Chemistry
1. The radius of fourth orbit in $\mathrm{He}^{+}$ion is ' $R_1{ }^{\prime} \mathrm{pm}$ and radius of third orbit in $\mat 2. The de-Broglie wavelengths of two fast moving particles $X, Y$ are $1 \mathrm{~nm}, 3 \mathrm{~nm}$ respectively. Mass o 3. Electronic configurations of four elements $A, B, C, D$ are given below
(A) $1 s^2 2 s^2 2 p^6 3 s^1$
(B) $1 s^2 2 s^2 2 4. A molecules has T -shape. The total number of electron pairs in the valence shell of central atom of it is 5. The sum of bond order values of $\mathrm{C}_2$ and $\mathrm{O}_2^{2+}$ is $x$, which is equal to sum of bond order value 6. At $27^{\circ} \mathrm{C}$ kinetic energy of 4 g of $\mathrm{H}_2$ is $x \mathrm{~J}$. What is the kinetic energy (in J 7. At $T(\mathrm{~K})$, hydrogen and oxygen gases are mixed in the ratio of $1: 2$ by mass in a closed vessel of volume ' $ 8. Which one of the following reactions is not feasible? 9. For which reaction $\Delta H \neq \Delta U ?$
10. At $298 \mathrm{~K}, \Delta_r U^{\ominus}$ and $\Delta_r S^{\ominus}$ for the following reaction are -10.5 kJ and $+44.1 11. Consider the following gaseous equilibrium reactions (I), (II) and (III) with equilibrium constants $K_1, K_2$ and $K_3$ 12. When 30 mL of $0.2 \mathrm{M} \mathrm{NH}_4 \mathrm{OH}$ is added to 30 mL of $2 \mathrm{M} \mathrm{NH}_4 \mathrm{Cl}$ s 13. Which set of elements form electron precise hydrides?
14. The correct order of density of $\mathrm{Be}, \mathrm{Mg}, \mathrm{Ca}, \mathrm{Sr}$ is
15. Identify the reaction in which diborane is produced on industrial scale? 16. Which of the following properties is not correct for silicones?
17. $$ \text { Match the following } $$
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border- 18. The element whose percentage composition in an organic compound can be determined by Carius method is
19. ' $x$ ' mg of an organic compound was analysed by Kjeldahl method. The ammonia evolved was absorbed in 50 mL of $0.5 \ma 20. The composition of a sample of wustite is $\mathrm{Fe}_{0.93} \mathrm{O}_{1.00}$. Percentage of iron in the form of $\ma 21. A solution of urea in water has a boiling point or $100.18^{\circ} \mathrm{C}$. What is the freezing point of the same s 22. At $T(\mathrm{~K})$, the vapour pressure of pure benzene and toluene are 75 and 22 mm Hg respectively. 23.4 g of benzene 23. At 298 K , the following reaction takes place for a cell at the hydrogen electrode
$$ \mathrm{H}^{+}(a q)+e^{-} \longrig 24. $A \rightarrow B$ is a first order reaction. The concentration of $A$ is decreased from $x \mathrm{~mol} \mathrm{~L}^{-1 25. The adsorption of a gas on a solid surface follows Freundlich adsorption isotherm.
At $T(\mathrm{~K})$, the gas pressure 26. Which one of the following acts as autocatalyst during titration of $\mathrm{KMnO}_4$ and oxalic acid in presence of dil 27. Consider the following.
Statement-I In the extraction of Al by Hall-Heroult process, pure $\mathrm{Al}_2 \mathrm{O}_3$ m 28. Which of the following is not correct? 29. The amphoteric oxide of vanadium ( V ) reacts with alkali and forms an oxo ion ' $X$ ' and with acid forms an oxo ion $Y 30. In which one of the following complexes the metal ion has $t_{2 g}^3 e_g^2$ configuration? 31. $$ \text { Match the following. } $$
Correct answer is 32. Consider the following
Statement-I Primary structure of protein represents its constitution.
Statement-II $\alpha$-Helix 33. The structure of the product ' $Z$ ' in the reaction sequence is 34. $$ \text { Match the following. } $$
$$ \begin{array}{llll} \hline & \text { List-I (Drugs) } & & \text { List-II (Effec 35. The reaction of benzene diazonium chloride with Cu and HCl is known as 36. Identify the correct set from the following
37. In the given reaction sequence, conversion of $X$ to $Y$ is an example of 38. IUPAC names of mesityl oxide and oxalic acid are respectively.
