TG EAPCET 2025 (Online) 2nd May Morning Shift | TS EAMCET Year Wise Previous Years Questions

Chemistry

1. The radius of stationary state $(n=2)$ of hydrogen atom is $x \mathrm{pm}$. The radius of stationary state $(n=3)$ of $\ 2. When electromagnetic radiation of wavelength 310 nm falls on the surface of a metal having work function 3.55 eV , the v 3. In which of the following options, elements are correctly arranged in the increasing order of their atomic radius? 4. $A, B C, D$ and $E$ are elements with atomic numbers 13 , $11,9,7$ and 16 respectively. Among these elements, ion of an 5. Identify the pair of molecules in which the hybridisation of the central atom is $s p^2$ with bent geometry. 6. Consider the following statements I. In the conversion of $\mathrm{O}_2$ to $\mathrm{O}_2^{2+}$ bond order decreases. II 7. The RMS velocity of dihydrogen is $\sqrt{7}$ times more than that of dinitrogen. If $T_{\mathrm{H}_2}$ and $T_{\mathrm{N 8. Which of the following solution has highest amount of solute? 9. At 298 K , the enthalpy change ( in kJ ) for the reaction given below is $$ \mathrm{CH}_4(g)+\mathrm{O}_2(g) \longrighta 10. For the reaction $\mathrm{N}_2 \mathrm{O}_4(g) \rightleftharpoons 2 \mathrm{NO}_2(g)$, the correct relation between degr 11. Oxidation state of hydrogen in compound $X$ is -1 and in compound $Y$ is $+1 . X$ and $Y$ are respectively 12. $$ \text { Match the following } $$ .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;borde 13. When burnt in excess of oxygen, sodium forms a compound $X$ and potassium forms a compound $Y$. The magnetic natures of 14. The correct order of atomic radii of group 13 elements is 15. Observe the following oxides. The number of amphoteric oxides from the given list is $\mathrm{CO}, \mathrm{B}_2 \mathrm{ 16. Among the following compounds, which one is not primarily responsible for depletion of ozone layer in stratosphere? 17. Consider the following sequence of reaction. In ' $Z$ ' the number of $s p^3$ carbons is ' $a$ ' and $s p^2$ carbons is 18. Which one of the following represents hyperconjugation effect? 19. Which of the following compounds will be suitable for estimation of nitrogen by Kjeldahl's method? 20. For the alkyne with formula $\mathrm{C}_6 \mathrm{H}_{10}$, the number of alkynes with acidic hydrogens is $x$ and numbe 21. A substance has a density of $2 \mathrm{~g} \mathrm{~cm}^{-3}$. It crystallises in the fcc crystal with an edge length o 22. Observe the following statements Statement I : The boiling point of 0.1 M urea solution is less than that of 0.1 M KCl s 23. At 298 K , if emf of the cell corresponding to the reaction $\mathrm{Zn}(s)+2 \mathrm{H}^{+}(a q) \longrightarrow \mathr 24. For the reaction $R \rightarrow P$, half life is independent of initial concentration of the reactant, $R$. Which one of 25. Which of the following is not correct about Freundlich adsorption isotherm? 26. Identify the reaction, which is not related to extraction of copper 27. Phosphorus on reaction with sulphuryl chloride gives a compound $X$, which on complete hydrolysis gives $Y$. $X$ and $Y$ 28. Xenon hexafluoride on partial hydrolysis gives ' $X$ ' and HF . The shape of ' $X$ ' is 29. Which of the following pairs of oxoacids have basicity as 2? 30. In acidic medium one mole each of $\mathrm{MnO}_4^{-}$and $\mathrm{Cr}_2 \mathrm{O}_7^{2-}$ is reduce by $x$ and $y$ mol 31. Which one of the following is not an ambidenate ligand? 32. ' $X$ ' is a polymer, which is mainly used for making unbreakable cups and laminated sheets. The monomers of ' $X$ ' are 33. Which of the following hormones is an example of polypeptide? 34. The structure of which artificial sweetener contains aspartic acid and phenylalanine parts? 35. Which of the following is the most reactive towards $\mathrm{S}_{\mathrm{N}} 1$ mechanism? 36. $$ \left(\mathrm{CH}_3\right)_3 \mathrm{CH} \xrightarrow{\mathrm{KMnO}_4} X \xrightarrow[573 \mathrm{~K}]{\mathrm{Cu}} Y 37. Consider the following reaction sequence. $(A)$ and $(C)$ are$$ \mathrm{CH}_3 \mathrm{CHO} \xrightarrow[\text { (ii) } \ 38. The increasing order of acidic strength of the following in aqueous solution is 39. The increasing order of boiling points of the following is $$ \begin{array}{cccc} \mathrm{CH}_3-\mathrm{O}-\mathrm{CH}_3 40. The major products $P$ and $Q$ from the following reactions are

