Chemistry
1. The wavelength of a particular electron transition for $\mathrm{He}^{+}$is 100 nm . The wavelength (in $\AA$ ) of H atom 2. The energy of second Bohr orbit of hydrogen atom is -3.4 eV . The energy of the fourth Bohr orbit of the $\mathrm{He}^{+ 3. $$ \text { Observe the following data : } $$
$$ \begin{array}{lllll} \hline \text { Ion } & Q^{a+} & X^{b+} & Y^{c+} & Z 4. $$ \text { Which of the following sets are correctly matched? } $$
$$ \begin{array}{llll} \hline & \text { Molecule } & 5. The order of dipole moments of $\mathrm{H}_2 \mathrm{O}(A), \mathrm{CHCl}_3(B)$ and $\mathrm{NH}_3(C)$ is
6. Identify the correct graph for an ideal gas $(y$-axis $=$ compressibility factor, $Z: x$-axis $=$ pressure, $p)$ 7. Identify the correct statements from the following:
I. Glass is an extremely viscous liquid.
II. Increase in temperature 8. Identify the correct statements about the following stoichiometric equation.
$$ a \mathrm{P}_4+b^{-} \mathrm{OH}+c \math 9. 5 moles of a gas is allowed to pass through a series of changes as shown in the graph, in a cyclic process. The processe 10. 1 mole of an ideal gas is allowed to expand isothermally and reversibly from $\mathrm{1L}$ to 5 L at 300 K . The change 11. Consider the following equilibrium reaction in gaseous state at $T(\mathrm{~K})$.
$$ A+2 B \rightleftharpoons 2 C+D $$
T 12. At $T(\mathrm{~K}) K_{\mathrm{sp}}$ of two ionic salts $M X_2$ and $M X$ is $5 \times 10^{-13}$ and $1.6 \times 10^{-11} 13. Consider the following.
Statement $\mathrm{IH}_2 \mathrm{O}_2$ acts as an oxidising as well as reducing agent in both ac 14. Identify the correct statements from the following.
I. All alkaline earth metals give hydrides on heating with hydrogen. 15. Select the correct statements from the following
(A) Aluminium liberates $\mathrm{H}_2$ gas with dil. HCl but not with a 16. The number of amphoteric oxides from the following is $\mathrm{CO}_2, \mathrm{GeO}_2, \mathrm{SnO}_2, \mathrm{PbO}_2$, $ 17. Which of the following statements is not correct?
18. Consider the sets I, II and III. Identify the set(s) which is (are) correctly matched.
I. Staggered ethane > eclipsed 19. What are $B$ and $C$ respectively in the following set of reactions?
20. The crystal system with edge lengths $a \neq b \neq c$ and axial angles $\alpha=\beta=\gamma=90^{\circ}$ is ' $x$ ' and 21. A solution is prepared by adding 124 g of ethylene glycol (molar mass $=62 \mathrm{~g} \mathrm{~mol}^{-1}$ ) to $x \math 22. The following graph is obtained for an ideal solution containing a non-volatile solute $x$-and $y$-axis represent, respe 23. Observe the following statements about dry cell
I. It is a primary battery.
II. Zinc vessel acts as cathode.
III. A past 24. For a reaction, the graph of $\ln k$ (on $y$-axis) and $\frac{1}{T}$ (on $x$-axis) is a straight line with a slope $-2 \ 25. Match the following
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;bord 26. The critical micelle concentration (CMC) of a soap solution is $5 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1}$. Identi 27. The metal purified by Mond process is $X$. The number of unpaired electrons in $X$ is
28. Complete hydrolysis of xenon hexafluoride gives HF along with compound $X$. The hybridisation in $X$ is
29. $\mathrm{KMnO}_4$ oxidises hydrogen sulphide in acidic medium, The number of moles of $\mathrm{KMnO}_4$ which react with 30. Identify the set which does not have ambidentate ligand(s)
31. The number of linear and crosslinked polymers in the following respectively are
Novolac, Nylon 6,6, Bakelite, PVC, melam 32. Which of the following represents the correct structure of $\beta-D-(-)$ - fructofuranose? 33. Which of the following statement is not correct for glucose?