39. Which one of the following compounds does not give benzoic acid when treated with alkaline $\mathrm{KMnO}_4$ ?
40. The sequence of reagents required to convert aniline to benzoic acid is
Mathematics
1. The range of the real valued function $f(x)=\cos ^{-1}\left(\frac{3}{\sqrt{9 x^2-12 x+22}}\right)$ is 2. $$ \text { Consider the following statements. } $$
$$ \begin{array}{cl} \hline \text { Statement I } & \begin{array}{l} 3. If $t_n=\frac{1}{4}(n+2)(n+3), n \in N$, then which one of the following is true?
Assertion (A) $\frac{1}{t_1}+\frac{1}{ 4. $A=\left[\begin{array}{ccc}0 & k & k \\ k & -4 & -6 \\ k & -3 & -5\end{array}\right]$ is a singular matrix for
5. If $A=\left[\begin{array}{ccc}1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6\end{array}\right]$ and the rank of $A$ is 2 , then t 6. $$ \left|\begin{array}{ll} 2 & 1 \\ 3 & 1 \end{array}\right|+\left|\begin{array}{cc} 1 & \frac{1}{3} \\ 3 & 1 \end{array 7. For any two non-zero complex numbers $z_1$ and $z_2$, if $\left|z_1+z_2\right|^2=\left|z_1\right|^2+\left|z_2\right|^2$, 8. If $1, \omega, \omega^2$ are the cube roots of unity, then
$$ 1\left(2+\frac{1}{\omega}\right)\left(2+\frac{1}{\omega^2} 9. $$ (1+\sqrt{3} i)^6-(\sqrt{3}+i)^6= $$ 10. If $\alpha, \beta$ are the roots of the equation $x^2+b x+c=0$ satisfying the conditions $\alpha+\beta=5$ and $\alpha^3+ 11. If $\frac{1}{2} \leq \frac{x^2+x+a}{x^2-x+a} \leq 2 \forall x \in R$, then $a=$ 12. If $\alpha, \beta, \gamma$ are the roots of the equation,
$$ \begin{aligned} & x^3+a x^2+b x+c=0, \text { then }(\alpha+ 13. If the sum of two roots of the equation $x^4+2 x^3-7 x^2-8 x+12=0$ is zero, then the sum of the squares of the other two 14. If 3 sisters and 8 brothers are together playing a game, then the number of ways in which all the sisters and brothers a 15. Out of 8 students in a classroom, 4 of them are chosen and they are arranged around a table.
If the remaining 4 are arra 16. The sum of all integers between 1 and 100 (both inclusive) which are divisible by 5 or 13 is 17. If the coefficients of $x^{10}$ and $x^{11}$ in the expansion of $\left(1+\alpha x+\beta x^2\right)(1+x)^{11}$ are 396 a 18. If $-\frac{2}{3} 19. If $x>\sqrt{3}$ and $\frac{x^2+1}{\left(x^2+2\right)\left(x^2+3\right)}$ is expanded in terms of powers of $x$, then the 20. If $\alpha$ is the maximum value and $\beta$ is the minimum value of $\cos ^2 \frac{x}{4}+\sin \frac{x}{4}, x \in R$, th 21. If $A$ and $B$ are positive acute angles satisfying $3 \cos ^2 A+2 \cos ^2 B=4$ and $\frac{3 \sin A}{\sin B}=\frac{2 \co 22. If $\sin x-\sin y=\frac{27}{65}$ and $\cos x-\cos y=\frac{-21}{65}$, then $\sin (x+y)=$ 23. The number of solutions of the equation $\sec x \cdot \cos 5 x+1=0$ in the interval $[0,2 \pi]$ is 24. If the equation $2 \cot ^{-1}\left(x^2+2 x+k\right)=\pi-3 \tan ^{-1} \left(x^2+2 x+k\right)$ has two distinct real solut 25. $$ \sec h^{-1}(\sin \alpha)= $$ 26. In $\triangle A B C$ if $\cos A \cos B+\sin A \sin B \sin C=1$, then $\sin A+\sin B+\sin C=$ 27. In $\triangle A B C$, if $a: b: c=4: 5: 6$, then $\frac{\cos A+3 \cos C}{\cos B}=$
28. In $\triangle A B C$, if $a=6, b=8$ and $c=10$, then $\frac{2 r_2 r_3}{r r_1}=$ 29. If the vectors $2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+l \hat{\mathbf{k}},-3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}-4 l \hat 30. A unit vector that is perpendicular to the vector $2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and coplanar 31. If the vectors $2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \hat{\mathbf{i}}+4 \hat{\mathbf{j}}+\hat{\mathbf 32. If the magnitudes of $\mathbf{a}, \mathbf{b}$ and $\mathbf{a}+\mathbf{b}$ are respectively 3,4 and 5 , then the magnitud 33. If $\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}},-\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\math 34. The mean and variance of the observations $x_1, x_2, x_3 \ldots x_{15}$ are respectively 2 and 4 . If the mean and varia 35. If 3 squares are chosen at random from the 64 squares of a chess board, then the probability that all of them lie along 36. Three letters are chosen at random from the letters of the word VARIABLE and all possible three letter words (with or wi 37. In a shoe rack there are 4 pairs of shoes and 4 shoes. are drawn one after the other at random without replacement. Then 38. A rational number is selected at random from the distinct rational numbers of the form $p / q$ formed with $p$ and $q$ b 39. The probability distribution of a discrete random variable $X$ is given below
$$ \begin{array}{lllll} \hline X=x & -1 & 40. If the average number of accidents occurring at a particular junction on a highway in a week is 5 , then the probability 41. Let $A(5,4)$ and $B(5,-4)$ be two points.
