Chemistry
1. The uncertainty in the position of electron $(\Delta x)$ is approximately 100 pm . The uncertainty in momentum (in $\mat 2. Which of the following statements are correct?
I. The energy of hydrogen atom in its ground state is -13.6 eV .
II. On t 3. Which of the following orders is not correct about the property shown against it? 4. Consider the following changes I and II
$$ \mathrm{O}_2^{-} \underset{\text { II }}{\longleftarrow} \mathrm{O}_2 \xright 5. The increasing order of number of lone pair of electrons on the central atom of the following molecules is
(I) $\mathrm{ 6. $$ \text { Which of the following is correct for an ideal gas? } $$ 7. At 256 K , rms speed of $\mathrm{SO}_2$ gas molecules is $3.16 \times 10^2 \mathrm{~ms}^{-1}$. What is the most probable 8. 209 g of an element reacts with chlorine to form 315.5 g of its chloride. What is the weight (in g ) of oxygen that reac 9. Consider the following :
Statement I : During isothermal expansion of an ideal gas its enthalpy decreases.
Statement II 10. The energy required to increase the temperature of 180 g of liquid water from $10^{\circ} \mathrm{C}$ to $15^{\circ} \ma 11. At $25^{\circ} \mathrm{C}$, the percentage of ionisation of $x \mathrm{M}$ acetic acid is 4.242 . What is the pH of the 12. At 298 K , the value of $K_c$ for the following reaction is $x \mathrm{~mol} \mathrm{~L}^{-1}$.
What is the approximate 13. $\mathrm{H}_2 \mathrm{O}_2$ with $\mathrm{KMnO}_4$ in acidic medium gives a manganese compound ' $X$ ' and in basic medi 14. Which of the following orders are correct against the stated property?
I. $\mathrm{NaO}_2
II. $\mathrm{Mg}(\mathrm{OH})_ 15. In the structure of diborane, the number of 2-centre-2-electron bonds is $X$ and 3-centre-2-electron bonds is $Y$. The v 16. $$ \text { Match the following } $$
$$ \begin{array}{clll} \hline & \text { List-I (Compound) } & & \text { List-II (Use 17. Identify the air pollutant which in high concentration leads to stiffness of flower buds? 18. The number of primary $\left(1^{\circ}\right)$, secondary $\left(2^{\circ}\right)$ and tertiary $\left(3^{\circ}\right)$ 19. The catalyst used for the isomerisation of $n$-alkanes to branched chain alkanes is 20. An element crystallises in bcc lattice. The atomic radius of the element is $2.598 \mathop {\rm{A}}\limits^{\rm{o}}$. Wh 21. A centi molar solution of acetic acid is $50 \%$ dissociated at $27^{\circ} \mathrm{C}$. The osmotic pressure of the sol 22. At 300 K vapour pressure of a pure liquid. ' $A$ ' is 70 mm Hg . It forms an ideal solution with another liquid ' $B$ '. 23. The specific conductance of 0.05 M NaOH solution is $0.0115 \mathrm{~S} \mathrm{~cm}^{-1}$ What is its molar conductance 24. Consider the reaction given below
$$ A+2 B \longrightarrow 3 C+2 D $$
If rate of disappearance of $B$ is $x \times 10^{- 25. Identify the catalytic reaction in which both reactants are in different phases. 26. Consider the following.
Statement-I : Gold sol is prepared by Bredig's arc method.