34. The synthetic detergent used in tooth paste is of type $X$. Animal starch is $Y . X$ and $Y$ respectively are
35. What are $X$ and $Y$ respectively in the following sets of reactions?
36. Identify the two reactions $A(\mathrm{I} \rightarrow \mathrm{II})$ and $B(\mathrm{I} \rightarrow \mathrm{III})$ respecti 37. An alcohol, $X\left(\mathrm{C}_5 \mathrm{H}_{12} \mathrm{O}\right)$ in the presence of $\mathrm{Cu} / 573 \mathrm{~K}$ g 38. A carbonyl compound $X\left(\mathrm{C}_8 \mathrm{H}_8 \mathrm{O}\right)$ undergoes disproportionation with conc. KOH on 39. What is the major product $Y$ in the following reaction sequence?
40. What are $X$ and $Y$ respectively in the following set of reactions?
Mathematics
1. If $f: R \rightarrow A$, defined by $f(x)=\cos x+\sqrt{3} \sin x-1$ is an onto function then $A=$
2. Let $g(x)=1+x-[x]$ and ${ }^{\prime}$
$$ f(x)= \begin{cases}-1, & x0\end{cases} $$
than or equal to $x$. Then for all $x 3. The remainder obtained when $(2 m+1)^{2 n}(m, n \in N)$ is divided by 8 is
4. A value of $\theta$ lying between 0 and $\pi / 2$ and satisfying $\left|\begin{array}{ccc}1+\sin ^2 \theta & \cos ^2 \th 5. If the system of equations $2 x+p y+6 z=8$, $x+2 y+q z=5$ and $x+y+3 z=4$ has infinitely many solutions, then $p=$
6. If $x^a y^b=e^m, x^c y^d=e^n, \Delta_1=\left|\begin{array}{ll}m & b \\ n & d\end{array}\right|$, $\Delta_2=\left|\begin{ 7. If $z$ and $w$ are two non-zero complex numbers such that $|z w|=1$ and $\arg z-\arg w=\frac{\pi}{2}$, then $\bar{z} w=$ 8. Let $z$ satisfy $|z|=1, z=1-\bar{z}$ and $\operatorname{Im}(z)>0$
Statement $\mathbf{I} z$ is a real number
Statement II 9. If $w_1$ and $w_2$ are two non-zero complex numbers and ${ }a, b$ are non-zero real numbers such that $\left|a w_1+b w_2 10. If $\alpha$ is the common root of the quadratic equations $x^2-5 x+4 a=0, x^2-2 a x-8=0$, where $a \in R$, then the valu 11. If $\alpha, \beta$ are the roots of $x^2-5 \gamma x-6 \delta=0$ and $\gamma, \delta$ are the roots of $x^2-5 \alpha x-6 12. The equation $x^{\frac{3}{4}\left(\log _2 x\right)^2+\log _2 x-\frac{5}{4}}=\sqrt{2}$ has
13. If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+p x^2+q x+r=0$, then $(\alpha+\beta)(\beta+\gamma)(\gamma+ 14. An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number o 15. $$ \sum_{r=1}^{15} r^2\left(\frac{{ }^{15} C_r}{{ }^{15} C_{r-1}}\right)= $$
16. A string of letters is to be formed by using 4 letters from all the letters of the word "MATHEMATICS". The number of way 17. $$ \frac{1}{81^n}-{ }^{2 n} C_1 \frac{10}{81^n}+{ }^{2 n} C_2 \frac{10^2}{81^n}-\ldots+\frac{10^{2 n}}{81^n}= $$