If $P$ is a point in the coordinate plane such that $\sqrt{A P B}=\frac{\pi}{4 42. When the axes are rotated through an angle $\theta$ about origin in anti-clockwise direction and then translated to the 43. If the perpendicular distances from the points $(2,3)$, $(4, a)$ and $(\alpha, \beta)$ on to the line $3 x+4 y-3=0$ are 44. The equation of the base of an equilateral triangle is $x+y=2$ and its opposite vertex is $(2,1)$. If $m_1, m_2$ are the 45. The triangle formed by the lines $2 x^2+x y-6 y^2=0$ and $x+y-1=0$ is 46. If $\left(\frac{2}{3}, 0\right)$ is the centroid of the triangle formed by the lines $4 x^2-y^2=0$ and $l x+m y+n=0$, th 47. From a point $P(-4,0)$, two tangents are drawn to the circle $x^2+y^2-4 x-6 y-12=0$ touching the circle at $A$ and $B$. 48. If the equation of the polar of the point $(\alpha,-1)$ with respect to the circle $x^2+y^2-4 x-6 y-12=0$ is $y=\beta$, 49. If $\theta$ is the angle between the tangents drawn from the point $(-1,-1)$ to the circle $x^2+y^2-4 x-6 y+c=0$ and $\c 50. If the power of the point $(1,6)$ with respect to the circle $x^2+y^2+4 x-6 y-a=0$ is -16 , then $a=$ 51. The radius of the circle passing through the points of intersection of the circles $x^2+y^2+2 x+4 y+1=0$, $x^2+y^2-2 x-4 52. The lengths of the two focal chords of the parabola $y^2=16 x$ is 25 units each. If these two chords cut the parabola at 53. If the tangents drawn from a point $P$ to the ellipse $4 x^2+9 y^2-16 x+54 y+61=0$ are perpendicular, then the locus of 54. $x+y+3=0,2 x-y+1=0$ are the equations of the asymptotes of a hyperbola.
If $(1,-2)$ is a point on this hyperbola, then t 55. If $\theta$ is the acute angle between the tangents drawn from the point $(1,1)$ to the hyperbola $4 x^2-5 y^2-20=0$, th 56. If $A(2,-1,1), B(2,5,1)$ and $C(0,-2,3)$ are the vertices of a triangle. If $D$ is the point of intersection of the side 57. A line segment $P Q$ has the length 63 and direction ratios $(3,-2,6)$. If this line makes an obtuse angle with $X$-axis 58. A plane $\pi$ given by $a x+b y+11 z+d=0$ is perpendicular to the planes $2 x-3 y+z=4$, $3 x+y-z=5$ and the perpendicula 59. The quadratic equation whose roots are $l=\lim\limits_{\theta \rightarrow 0}\left(\frac{3 \sin \theta-4 \sin ^3 \theta}{ 60. $$ \mathop {\lim }\limits_{x \to \infty } \frac{3 x+4 \cos ^2 x}{\sqrt{x^2-5 \sin ^2 x}}= $$
61. If a function,
$$ f(x)=\left\{\begin{array}{cc} \frac{\sqrt[3]{1+a x^2+b x^3}-\sqrt[3]{1-a x^2-b x^3}}{x^2}, & x0 \end{a 62. If $y=\log \left(\sec \left(\tan ^{-1} x\right)\right)(x>0)$, then $\frac{d y}{d x}$ at $x=1$ is 63. If $y=\sin ^{-1} \frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}$ and $\frac{-3 \pi}{2} 64. If $x=\sqrt{2} e^t(\sin t-\cos t)$ and $y=\sqrt{2} e^t(\sin t+\cos t)$, then $\left(\frac{d^2 y}{d x^2}\right)_{t=\frac{ 65. $P$ and $Q$ are the ends of a diameter of the circle $x^2+y^2=a^2\left(a>\frac{1}{\sqrt{2}}\right) . s$ and $t$ are the 66. Let $P(x)=x^4+a x^3+b x^2+c x+d$ be such that $x=0$ is the only real root of $P^1(x)=0$. If $P(-1) 67. If the volume of a sphere is increasing at the rate of 12 c.c. $/ \mathrm{sec}$, then the rate (in $\mathrm{sq} . \mathr 68. If the lengths of the tangent, subtangent, normal and subnormal for the curve $y=x^2+x-1$ at the point $(1,1)$ are $a, b 69. $$ \int \frac{x+1}{x^3-1} d x= $$ 70. $$ \int \frac{x^4-16 x^2+2 x+8}{x^3-4 x^2+2} d x= $$ 71. $$ \int \frac{\sec ^2 x}{(\sec x+\tan x)^{\frac{5}{2}}} d x= $$ 72. $$ \int \frac{1}{\cos x}\left[\frac{1}{\sin x}-\frac{1}{\sin x+3 \cos x}\right] d x= $$ 73. $$ \int \cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right) d x= $$ 74. $$ \int_0^x \frac{t^2}{\sqrt{a^2+t^2}} d t= $$ 75. The area (in sq. units) of the region bounded by the lines $x=0, x=\frac{\pi}{2}$ and $f(x)=\sin x, g(x)=\cos x$ is