Statement-II : Bredig's arc method in 27. $$ \text { Which of the following sets are correctly matched? } $$
$$ \begin{array}{cll} \hline & \text { Metal } & \tex 28. The oxides of nitrogen obtained by the reaction of nitric acid with (i) $\mathrm{P}_4 \mathrm{O}_{10'}$ (ii) $\mathrm{P} 29. $$ \text { Match the following } $$
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-s 30. The ion with $4 f^7$ configuration is 31. Which of the following is the common monomer for the polymers bakelite and melamine? 32. Activation energy for the hydrolysis of sucrose by acid is $X \mathrm{~kJ} \mathrm{~mol}^{-1}$ whereas activation energy 33. The structure of the nitrogen containing heterocyclic base given below represents 34. What is the drug used to control depression and hypertension? 35. What are $X$ and $Y$ respectively, in the following set of reactions? 36. In the following sequence of reactions, what is the end product $(D)$ ?
$$ \mathrm{C}_2 \mathrm{H}_5 \mathrm{Br} \xright 37. $$ \text { The most acidic carboxylic acid is } $$ 38. A carbonyl compound $X\left(\mathrm{C}_8 \mathrm{H}_8 \mathrm{O}\right)$ gives yellow precipitate with NaOI .
Hemiacetal 39. Which of the following does not involve in Friedel-Craft reaction? 40. Consider the following
Statement I : $\mathrm{CH}_3 \mathrm{NH}_2$ is more basic than $\mathrm{NH}_3$ but $\mathrm{C}_6
Mathematics
1. The set of real values of $x$ such that $f(x)=\sqrt{\frac{[x]-1}{\left.[x]^2-[x]-6\right]}}$ is a real valued function i 2. If a function $f: Z \rightarrow Z$ is defined by $f(x)=x-(-1)^x$, then $f(x)$ is 3. If $2 \cdot 5+5 \cdot 9+8 \cdot 13+11 \cdot 17+\ldots$ to $n$ terms $=a n^3+b n^2+c n+d$, then $a-b+c-d=$ 4. If $A=\left[\begin{array}{ccc}1 & 2 & -2 \\ 2 & -1 & 2 \\ -1 & 1 & -2\end{array}\right]$, then $A+2 A^{-1}=$ 5. If $A=\left[\begin{array}{ccc}a & b & c \\ d & e & f \\ l & m & n\end{array}\right]$ is a matrix such that $|A|>0$ and $ 6. In solving a system of linear equations $A X=B$ by Cramer's rule, in the usual notation, if $\Delta_1=\left|\begin{array 7. If $a=\operatorname{Im}\left(\frac{1+z^2}{2 i z}\right)$ and $z$ is any non-zero complex number such that $|z|=1$, then 8. If $(3+4 i)^{2025}=5^{2023}(x+i y)$, then $\sqrt{x^2+y^2}=$ 9. If $\left(\frac{\cos \theta+i \sin \theta}{\sin \theta+i \cos \theta}\right)^{2024}+\left(\frac{1+\cos \theta+i \sin \th 10. The roots $\alpha, \beta$ of the equation $x^2-6(k-1) x+4(k-2)=0$ are equal in magnitude but opposite in sign, if $\alph 11. If $a x^2+b x+c 12. If $a \pm i b$ and $b \pm a i$ are the roots of $x^4-10 x^3+50 x^2-130 x+169=0$, then $\frac{a}{b}+\frac{b}{a}=$ 13. If $x^2-5 x+6$ is a factor of $f(x)=x^4-17 x^3+k x^2-247 x+210$, then the other quadratic factor of $f(x)$ is 14. If all the letters of the word COMBINATION are arranged in all possible ways to form 11 letter words (with or without me 15. The number of ways of distributing 3 dozen fruits (no two fruits are identical) to 9 persons such that each gets the sam 16. If $\binom{p}{q}={ }^p C_q$ and $\sum\limits_{i=0}^m\binom{10}{i}\binom{20}{m-i}$ is maximum, then $m=$ 17. Coefficient of $x^2$ in the expansion of $\left(x^2+x-2\right)^5$ is 18. If $P_n$ denotes the product of the binomial coefficients in the expansion of $(1+x)^n$, then $\frac{P_{n+1}}{P_n}=$ 19. The coefficient of $x^3$ in the expansion of $\frac{x^4+1}{\left(x^2+1\right)(x-1)}$ when it is expressed in terms of po 20. $$ \begin{aligned} \frac{1}{\sin 1^{\circ} \sin 2^{\circ}}+\frac{1}{\sin 2^{\circ} \sin 3^{\circ}}+\frac{1}{\sin 3^{\cir 21. $$ \cos ^3 \frac{\pi}{8} \cos \frac{3 \pi}{8}+\sin ^3 \frac{\pi}{8} \sin \frac{3 \pi}{8}= $$ 22. If $A+B+C=\frac{\pi}{4}$, then $\sin 4 A+\sin 4 B+\sin 4 C=$ 23. Number of solutions of the equation $\cos \theta+\cos 2 \theta-\sqrt{3}(\sin \theta+\sin 2 \theta)+1=0$ lying in the int 24. If $x$ is a real number, then the number of solutions of $\tan ^{-1}(\sqrt{x(x+1)})+\sin ^{-1}\left(\sqrt{x^2+x+1}\right 25. Domain of the real valued function $f(x)=\log \left(x^2-1\right)+x \operatorname{coth}^{-1} x$ is 26. In a $\triangle A B C$, if $\sin \frac{A}{2}=\frac{1}{4} \sqrt{\frac{3}{5}}, a=2, c=5$ and $b$ is an integer, then the a 27. In a $\triangle A B C$ if $a+c=5 b$, then $\cot \frac{A}{2} \cot \frac{C}{2}=$ 28. In a $\triangle A B C$, if $r_1=3, r_2=4, r_3=6$, then $b=$ 29. Let the position vectors of the vertices of a $\triangle A B C$ be $\mathbf{a , b}, \mathbf{c}$. If on the plane of the 30. The point of intersection of the lines represented by $\mathbf{r}=(\hat{\mathbf{i}}-6 \hat{\mathbf{j}}+2 \hat{\mathbf{k} 31. $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are three vectors such that $|\mathbf{a}|=2,|\mathbf{b}|=3$, $|\mathbf{c}|=5,|\math 32. If the points $A, B, C, D$ with positions vectors $\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, \hat{\mathbf{i}}- 33. $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are unit vectors. If $\mathbf{a}, \mathbf{b}$ are perpendicular vectors, $(\mathbf{ 34. If the variance of the first $n$ natural numbers is 10 and the variance of the first $m$ even natural numbers is 16 , th 35. Given $f(x)=x^2-5 x+4$. Out of first 20 natural numbers, if a number $x$ is chosen at random, then the probability that 36. A problem in Algebra is given to two students $A$ and $B$ whose chances of solving it are $\frac{2}{5}$ and $\frac{3}{4} 37. Three dice are thrown simultaneously and the sum of the numbers appeared on them is noted. If $A$ is the event of gettin 38. A manufacturing company of bulbs has 3 units $A, B$ and $C$ which produce $25 \%, 35 \%$ and $40 \%$ of the bulbs respec 39. The probability distribution of a random variable $X$ is given below$$ \begin{array}{ccccccc} \hline X & 1 & 2 & 3 & 4 & 40. The probability that a student gets distinction in a Mathematics test is $\frac{2}{3}$. If five such tests are conducted 41. If $P$ is a variable point which is at a distance of 2 units. from the line $2 x-3 y+1=0$ and $\sqrt{13}$ units from the 42. If the equation $3 x^2+4 y^2-x y+k=0$ is the transformed equation of $3 x^2+4 y^2-x y-5 x-7 y+2=0$ after shifting the or 43. If the intercept of a straight line $L$ made between the straight lines $5 x-y-4=0$ and $3 x+4 y-4=0$ is bisected at the 44. $A$ line $L$ passes through the point $P(1,2)$ and makes an angle of $60^{\circ}$ with $O X$ in the positive direction. 45. The equation $(2 p-3) x^2+2 p x y-y^2=0$ represents a pair of distinct lines