18. If $x$ is positive real number and the first negative term in the expansion of $(1+x)^{\frac{27}{5}}$ is $t_k$, then $k= 19. If $\frac{x^2}{\left(x^2+2\right)\left(x^4-1\right)}=\frac{A}{x^2-1}+\frac{B}{x^2+1}+\frac{C}{x^2+2}$, then $A+B-C=$
20. If $\cos x+\sin x=\frac{1}{2}$ and $0
21. If $\sin \theta+2 \cos \theta=1$ and $\theta$ belongs to 4 th quadrant (not lying on the coordinate axes), then $7 \cos 22. If $A$ and $B$ are acute angles satisfying $3 \cos ^2 A+2 \cos ^2 B=4$ and $\frac{3 \sin A}{\sin B}=\frac{2 \cos B}{\cos 23. Statement I In the interval $[0,2 \pi]$, the number of common solutions of the equations $2 \sin ^2 \theta-\cos 2 \theta 24. The equation $\cos ^{-1}(1-x)-2 \cos ^{-1} x=\frac{\pi}{2}$ has
25. If $\sinh ^{-1}(2)+\sinh ^{-1}(3)=\alpha$, then $\sinh \alpha=$
26. In $\triangle A B C$, if $A, B, C$ are in arithmetic progression, then
$$ \sqrt{a^2-a c+c^2} \cdot \cos \left(\frac{A-C} 27. If in $\triangle A B C, B=45^{\circ}, a=2(\sqrt{3}+1)$ and area of $\triangle A B C$ is $6+2 \sqrt{3}$ sq. units, then t 28. In a $\triangle A B C$, if $\sin ^2 B=\sin A$ and $2 \cos ^2 A=3 \cos ^2 B$, then the triangle is
29. $P$ is the circumcentre of $\triangle A B C$. If the position vectors of $A, B, C$ and $P$ are $\mathbf{a}, \mathbf{b}, 30. If the position vectors of $A, B, C, D$ are $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}- 31. The set of all real values of $c$ so that the angle between the vectors $\mathbf{a}=c x \hat{\mathbf{i}}-6 \hat{\mathbf{ 32. Let $\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \mathbf{b}=3 \hat{\mathbf{i}}+3 \hat{\mathbf{j}} 33. If $\mathbf{u}, \mathbf{v}, \mathbf{w}$ are non-coplanar vectors and $p, q$ are real numbers, then the equality $[3 \mat 34. If $\sum_{i=1}^9\left(x_i-5\right)=9$ and $\sum_{i=1}^9\left(x_i-5\right)^2=45$, then the standard deviation of the nine 35. Two students appeared simultaneously for an entrance exam. If the probability that the first student gets qualified in t 36. For three events $A, B$ and $C$ of a sample space, $P$ (exactly one of $A$ or $B$ occurs ) $=P$ (exactly one of $B$ or $ 37. $A$ bag $P$ contains 4 red and 5 black balls another bag Q contains 3 red and 6 black balls. If one ball is drawn at ran 38. On every evening, a student either watches TV or reads a book. The probability of watching TV is $\frac{4}{5}$ If he wat 39. Let $X$ be the random variable taking values $1,2, \ldots n$ for a fixed positive integer $n$. If $P(X=k)=\frac{1}{n}$ f 40. A radar system can detect an enemy plane in one out of ten consecutive scans.