Mathematics

1. If $f(x)=\tan \left(\frac{\pi}{\sqrt{x+1}+4}\right)$ is a real valued function, then the range of $f$ is 2. The range of the real value function $f(x)=\sin ^{-1}\left(\sqrt{x^2+x+1}\right)$ is 3. $1+(1+3)+(1+3+5)+(1+3+5+7)+\ldots$ to 10 terms $=$ 4. If the augmented matrix corresponding to the system of equations $x+y-z=1,2 x+4 y-z=0$ and $3 x+4 y+5 z=18$ is transform 5. If $\left|\begin{array}{ccc}9 & 25 & 16 \\ 16 & 36 & 25 \\ 25 & 49 & 36\end{array}\right|=K$, then $K, K+1$ are the root 6. $A=\left[\begin{array}{ccc}1 & -3 & -5 \\ -2 & 4 & -6 \\ 7 & -11 & 13\end{array}\right]$, then $\sqrt{|\operatorname{adj 7. If $\Delta_r=\left|\begin{array}{cc}\frac{1}{3 r-2} & \frac{2}{3 r-5} \\ 0 & \frac{3}{3 r+1}\end{array}\right|$ then $\s 8. If $\frac{2+3 i}{i-2}-\frac{4 i-3}{3+4 i}=x+i y$, then $3 x+y=$ 9. Let $z=x+i y$ and $P(x, y)$ be a point on the argand plane. If $z$ satisfies the condition $\arg \left(\frac{z-3 i}{z+2 10. If $\omega$ is a complex cube root of unity and $x=\omega^2-\omega+2$, then 11. The product of all the values of $(\sqrt{3}-i)^{\frac{3}{7}}$ is 12. $\alpha, \beta$ are the roots of the equation $\sin ^2 x+b \sin x+c=0$. If $\alpha+\beta=\frac{\pi}{2}$, then $b^2-1=$ 13. The number of integral values of ' $a$ ' for which the quadratic equation $a x^2+a x+5=0$ cannot have real roots is 14. If the roots of the equation $32 x^3-48 x^2+22 x-3=0$ are in arithmetic progression, then the square of the common diffe 15. If the sum of two roots of the equation $x^4-2 x^3+x^2+4 x-6=0$ is zero, then the sum of the squares of the other two ro 16. A student has to answer a multiple-choice question having 5 alternatives in which two or more than two alternatives are 17. Number of triangles whose vertices are the points $(x, y)$ in the $X Y$-plane with integer coordinates satisfying $0 \le 18. If all the letters of the word 'HANDLE' are permuted in all possible ways and the words (with or without meaning) thus f 19. If the coefficient of 3rd term from the beginning in the expansion of $\left(a x^2-\frac{8}{b x}\right)^9$ is equal to t 20. If the expression $5^{2 n}-48 n+k$ is divisible by 24 for all $n \in N$, then the least positive integral value of $k$ i 21. If $\frac{x^3+3}{(x-3)^3}=a+\frac{b}{x-3}+\frac{c}{(x-3)^2}+\frac{d}{(x-3)^3}$, then $(a+d)-(b+c)=$ 22. If $\sin A=-\frac{60}{61}, \cot B=-\frac{40}{9}$ and neither $A$ and $B$ is in 4th quadrant, then $6 \cot A+4 \sec B=$ 23. The period of the function $f(x)=\frac{2 \sin \left(\frac{\pi x}{3}\right) \cos \left(\frac{2 \pi x}{5}\right)}{3 \tan \ 24. If $A+B+C=4 S$, then $\sin (2 S-A)$ $$ +\sin (2 S-B)+\sin (2 S-C)-\sin 2 S= $$ 25. The general solution of the equation $\sqrt{6-5 \cos x+7 \sin ^2 x}-\cos x=0$ also satisfies the equation 26. $$ \tan ^{-1} \frac{3}{5}+\tan ^{-1} \frac{6}{41}+\tan ^{-1} \frac{9}{191}= $$ 27. If $2 \tanh ^{-1} x=\sinh ^{-1}\left(\frac{4}{3}\right)$, then $\cosh ^{-1}\left(\frac{1}{x}\right)=$ 28. If $p_1, p_2, p_3$ are the altitudes and $a=4, b=5, c=6$ are the sides of a $\triangle A B C$, then $\frac{1}{p_1^2}+\fr 29. Let the angles $A, B, C$ of a $\triangle A B C$ be in arithmetic progression. If the exradii $r_1, r_2, r_3$ of $\triang 30. The position vectors of two points $A$ and $B$ are $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ and $7 \hat{ 31. The point of intersection of the line joining the points $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}, 2 \hat{\ 32. If $\mathbf{a}$ and $\mathbf{b}$ are two vectors such that $|\mathbf{a}|=5,|\mathbf{b}|=12$ and $|\mathbf{a}-\mathbf{b}| 33. If $\mathbf{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and $\mathbf{b}=2 \hat{\mathbf{i}}+\hat{\mathbf{j 34. The shortest distance between the lines $$ \begin{aligned} & \mathbf{r}=(3 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+2 \hat{\m 35. The mean deviation from the median for the following data is $$ \begin{array}{cllllll} x_i & 2 & 9 & 8 & 3 & 5 & 7 \\ \h 36. If three smallest squares are chosen at-random on a chess board, then the probability of getting them in such a way that 37. If three cards are drawn randomly from a pack of 52 playing cards then the probability of getting exactly, one spade car 38. Urn A contains 6 white and 2 black balls; run B contains 5 white and 3 black balls and urn C contains 4 white and 4 blac 39. If three dice are thrown, then the mean of the sum of the numbers appearing on them is 40. If $X \sim B(7, P)$ is a binomial variate and $P(X=3)=P(X=5)$, then $P=$ 41. If the points $A(2,3), B(3,2)$ form a triangle with a variable point $p\left(t, t^2\right)$, where $t$ is a parameter, t 42. If $(h, k)$ is the new origin to be chosen to eliminate first degree terms from the equation $S \equiv 2 x^2-x y-y^2-3 x 43. A line $L$ perpendicular to the line $5 x-12 y+6=0$ makes positive intercept on the $Y$-axis. If the distance from the o 44. If a line $L$ passing through a point $A(2,3)$ intersects another line $4 x-3 y-19=0$ at the point $B$ such that $A B=4$ 45. A variable straight-line $L$ with negative slope passes through the point $(4,9)$ and cuts the positive coordinate axes 46. If $4 x^2+12 x y+9 y^2+2 g x+2 f y-1=0$ represent a pair of parallel lines, then 47. If the equation of the circle passing through the points $(-1,0),(-1,1),(1,1)$ is $a x^2+a y^2+2 g x+2 f y-2=0$, then $a 48. For the circle $x-2=5 \cos \theta, y+1=5 \sin \theta$, where $\theta$ is the perimeter, the line $x=1+\frac{r}{2}, y=-2+ 49. If $x-2 y=0$ is a tangent drawn at a point $P$ on the circle $x^2+y^2-6 x+2 y+c=0$, then the distance of the point $(6,3 50. If $A, B$ are the points of contact of the tangents drawn from the point $(-3,1)$ to the circle $x^2+y^2-4 x+2 y-4=0$, t 51. If the angle between the circles $x^2+y^2-2 x+k y+1=0$ and $x^2+y^2-k x-2 y+1=0$ is $\cos ^{-1}\left(\frac{1}{4}\right)$ 52. A circle $C$ passing through the point $(1,1)$ bisects the circumference of the circle $x^2+y^2-2 x=0$. If $C$ is orthog 53. If the normal drawn at $P(8,16)$ to the parabola $y^2=32 x$ meets the parabola again at $Q$, then the equation of the ta 54. The focal distance of a point $(5,5)$ on the parabola $x^2-2 x-4 y+5=0$ is 55. If $S$ and $S^{\prime}$ are the foci of an ellipse $\frac{x^2}{169}+\frac{y^2}{144}=1$ and the point $B$ lying on positi 56. One of the foci of an ellipse is $(2,-3)$ and its corresponding directrix is $2 x+y=5$. If the eccentricity of the ellip 57. If the product of the perpendicular distances from any point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ to its 58. If $A(0,3,4), B(1,5,6), C(-2,0,-2)$ are the vertices of a $\triangle A B C$ and the bisector of angle $A$ meets the side 59. If the direction cosines of two lines satisfy the equation $2 l+m-n=0, l^2-2 m^2+n^2=0$ and $\theta$ is the angle betwee 60. If the equation of the plane passing through the points $(2,1,2),(1,2,1)$ and perpendicular to the plane $2 x-y+2 z=1$ i 61. If $[x]$ is the greatest integer function, then $$ \mathop {\lim }\limits_{x \to 3} \frac{(3-|x|+\sin |3-x|) \cos [9-3 x 62. Let ' $a$ ' be a positive real number. If a real valued function $f(x)=\left\{\begin{array}{cl}\frac{6^x-3^x-2^x+1}{1-\c 63. If $f(x)=\sqrt{\cos ^{-1} \sqrt{1-x^2}}$, then $f^{\prime}\left(\frac{1}{2}\right)=$ 64. If $y=f(\cosh x)$ and $f^{\prime}(x)=\log \left(x+\sqrt{x^2-1}\right)$, then $\frac{d^2 y}{d x^2}=$ 65. If $\left(x^2-3 x+2\right)^{\frac{y}{x^{2-1}}}=x+2$, then $\left(\frac{d y}{d x}\right)_{x=0}=$ 66. If $x=\frac{t^2}{1+t^5}, y=\frac{2 t^3}{1+t^5}$ and $t \neq-1$ is a perimeter, then $\frac{d y}{d x}=$ 67. The acute angle between the curves $y=3 x^2-2 x-1$ and $y=x^3-1$ at their point of intersection which lies in the first 68. If the rate of change of the slope of the tangent drawn to the curve $y=x^3-2 x^2+3 x-2$ at the point $(2,4)$ is $k$ tim 69. If $1^{\circ}=0.0175$ radians, then the approximate value of $\sec 58^{\circ}$ is 70. If $f(x)=x+\log \left(\frac{x-1}{x+1}\right)$ is a well-defined real valued function, then $f$ is 71. A real valued function $f(x)=\left|x^2-3 x+2\right|+2 x-3$ is defined on $[-2,1]$. If $m$ and $M$ are absolute minimum a 72. $$ \int \frac{2 \sin x-3 \cos x}{4 \cos x-3 \sin x} d x= $$ 73. $$ \int e^{4 x}(\sin 3 x-\cos 3 x) d x= $$ 74. $$ \int\left(\frac{1-\log x}{1+(\log x)^2}\right)^2 d x= $$ 75. If $\int(x+2) \sqrt{x^2-x+2} d x=\frac{1}{3} f(x)+\frac{5}{8} g(x)+\frac{35}{16} h(x)+C$ then $f(-1)+g(-1)+h\left(\frac{ 76. $$ \int_0^2 \sqrt{(x+3)(2-x)} d x= $$ 77. $$ \int_0^{\pi / 4} x^2 \sin 2 x d x $$ 78. $$ \int_{-2 \pi}^{2 \pi} \sin ^4 x \cos ^6 x d x= $$ 79. If $\cos x \frac{d y}{d x}=y \sin x-1, x \neq(2 n+1) \frac{\pi}{2}, n \in Z$ is the differential equation corresponding 80. The general solution of the differential equation $2 d x+d y=(6 x y+4 x-3 y) d x$ is