76. $$ \int_{\frac{5}{6}}^\pi \cos ^{-4} x d x= $$ 77. $$ \int\limits_0^{\frac{3 \pi}{2}} \frac{\cos ^3 x}{\cos ^3 x+\sin ^3 x} d x= $$ 78. The general solution of the differential equation $\sec (x-y+1) d y=d x$ is 79. The differential equation for which $y^2=4 a(x+a)$ ( $a$ is the parameter) is the general solution is
80. The general solution of the differential equation $\frac{d y}{d x}=\frac{2 x y-4 x+y-2}{2 x y+x-4 y-2}$ is
Physics
1. Of the following, the pair of physical quantities not having the same dimensional formula is 2. If the distance travelled by a freely falling body in the last but one second of its motion is 5 m , then the last secon 3. The angle of projection of a projectile whose path is shown in the given figure is 4. If the equation of motion of a projectile is $y=A x-B x^2$, then the ratio of the maximum height reached and the range o 5. A wire of length 2.5 m is fixed at one end and a box of mass 4 kg is tied at the other end. If the wire rotates in a hor 6. If the tension in the horizontal wire shown in the figure is 30 N , then the weight $W$ and tension in the wire $O A$ ar 7. A car of mass 2000 kg is accelerating from rest. If its engine is supplying constant power of 10 kW , then the velocity 8. A body of mass ' $M$ ' is moving with a uniform speed of ' $V^{\prime}$ on a frictionless horizontal surface under the i 9. Radius of gyration of a thin uniform rod of length ' $L$ ' about an axis passing through its centre and perpendicular to 10. A thin circular ring and a circular disc of equal mass are rolling without sliding. If their linear velocities are equal 11. A body of mass 4 kg attached to a spring of force constant $64 \mathrm{Nm}^{-1}$ executes simple harmonic motion on a fr 12. A particle is executing simple harmonic motion with amplitude $A$. At a distance ' $x$ ' from the mean position, when th 13. A mass of $6 \times 10^{24} \mathrm{~kg}$ is to be compressed in the form of a solid sphere such that the escape velocit 14. If the pressure on a body is increased from 200 kPa to 250 kPa , the volume of the body decreases by $0.25 \%$. The comp 15. A mercury drop of radius 1 cm is divided into $10^6$ droplets of equal size. If surface tension of mercury is $35 \times 16. Steam at $100^{\circ} \mathrm{C}$ is passed into 114 g of water at $30^o$ The mass of water present in the mixture when 17. In a Carnot engine if the work done during isothermal expansion is $25 \%$ more than the work done during isothermal com 18. The work done to increase the volume of 2 moles of an ideal gas from V to 2 V at a constant temperature $T$ is W . The w 19. If the given graph shows the logarithmic values of pressure ( $p$ ) and volume ( $V$ ) of an ideal gas, then the ratio o 20. The internal energy of one mole of a rigid diatomic gas at absolute temperature $T$ is 21. In a closed organ pipe, the number of nodes formed in fifth and ninth harmonics are respectively 22. A light ray falls on a rectangular glass slab as shown in the figure. If total internal reflection occurs at the vertica 23. In Young's double slit experiment, the distance between the slits is 0.2 cm , the distance