The probability that it can detect an enem 41. The locus of the third vertex of a right-angled triangle, the ends of whose hypotenuse are $(1,2)$ and $(4,5)$ is
42. The coordinate axes are rotated about the origin in the counter clockwise direction through an angle $60^{\circ}$. If a 43. The image of a point $(2,-1)$ with respect to the line $x-y+1=0$ is
44. If a straight line is at a distance of 10 units from the origin and the perpendicular drawn from the origin to it makes 45. If one of the lines given by the pair of lines $3 x^2-2 y^2+a x y=0$ is making an angle $60^{\circ}$ with $X$-axis, then 46. $A$ straight line passing through the origin $O$ meets the parallel lines $4 x+2 y=9$ and $2 x+y+6=0$ at the points $P$ 47. A circle is drawn with its centre at the focus of the parabola $y^2=2 p x$ such that it touches the directrix of the par 48. A circle touches both the coordinate axes and the straight line $L \equiv 4 x+3 y-6=0$ in the first quadrant. If this ci 49. If the smallest circle through the points of intersection of $x^2+y^2=a^2$ and $x \cos \alpha+y \sin \alpha=p, 0
50. If the lines $3 x-4 y+4=0$ and $6 x-8 y-7=0$ are the tangents to the same circle, then the area of that circle (in sq. u 51. Circles are drawn through the point $(2,0)$ to cut intercepts of length 5 units on the $X$-axis. If their centre lie in 52. If the locus of a point that divides a chord of slope 2 of the parabola $y^2=4 x$ internally in the ratio $1: 2$ is a pa 53. Assertion (A) The length of the latus rectum of an ellipse is 4 . The focus and its corresponding directrix are respecti 54. If the eccentricity of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ passing through the point $(4,6)$ is 2 , then t 55. A hyperbola passes through the point $P(\sqrt{2}, \sqrt{3})$ and has foci at $( \pm 2,0)$. Then, the point that lies on 56. The circumradius of the triangle formed by the points $(2,-1,1),(1,-3,-5)$ and $(3,-4,-4)$ is
57. Let $A(2,3,5), B(-1,3,2)$ and $C(\lambda, 5, \mu)$ be the vertices of $\triangle A B C$. If the median through the verte 58. Equation of the plane passing through the origin and perpendicular to the planes $x+2 y-z=1$ and $3 x-4 y+z=5$ is
59. $$\mathop {\lim }\limits_{x \to {\pi \over 4}} \frac{2 \sqrt{2}-(\cos x+\sin x)^3}{1-\sin 2 x}= $$ 60. Let $[x]$ denote the greatest integer less than or equal to $x$. Then,
$$ \lim _{x \rightarrow 2^{+}}\left(\frac{[x]^3}{ 61. If the function $f$ defined by
$$ f(x)=\left\{\begin{array}{cc} \frac{1-\cos 4 x}{x^2}, & x0 \end{array}\right. $$
is co 62. The domain of the derivative of the function $f(x)=\frac{x}{1+|x|}$ is
63. If $x=\sqrt{2^{\operatorname{cosec}^{-1} t}}$ and $y=\sqrt{2^{\sec ^{-1} t}},|t| \geq 1$, then $\frac{d y}{d x}=$
64. If $(a+\sqrt{2} b \cos x)(a-\sqrt{2} b \cos y) =a^2-b^2$, where $a>b>0$, then at $\left(\frac{\pi}{4}, \frac{\pi}{4}\rig 65. Consider the quadratic equation $a x^2+b x+c=0$, where $2 a+3 b+6 c=0$ and let $g(x)=\frac{a x^3}{3}+\frac{b x^2}{2}+c x 66. The difference between the absolute maximum and absolute minimum values of the function $f(x)=2 x^3-15 x^2+36 x-30$ on $ 67. If $f(x)=x e^{x(1-x)}, x \in R$, then $f(x)$ is
68. The angle between the curves $y^2=x$ and $x^2=y$ at the point $(1,1)$ is
69. If $\int \frac{5 \tan x}{\tan x-2} d x=a x+b \log |\sin x-2 \cos x|+c$, then $a+b=$
70. $$ \int x \cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right) d x(x>0)= $$
71. $$ \int \frac{d x}{(1+\sqrt{x}) \sqrt{x-x^2}}= $$
72. $$ \int \sin ^{-1}\left(\sqrt{\frac{x}{a+x}}\right) d x= $$