46. The equation of a chord $A B$ of an ellipse $2 x^2+y^2=1$ is $x-y+1=0$. If $O$ is the origin, then $\sqrt{A O B}=$ 47. If a circle $S$ passes through the origin and makes an intercept of length 4 units on the line $x=2$, then the equation 48. A circle touches the line $2 x+y-10=0$ at $(3,4)$ and passes through the point $(1,-2)$. Then, a point that lies on the 49. If $(a, b)$ is the common point for the circles $x^2+y^2-4 x+4 y-1=0$ and $x^2+y^2+2 x-4 y+1=0$, then $a^2+b^2=$ 50. The angle between the tangents drawn from the point $(2,2)$ to the circle $x^2+y^2+4 x+4 y+c=0$ is $\cos ^{-1}\left(\fra 51. If the circle $S=x^2+y^2+2 g x+4 y+1=0$ bisects the circumference of the circle $x^2+y^2-2 x-3=0$, then the radius of ci 52. The angle between the tangents drawn from the point $(1,4)$ to the parabola $y^2=4 x$ is
53. The square of the slope of a common tangent drawn to the circle $4 x^2+4 y^2=25$ and the ellipse $4 x^2+9 y^2=36$ is 54. The tangents drawn to the hyperbola $5 x^2-9 y^2=90$ through a variable point $P$ make the angles $\alpha$ and $\beta$ w 55. If $\theta$ is the acute angle between the asymptotes of a hyperbola $7 x^2-9 y^2=63$, then $\cos \theta=$ 56. If $O(0,0,0), A(1,2,1), B(2,1,3)$ and $C(-1,1,2)$ are the vertices of a tetrahedron, then the acute angle between its fa 57. If the angles between the sides of the $\triangle A B C$ formed by $A(2,3,5), B(-1,3,2)$ and $C(3,5,-2)$ are $\alpha, \b 58. If the four points $(6,2,4),(1,3,5),(1,-2,3)$ and $(6, k, 2)$ are coplanar, then $k=$ 59. $$ \mathop {\lim }\limits_{x \to - \infty } \frac{5 x^3-x^2 \sin 5 x}{x \cos 4 x+7|x|^3-4|x|+3}= $$
60. If $\mathop {\lim }\limits_{x \to {a^ + }} f(x)=p, \mathop {\lim }\limits_{x \to {a^ - }} f(x)=m$ and $f(a)=k$, then whi 61. If a function $f$ defined by
$$ f(x)=\left\{\begin{array}{cc} \frac{1-\cos 4 x}{x^2}, & x
is continuous at $x=0$, then $ 62. If $y=\tanh ^{-1} \sqrt{\frac{1-x}{1+x}}$, then $\frac{d y}{d x}=$ 63. If $x^2+y^2=t-\frac{1}{t}$ and $x^4+y^4=t^2+\frac{1}{t^2}$, then $\frac{d y}{d x}=$ 64. If $y=(a x+b) \cos x$, then
$$ y_2+y_1 \sin 2 x+y\left(1+\sin ^2 x\right)= $$ 65. If the normal drawn at the point $P$ on the curve $y=x \log x$ is parallel to the line $2 x-2 y=3$, then $P=$ 66. If the curves $y^2=16 x$ and $9 x^2+\alpha y^2=25$ intersect at right angles, then $\alpha=$ 67. If the function $y=\sin x(1+\cos x)$ is defined in the interval $[-\pi, \pi]$, then $y$ is strictly increasing in the in 68. If the velocity of a particle moving on a straight line is proportional to the cube root of its displacement, then its a 69. If $\int e^{\sin x}(1+\sec x \tan x) d x=e^{\sin x} f(x)+c$, then in $0 \leq x \leq 2 \pi$, then number of solutions of 70. If $\int \frac{d