between the screen and the sl 24. A particle of mass 0.2 g and charge 2 C is released from rest in a uniform electric field of $20 \mathrm{NC}^{-1}$. The 25. If 27 indentical charged conducting spheres each of capacitance $10 \mu \mathrm{~F}$ combine to form a big sphere, then 26. The capacitance of a spherical capacitor is 100 pF . If the spacing between the two spheres is 1 cm , then the radius of 27. A wire of resistance ' $R$ ' is bent in the form of a circular loop. Two points on the circle seperated by a quarter cir 28. When a wire is connected in the left gap of a metre bridge, the balancing point is at 40 cm from the left end of the bri 29. If a charged particle enters a uniform magnetic field normally with certain velocity, then the time period of revolution 30. A long straight wire of circular cross-section of radius ' $a$ ' is carrying a steady current. The current is distribute 31. Materials suitable for permanent magnets should have
32. If a wheel with 24 metallic spokes each 40 cm long is rotated with a speed of $180 \mathrm{rev} / \mathrm{min}$ in a pla 33. If a resistor of resistance $4 \Omega$, a capacitor of capacitive reactance $6 \Omega$ and an inductor of inductive reac 34. The ratio of the magnitudes of the electric field and $10^8$ times the magnetic field of a plane electromagnetic wave is 35. If a proton and an alpha particle are accelerated through the same potential difference, then the ratio of their de-Brog 36. Of the following, Bohr's atomic model is applicable to 37. The ratio of the orders of the spacings of nuclear energy levels and atomic energy levels is 38. The voltage gain and the current amplification factor of a transistor in common emitter configuration are 300 and 60 res 39. The logic gate equivalent to the circuit shown in the figure is 40. If the maximum and minimum amplitudes of a modulated wave are 25 V and 5 V respectively, then the modulation index is
1
AP EAPCET 2025 - 23rd May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$$ \int \frac{1}{\cos x}\left[\frac{1}{\sin x}-\frac{1}{\sin x+3 \cos x}\right] d x= $$
A
$\frac{1}{3} \log \left|\frac{\sin x}{\sin x+3 \cos x}\right|+C$
B
$\log \left|\frac{\cos x}{\sin x+3 \cos x}\right|+c$
C
$\frac{1}{3} \log \left|\frac{\cos x}{\sin x+3 \cos x}\right|+C$
D
$\log \left|\frac{\sin x}{\sin x+3 \cos x}\right|+c$
2
AP EAPCET 2025 - 23rd May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$$ \int \cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right) d x= $$
A
$2\left[x \tan ^{-1} x-\log \sqrt{1+x^2}\right]+C$
B
$2 x \tan ^{-1} x+\log \sqrt{1+x^2}+C$
C
$x \tan ^{-1} x+\log \sqrt{1-x^2}+C$
D
$2\left[\tan ^{-1} x-\log \sqrt{1+x^2}\right]+C$
3
AP EAPCET 2025 - 23rd May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$$ \int_0^x \frac{t^2}{\sqrt{a^2+t^2}} d t= $$
A
$\frac{x}{2} \sqrt{a^2+x^2}+\log \left|x+\sqrt{a^2+x^2}\right|$
B
$\sqrt{a^2+x^2}-a^2 \sinh ^{-1} \frac{x}{a}$
C
$\frac{x}{2} \sqrt{a^2+x^2}+\frac{a^2}{4} \log \left|x+\sqrt{a^2+x^2}\right|$
D
$\frac{x}{2} \sqrt{a^2+x^2}-\frac{a^2}{2} \sinh ^{-1} \frac{x}{a}$
4
AP EAPCET 2025 - 23rd May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The area (in sq. units) of the region bounded by the lines $x=0, x=\frac{\pi}{2}$ and $f(x)=\sin x, g(x)=\cos x$ is
A
$2(\sqrt{2}-1)$
B
$2(\sqrt{2}+1)$
C
$2(\sqrt{3}-1)$
D
$3 \sqrt{2}+1$
Paper Analysis
Total Questions
Chemistry 40
Mathematics 80
Physics 40
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