, the physical quantity which is same for two bodies in thermal equilibrium is 18. If a refrigerator of coefficient of performance of 5 has a freezer at a temperature of $-13^{\circ} \mathrm{C}$, then th 19. From the figure shown for a thermodynamic system, match the curves with their respective thermodynamic processes.
( $p=$ 20. If 2 moles of an ideal monoatomic gas at a temperature of $27^{\circ} \mathrm{C}$ is mixed with 4 moles of another ideal 21. Two sound waves of wavelengths 99 cm and 100 cm produce 10 beats in a time of $t$ seconds. If the speed of sound in air 22. If the far point of a short sighted person is 400 cm , then the power of the lens required to enable him to see very dis 23. In Young's double slit experiment, the wavelengths of red and blue lights used are $7.5 \times 10^{-5} \mathrm{~cm}$ and 24. The force between two point charges kept with a separation of 9 cm in air is 98 N . If a dielectric slab of constant 4, 25. Three point charges shown in the figure lie along a straight line. The energy required to exchange the position of centr 26. A capacitor of capacitance $2 \mu \mathrm{~F}$ is charged to 50 V and then disconected from the source. Later the gap be 27. A wire of resistance $100 \Omega$ is stretched, so that its length increases by $20 \%$. The stretched wire is then bent 28. In a potentiometer experiment, when two cells of emfs $E_1$ and $E_2\left(E_2>E_1\right)$ are connected in series, the b 29. The magnetic field at a distance of 10 cm from a long straight thin wire carrying a current of 4 A is 30. A velocity selector is to be constructed to select ions with a velocity of $6 \mathrm{~km} \mathrm{~s}^{-1}$. If the ele 31. A closely wound solenoid of 1200 turns and area of cross-section $5 \mathrm{~cm}^2$ carries a current. If the magnetic m 32. If the magnetic field inside a solenoid is $B$, then the magnetic energy stored in it per unit volume is ( $c=$ speed of 33. The resonant frequency of an LC circuit is $f_0$. If a dielectric slab of constant 16 is inserted completely between the 34. In a plane electromagnetic wave, the magnetic field is given by $\mathbf{B}=3 \times 10^{-7} \sin \left(100 \pi x+10^{12 35. If the linear momentum of a proton is changed by $p_0$ then the de-Broglie wavelength associated with the proton changes 36. If an electron in the excited state falls to ground state, a photon of energy 5 eV is emitted, then the wavelength of th 37. An element $X$ of a half-life of $1.4 \times 10^9$ years decays to form another stable element $Y$. A sample is taken fr 38. A Zener diode of breakdown voltage 20 V is connected as shown in the given circuit. The current through Zener diode is 39. The voltage gains of two amplifiers connected in series are 8 and 12.5 . If the voltage of the input signal is $200 \mu 40. If the sum of heights of transmitting and receiving antennas in line of sight of communication is ' $h$ ' then the heigh
1
AP EAPCET 2025 - 21st May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$$ \int(\log x)^3 x^4 d x= $$
A
$x^5\left[\frac{1}{5}(\log x)^3-\frac{3}{25}(\log x)^2+\frac{6}{125} \log x-\frac{6}{625}\right]+C$
B
$x^5\left[\frac{1}{5}(\log x)^3-\frac{2}{25}(\log x)^2+\frac{6}{125} \log x-\frac{12}{125}\right]+C$
C
$x^5\left[\frac{1}{5}(\log x)^3-\frac{4}{25}(\log x)^2-\frac{9}{125} \log x-\frac{8}{125}\right]+C$
D
$x^5\left[\frac{1}{5}(\log x)^3+\frac{3}{25}(\log x)^2-\frac{6}{125} \log x-\frac{6}{125}\right]+C$
2
AP EAPCET 2025 - 21st May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$$ \int \frac{\sin 2 x}{\sin ^2 x+3 \cos x-3} d x $$
A
$2 \log \left|\frac{\cos x-2}{\cos x-1}\right|+C$
B
$\log \left(\frac{(\cos x-2)^2}{(\cos x-1)^4}\right)+C$
C
$\log \left(\frac{(\cos x-2)^2}{|\cos x-1|}\right)+C$
D
$\log \left(\frac{(\cos x-2)^4}{(\cos x-1)^2}\right)+C$
3
AP EAPCET 2025 - 21st May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\int \frac{d x}{\sin ^3 x+\cos ^3 x}=A \log \left|\frac{\sqrt{2}+t}{\sqrt{2}-t}\right|+B \tan ^{-1}(t)+C$, then $\left(\frac{B}{A}, t\right)=$
A
$(3 \sqrt{2}, \sin x-\cos x)$
B
$(2 \sqrt{2}, \sin x-\cos x)$
C
$\left(\frac{\sqrt{2}}{3}, \sin x-\cos x\right)$
D
$\left(\frac{3}{\sqrt{2}}, \sin x+\cos x\right)$
4
AP EAPCET 2025 - 21st May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$$ \int_{\pi / 4}^{\pi / 3} \frac{\cos x-\sin x}{\sin 2 x} d x= $$
A
$\frac{1}{2} \log \left[\frac{(3+2 \sqrt{2})(2-\sqrt{3})}{\sqrt{3}}\right]$
B
$\frac{1}{2} \log \left[\frac{(3-2 \sqrt{2})(2+\sqrt{3})}{\sqrt{3}}\right]$
C
$\log \left[\frac{(3-2 \sqrt{2})(2-\sqrt{3})}{\sqrt{3}}\right]$
D
$\log \left[\frac{(3+2 \sqrt{2})(2-\sqrt{3})}{\sqrt{3}}\right]$
Paper Analysis
Total Questions
Chemistry 40
Mathematics 80
Physics 40
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