x}{(x-1)^{\frac{3}{2}}(x-3)^{\frac{1}{2}}}=\sqrt{f(x)}+C$, then $f(-1)-f(0)=$ 71. $$ \int \frac{x}{\left(1-x^2\right) \sqrt{2-x^2}} d x= $$ 72. $\int\left(\frac{1+x+\sqrt{x+x^2}}{\sqrt{x}+\sqrt{1+x}}\right) d x=$ 73. If $\int x^2 \cos ^2 x d x=\frac{1}{6} f(x)+g(x) \sin 2 x +h(x) \cos 2 x+c$, then $f(1)+g(2)+h\left(\frac{1}{2}\right)=$ 74. $$ \int_0^{\frac{\pi}{2}} \log |\tan x+\cot x| d x= $$ 75. $$ \int_0^\pi x \cdot \sin ^5 x \cdot \cos ^6 x d x= $$ 76. $$ \int_{\frac{1}{2}}^{\frac{1}{\sqrt{2}}} \frac{1}{\left(x+\sqrt{1-x^2}\right)\left(1-x^2\right)} d x= $$ 77. The area of the region (in sq. units) enclosed between the curves $y=|x|, y=[x]$ and the ordinates $x=-1$, $x=0, x=1$ is 78. The general solution of the differential equation $\frac{d y}{d x}+x y=4 x-2 y+8$ is 79. The general solution of the differential equation $\left(x+2 y^3\right) \frac{d y}{d x}-y=0, y>0$ is 80. The general solution of the differential equation $\frac{d y}{d x}+\frac{x+y+1}{x-3 y+5}=0$ is
Physics
1. If the maximum and minimum temperatures at a place on a day are measured as $44^{\circ} \mathrm{C} \pm 0.5^{\circ} \math 2. If a ball projected vertically upwards with certain initial velocity from the ground crosses a point at a height of 25 m 3. If a particle of mass ' $m$ ' covers half of the horizontal circle with constant speed ' $v$ ', then the change in its k 4. A car is moving with a velocity of $4 \mathrm{~ms}^{-1}$ towards east. After a time of 4 s , if it is heading north-east 5. A body of mass 5 kg starts from the origin with an initial velocity $(30 \hat{\mathbf{i}}+40 \hat{\mathbf{j}}) \mathrm{m 6. A block of mass 10 kg moving with a speed of $5 \hat{\mathrm{i}} \mathrm{ms}^{-1}$ on a frictionless horizontal surface 7. The bob of a simple pendulum of length 200 cm is released from horizontal position. If $10 \%$ of its initial energy is 8. A steel sphere of radius 1.2 cm collides a second steel sphere at rest. If the collision is elastic and after the collis 9. Ratio of angular velocity of hour hand of a watch and the angular velocity of rotation of Earth is 10. If two bodies of masses 2 kg and 3 kg are moving at right angles with velocities $20 \mathrm{~ms}^{-1}$ and $10 \mathrm{ 11. The kinetic energy of a particle executing simple harmonic motion at a displacement of 3 cm from the mean position is 4 12. A body of mass 1 kg is attached to the lower end of a vertically suspended spring of force constant $600 \mathrm{~N}-\ma 13. If the angular velocity of a planet about its axis is halved, the distance of the stationary satellite of this planet fr 14. When a wire of length ' $L$ ' clamped at one end is pulled by a force ' $F$ ' from the other end, its length increases b 15. A liquid drop of diameter $D$ splits into 3375 small identical drops. If $S$ is the surface tension of the liquid, then 16. When a sphere is taken to the bottom of a sea of depth 1 km , it contracts in volume by $0.01 \%$, then the Bulk modulus 17. If a gas of volume 400 cc at an initial pressure $p$ is suddenly compressed to 100 cc , then its final pressure is
(The 18.