Physics

1. For any fixed distance, the electromagnetic force between two protons is $10^n$ times of the gravitational force between 2. If $A, B$ and $C$ are three different physical quantities with different dimensional formulae, then the combination whic 3. The driver of a bus moving with a velocity of $72 \mathrm{~km} / \mathrm{h}$ observes a boy walking across the road at a 4. A helicopter flying horizontally with a velocity of $288 \mathrm{~km} / \mathrm{h}$ drops a bomb. If the line joining th 5. A man of mass 60 kg is standing in a lift moving up with a retardation of $2.8 \mathrm{~ms}^{-2}$. The apparent weight o 6. The initial and final velocities of a body projected vertically from the ground are $20 \mathrm{~ms}^{-1}$ and $18 \math 7. A particle is acted upon by a force of constant magnitude such that its velocity and acceleration are always perpendicul 8. If the moment of inertia of a uniform solid cylinder about the axis of the cylinder is $\frac{1}{n}$ times its moment of 9. Two blocks of masses in the ratio $m: n$ are connected by a light inextensible string passing over a frictionless fixed 10. The amplitude of a particle executing simple harmonic motion is 6 cm . The distance of the point from the mean position 11. If a body is projected vertically from the surface of the Earth with a speed of $8000 \mathrm{~ms}^{-1}$, then the maxim 12. If a brass sphere of radius 36 cm is submerged in a lake at a depth where the pressure is $10^7 \mathrm{~Pa}$, then the 13. The work done in blowing a soap bubble of diameter 3 cm is (surface tension of soap solution $=0.035 \mathrm{Nm}^{-1}$ ) 14. If the terminal velocity of a metal sphere of mass 8 g falling through a liquid is $3 \mathrm{cms}^{-1}$, then the termi 15. The length of a metal rod is 20 cm and its area of cross-section is $4 \mathrm{~cm}^2$. If one end of the rod is kept at 16. The heat required to convert 8 g of ice at a temperature of $-20^{\circ} \mathrm{C}$ to steam at $100^{\circ} \mathrm{C} 17. Two moles of a gas at a temperature of $327^{\circ} \mathrm{C}$ expands adiabatically such that its volume increases by 18. The molar specific heat of a monoatomic gas at constant pressure is (Universal gas constant $=8.3 \mathrm{~J} \mathrm{~m 19. The fundamental frequency of transverse wave of a stretched string subjected to a tension $T_1$ is 300 Hz . If the lengt 20. Two sound waves each of intensity $I$ are superimposed. If the phase difference between the waves is $\frac{\pi}{2}$, th 21. The angle of a prism made of a material of refractive index $\sqrt{2}$ is $90^{\circ}$. The angle of incidence for a lig 22. The total magnification produced by a compound microscope is 24 when the final image is formed at the least distance of 23. In Young's double slit experiment with light of wavelength $\lambda$, the intensity of light at a point on the screen wh 24. A thin spherical shell of radius $R$ and surface charge density $\sigma$ is placed in a cube of side $5 R$ with their ce 25. As shown in the figure, a dielectric of constant $K$ is placed between the plates of a parallel plate capacitor and is c 26. The drift speed of electrons in a material is found to be $0.3 \mathrm{~ms}^{-1}$ when an electric field of $2 \mathrm{V 27. The power of an electric motor is 242 W when connected to a 220 V supply. When the motor is operated at 200 V , the curr 28. A proton and an alpha particle moving with equal speeds enter normally into a uniform magnetic field. The ratio of times 29. A solenoid of length 50 cm and radius 10 cm has two closely wound layers of windings 100 turns each. If a current of 2.5 30. If the magnetic susceptibility of a substance is 0.6 , then the ratio of permeability of the substance and permeability 31. The plane of a circular coil of resistance $7.5 \Omega$ is placed perpendicular to a uniform magnetic field. The flux $\ 32. The frequency of an alternating voltage is 50 Hz . The time taken for instantaneous voltage to increase from zero to hal 33. The dielectric constant of a medium is 8 and its relative permeability is 200 . If an electromagnetic wave of frequency 34. Photons of energy 4.5 eV are incident on a photosensitive material of work function 3 eV . The de-Broglie wavelength ass 35. If the difference in the frequencies of the first and second lines of Lyman series of hydrogen atom is $f$, then the dif 36. The average energy of a neutron produced in the fission of ${ }_{92}^{235} \mathrm{U}$ is 37. If $96.875 \%$ of a radioactive substance decays in 10 days, then the half life of the substance is (in days) 38. The power gain and voltage gain of a transistor connected in common emitter configuration are 1800 and 60 respectively. 39. Six logic gates are connected as shown in the figure. The values of $y_1, y_2$ and $y_3$ respectively are 40. For commercial telephonic communication, the frequency range adequate for speech signals is

TG EAPCET 2025 (Online) 2nd May Morning Shift

MCQ (Single Correct Answer)

-0

Let ' $a$ ' be a positive real number. If a real valued function

$f(x)=\left\{\begin{array}{cl}\frac{6^x-3^x-2^x+1}{1-\cos \left(\frac{x}{a}\right)} & \text { if } x \neq 0 \\ \log 3 \log 4 & \text { if } x=0\end{array}\right.$ is continuous at $x=0$, then $a=$

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