73. If $\int \frac{x}{x \tan x+1} d x=\log f(x)+k$, then $f\left(\frac{\pi}{4}\right)=$
74. $$ \int_0^1 \frac{2 x+5}{x^2+3 x+2} d x= $$
75. The area (in sq units) of the region given by $R=\left\{(x, y) ; \frac{y^2}{2} \leq x \leq y+4\right\}$ is
76. $$ \int_0^1 x^{\frac{5}{2}}(1-x)^{\frac{3}{2}} d x= $$
77. $$ \lim _{n \rightarrow \infty}\left[\begin{array}{c} \frac{1}{n^2} \sec ^2 \frac{1}{n^2}+\frac{2}{n^2} \sec ^2 \frac{4} 78. The general solution of the differential equation $\left(x \sin \frac{y}{x}\right) d y=\left(y \sin \frac{y}{x}-x\right) 79. The general solution of the differential equation $\cos (x+y) d y=d x$ is
80. If $A x^3+B x y=4$ ( $A$ and $B$ are arbitrary constants) is the general solution of the differential equation $F(x) \fr
Physics
1. The physical quantity having the dimensions of the square root of the ratio of the kinetic energy and surface tension is 2. If the displacement ( $s$ in metre) of a moving particle in terms of time $(t$ in second $) s=t^3-6 t^2+18 t+9$, then th 3. If a force $(\beta \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}) \mathrm{N}$ acting on a body displaces it thr 4. If two bodies $A$ and $B$ are projected with same velocity but with different angles $\theta_1$ and $\theta_2$ respectiv 5. The apparent weight of a girl of mass 30 kg when she is in a lift moving vertically upwards with an acceleration of $2 \ 6. If a stone of mass 0.5 kg tied to one end of a wire is whirled in a circular path of radius 2 m with a speed $40 \mathrm 7. A body is projected vertically upwards with a velocity of $20 \mathrm{~ms}^{-1}$. If the potential energy of the body at 8. A body falls freely on to a hard horizontal surface. If the coefficient of restitution between the surface and the body 9. Two bodies of masses $M$ and $4 M$ initially at rest, start moving towards each other due to their mutual attraction. Th 10. The angular velocity of a body changes from $6 \mathrm{rad} \mathrm{s}^{-1}$ to $21 \mathrm{rad} \mathrm{s}^{-1}$ in a t 11. If the displacement of a particle executing simple harmonic motion is given by $x=0.5 \cos (125.6 t)$, then the time per 12. The amplitude of a damped harmonic oscilator becomes $50 \%$ of its initial value in a time of 12 s . If the amplitude o 13. The escape velocity of a body from a planet of mass $M$ and radius $R$ is $14 \mathrm{~km} \mathrm{~s}^{-1}$. The escape 14. The stress-strain graph of two wires $A$ and $B$ is shown in the figure. If $Y_A$ and $Y_B$ are Young's moduli of materi 15. If two soap bubbles each of radius 2 cm combine in vacuum under isothermal conditions, then the radius of the new bubble 16. A rectangular slab consists of two cubes of copper and brass of equal sides having thermal conductivities in the ratio $ 17. The efficiency of a Carnot's heat engine is $\frac{1}{3}$. If the temperature of the source is decreased by $50^{\circ} 18. The change in internal energy of given mass of a gas, when its volume changes from $V$ to $3 V$ at constant pressure $p$ 19. A monoatomic gas at a pressure of 100 kPa expands adiabatically such that its final volume becomes 8 times its initial v 20. If a gaseous mixture consists of 3 moles of oxygen and 4 moles of argon at an absolute temperature $T$, then the total i 21. A sound wave of frequency 500 Hz travels between two points $X$ and $Y$ separated by a distance of 600 m in a time of 2 22. A ray of light incidents at an angle of $60^{\circ}$ on the first face of a prism. The angle of the prism is $30^{\circ} 