A Carnot engine having efficiency $60 \%$ receives heat from a source at a temperature 600 K . For the same sink temper 19. A gaseous mixture consists of 2 moles of oxygen and 4 moles of argon at an absolute temperature $T$. Neglecting all vibr 20. The average translational kinetic energy of the oxygen molecules at a temperature of $127^{\circ} \mathrm{C}$ is
(Boltzm 21. The speed of a stationary wave represented by the equation
$$ y=0.7 \sin \left(\frac{7 \pi}{4} x\right) \cos (350 \pi t) 22. Two thin convex lenses are kept in contact coaxially. If the focal length of the combination of the lenses is 4 cm and s 23. For an observer on the Earth, if a spectral line of wavelength $6600\mathop {\rm{A}}\limits^{\rm{o}}$ emitted by a star 24. Three particles of each charge $q$ are placed at the vertices of an equilateral triangle of side $L$. The work to be don 25. The radii of the inner and outer spheres of a spherical capacitor are 8 cm and 9 cm respectively. The outer sphere is ea 26. If 27 charged water droplets, each of radius $10^{-3} \mathrm{~m}$ and charge $10^{-12} \mathrm{C}$ coalesce to form a s 27. A straight wire of resistance $18 \Omega$ is bent in the form of an equilateral triangular loop. The effective resistanc 28. The power dissipated by a uniform wire of resistance $100 \Omega$ when a potential difference of 120 V is applied across 29. If a straight current carrying wire of linear density $0.12 \mathrm{~kg} \mathrm{~m}^{-1}$ is suspended in mid air by a 30. Two concentric loops $A$ and $B$ of same radius $2 \pi \mathrm{~cm}$ are placed at right angles to each other. If the cu 31. A short bar magnet is placed in a uniform magnetic field of 2 T such that the axis of the magnet makes an angle of $45^{ 32. A horizontal telegraph wire of length 30 m spread east to west fell down freely from a height of 20 m . If the resistanc 33. In an LCR series circuit, if the potential differences across inductor, capacitor and resistor are $60 \mathrm{~V}, 30 \ 34. A plane electromagnetic wave of frequency 25 MHz propagates in vacuum along positive $x$-direction. At a particular poin 35. A particle of mass $8 \mu \mathrm{~g}$ in motion collides with another stationary particle of mass $4 \mu \mathrm{~g}$. 36. The difference between the frequencies of the first and second Lyman lines of hydrogen atom is ( $R=$ Rydberg constant a 37. If the half-life of a radioactive element is 12.5 hours, then the time taken to disintegrate 256 g of the substance into 38. A transistor works as an amplifier when 39. If five logic gates are connected as shown in the figure, then the values of $y_1, y_2$ and $y_3$, are respectively 40. In amplitude modulation of waves, the maximum amplitude is 30 mV and minimum amplitude is 5 mV , then the modulation ind
1
AP EAPCET 2025 - 21st May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $y=\tanh ^{-1} \sqrt{\frac{1-x}{1+x}}$, then $\frac{d y}{d x}=$
A
$-\frac{1}{2 \sqrt{1-x^2}}$
B
$\frac{-1}{2 x \sqrt{1-x^2}}$
C
$\frac{2}{1+x^2}$
D
$\frac{1}{2 x \sqrt{1+x^2}}$
2
AP EAPCET 2025 - 21st May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $x^2+y^2=t-\frac{1}{t}$ and $x^4+y^4=t^2+\frac{1}{t^2}$, then $\frac{d y}{d x}=$
A
$\frac{y}{x}$
B
$\frac{y^2}{x^2}$
C
$\sqrt{\frac{y}{x}}$
D
$-\frac{y}{x}$
3
AP EAPCET 2025 - 21st May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $y=(a x+b) \cos x$, then
$$ y_2+y_1 \sin 2 x+y\left(1+\sin ^2 x\right)= $$
A
$y_2 \cos ^2 x$
B
$y_2 \sin ^2 x$
C
$y_1 \sin ^2 x$
D
$y \sin ^2 x$
4
AP EAPCET 2025 - 21st May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If the normal drawn at the point $P$ on the curve $y=x \log x$ is parallel to the line $2 x-2 y=3$, then $P=$
A
$(e, e)$
B
$\left(\frac{1}{e}, \frac{-1}{e}\right)$
C
$\left(\frac{1}{e^2}, \frac{-2}{e^2}\right)$
D
$\left(e^3, 3 e^3\right)$
Paper Analysis
Total Questions
Chemistry 40
Mathematics 80
Physics 40
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