23. In an experiment, two polariods are arranged such that the intensity of the polarised light emerged from the second pola 24. If two particles $A$ and $B$ of charges $1.6 \times 10^{-19} \mathrm{C}$ and $3.2 \times 10^{-19} \mathrm{C}$ respective 25. If four charges $+12 \mathrm{nC},-20 \mathrm{nC},+32 \mathrm{nC}$ and -15 nC are arranged at the four vertices of a squa 26. Four capacitors are connected as shown in the figure. If $C_1, C_2, C_3$ and $C_4$ are in the ratio of $1: 2: 3: 4$, the 27. In the given circuit, the internal resistance of the cell is zero. If $i_1$ and $i_2$ are the readings of the ammeter wh 28. In a meter bridge, the null point is located at 20 cm from left end of the wire when resistances $R$ and $S$ are connect 29. If a wire of length ' $L$ ' carrying a current ' $i$ ' is bent in the shape of a semi-circular arc as shown in the figur 30. A galvanometer having 30 divisions has a current sensitivity of $0.0625 \frac{d i \nu}{\mu A}$. If it is converted into 31. If the given figure shows the relation between magnetic field ( $B$-along $Y$-axis) and magnetic intensity ( $H$-along $ 32. A coil having 100 square loops each of side 10 cm is placed such that its plane is normal to a magnetic field, which is 33. An AC source of internal resistance $10^3 \Omega$ is connected to a transformer. The ratio of the number of turns in the 34. If $11 \%$ of the power of a 200 W bulb is converted to visible radiation, then the intensity of the light at a distance 35. The de-Broglie wavelength associated with an electron accelerated through a potential difference of $\frac{200}{3} \math 36. The ratio of the shortest wavelengths of Bracket and Balmer series of hydrogen atom is
37. If the binding energy per nucleon of deuteron $\left({ }_1 \mathrm{H}^2\right)$ is 1.15 MeV and an $\alpha$-particle has 38. In a transistor, if the collector current is $98 \%$ of emitter current, then the ratio of the base and collector curren 39. In the given circuit, if $A=0, B=1$ and $C=1$ are inputs, then the values of $y_1$ and $y_2$ are respectively 40. In amplitude modulation, if a message signal of 5 kHz 2 is modulated by a carrier wave of frequency 900 kHz , then the f
1
AP EAPCET 2025 - 27th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\int \frac{5 \tan x}{\tan x-2} d x=a x+b \log |\sin x-2 \cos x|+c$, then $a+b=$
A
2
B
3
C
4
D
-1
2
AP EAPCET 2025 - 27th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$$ \int x \cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right) d x(x>0)= $$
A
$-x+\left(1+x^2\right) \tan ^{-1} x+C$
B
$x-\left(1+x^2\right) \cot ^{-1} x+C$
C
$-x+\left(1+x^2\right) \cot ^{-1} x+C$
D
$x-\left(1+x^2\right) \tan ^{-1} x+C$
3
AP EAPCET 2025 - 27th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$$ \int \frac{d x}{(1+\sqrt{x}) \sqrt{x-x^2}}= $$
A
$-2 \sqrt{\frac{1+\sqrt{x}}{1-\sqrt{x}}}+C$
B
$-\sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}}+C$
C
$-2 \sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}}+C$
D
$2 \sqrt{\frac{1+\sqrt{x}}{1-\sqrt{x}}}+C$
4
AP EAPCET 2025 - 27th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$$ \int \sin ^{-1}\left(\sqrt{\frac{x}{a+x}}\right) d x= $$
A
$(a+x) \tan ^{-1} \sqrt{\frac{x}{a}}+a x+C$
B
$(a+x) \tan ^{-1} \sqrt{\frac{x}{a}}+\sqrt{a x}+C$
C
$(a+x) \tan ^{-1} \sqrt{\frac{a}{x}}-\sqrt{a x}+C$
D
$(a+x) \tan ^{-1} \sqrt{\frac{x}{a}}-\sqrt{a x}+C$
Paper Analysis
Total Questions
Chemistry 40
Mathematics 80
Physics 40
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