TG EAPCET 2025 (Online) 3rd May Evening Shift | TS EAMCET Year Wise Previous Years Questions

Chemistry

1. In the atomic spectrum of hydrogen, the wavelengths of the spectral lines corresponding to electronic transitions (i) $n 2. Work functions of four metals $M_1, M_2, M_3$ and $M_4$ are $4.8,4.3,4.75$ and 3.75 eV respectively. The metals which do 3. In second period of the modern periodic table, two elements $X$ and $Y$ have higher first ionisation enthalpy values tha 4. Consider the following pairs of elements and identify the pairs of elements which have nearly same atomic radius. I. Y, 5. If the sum of bond orders of $\mathrm{O}_2^{-}$and $\mathrm{O}_2^{2-}$ is $x$, then bond order of $\mathrm{O}_2^{2+}$ wi 6. Identify the molecule / ion in which the ratio of $\sigma$ to $\pi$-bonds is $3: 2$ 7. At 298 K , a flask ' $A$ ' of unknown volume $(V)$ contains oxygen at 5 atm . Another flask ' $B$ ' of volume 2 L contai 8. In which of the following, oxidation state of nitrogen is lowest? 9. Which of the following processes are reversible? I. Vaporisation of a liquid at its boiling point. II. Expansion of gas 10. At $T(\mathrm{~K})$ in a saturated solution of $\mathrm{MgCO}_3$ and $\mathrm{Ag}_2 \mathrm{CO}_3$, if the concentration 11. Temperature of maximum density of $\mathrm{H}_2 \mathrm{O}$ is $y \mathrm{~K}$ and $\mathrm{D}_2 \mathrm{O}$ is $x \math 12. How many of the following metals give oxides and nitrides when burnt in air? Be, Na, Mg, Ba, Sr, Li, K 13. Identify the incorrect order against the property given in brackets 14. Diborane on hydrolysis gives a compound $X$. The correct statement about $X$ are I. It is a tribasic acid II. It is a we 15. Choose the correct statement about allotropes of carbon. I. Graphite has layered structure. II. Buckminster fullerene is 16. Which of the following is a lung irritant that can lead to an acute respiratory disease in children? 17. Arrange the following in decreasing order of their boiling points (A) 2-methylbutane (B) 2, 2-dimethyl propane (C) Penta 18. $$ \text { Which of the following is not an aromatic species? } $$ 19. In the estimation of nitrogen by Kjeldahl's method 0.933 g of an organic compound ' $X$ ' was analysed. Ammonia evolved 20. Which of the following is a least stable carbocation? 21. The incorrect statement about crystals with schottky defect is 22. Two liquids ' $A$ ' and ' $B$ ' form an ideal solution. At 300 K , the vapour pressure of a solution containing 1 mole o 23. The mole conductivity of acetic acid solution at infinite dilution is $390 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1} 24. The half-life of a zero order reaction $A \rightarrow$ products, is 0.5 hour. The initial concentration of $A$ is $4 \ma 25. $$ \text { Match the following. } $$ $$ \begin{array}{llll} \hline & \text { List-I (Type of colloid) } & & \text { List 26. Observe the following statements Statement I : The choice of reducing agent for the reduction of an oxide ore can be pre 27. Which one of the orders is correctly matched with the property mentioned against it? 28. Noble gas ' $X$ ' is used as a diluent for oxygen in modern diving apparatus and noble gas ' $Y$ ' is used mainly to pro 29. The dibasic oxoacid of phosphorus on disproportionation given two products $A$ and $B . A$ and $B$ are respectively. 30. The number of moles of oxalate ions oxidised by one mole of permanganate ions in acidic medium is 31. Total number of geometrical isomers possible for the complexes $\left[\mathrm{NiCl}_4\right]^{2-}$, $\left[\mathrm{CoCl} 32. $$ \text { Match the following. } $$ The correct answer is 33. Maltose on hydrolysis gives two monosaccharide units. The incorrect statement about the monosaccharides formed is 34. Identify the pair of drugs which act as antihistamines? 35. Identify the product ' $Y$ ' in the given sequence of reactions 36. $$ \begin{aligned} &\text { What is ' } Z \text { ' in the given set of reactions? }\\ &\mathrm{C}_6 \mathrm{H}_ 37. Which of the following reactions is an example of Clemmensen reduction? 38. Which of the following can undergo Hell-Volhard-Zelinsky reaction? 39. $$ \text { Which of the following has lowest } \mathrm{p} K_a \text { value? } $$ 40. The correct statement about the products $B$ and $C$ in the given reactions are $$ \mathrm{CH}_3 \mathrm{CH}_2 \mathrm{O

Mathematics

1. Let $f: R \rightarrow R$ be defined by $f(x)=5^{-|x|}+\operatorname{sgn}\left(5^{-x}\right)$, where sgn $x$ denotes sign 2. If the range of the real valued function $f(x)=\frac{x^2+x+k}{x^2-x+k}$ is $\left[\frac{1}{3}, 3\right]$, then $k=$ 3. The value of the greatest integer $k$ satisfying the inequation $2^{n+4}+12 \geq k(n+4)$ for all $n \in N$ is 4. If the system of simultaneous linear equations $x-2 y+z=0,2 x+3 y+z=6$ and $x+2 y+p z=q$ has infinitely many solutions, 5. If the system of linear equations $(\sin \theta) x-y+z=0$, $x-(\cos \theta) y+z=0, x+y+(\sin \theta) z=0$ has non-trivia 6. If $A=\left[\begin{array}{lll}1 & 2 & 3 \\ 2 & 1 & 1 \\ 1 & 3 & 1\end{array}\right]$ and $B=\left[\begin{array}{lll}2 & 7. If $A=\left[\begin{array}{lll}1 & 5 & 2 \\ 4 & 1 & 3 \\ 2 & 6 & 3\end{array}\right]$, then $\left|(\operatorname{adj} A 8. The amplitude of the complex number $\frac{(\sqrt{3}+i)(1-\sqrt{3} i)}{(-1+i)(-1-i)}$ is 9. If a complex number $z=x+i y$ represents a point $p(x, y)$ in the argand plane and $z$ satisfies the condition that the 10. $$ (\sqrt{3}+i)^{10}+(\sqrt{3}-i)^{10}= $$ 11. Number of real values of $(-1-\sqrt{3 i})^{3 / 4}$ is 12. If $\tan \theta$ and $\cot \theta$ are two distinct roots of the equation $a x^2+b x+c=0, a \neq 0, b \neq 0$, then 13. Sum of all the roots of the equation $||2 x-3|-4|=2$ is 14. If the quotient and remainder obtained when the expression $3 x^5-6 x^4+2 x^3+4 x^2-5 x+8$ is divided by the expression 15. If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $12 x^4-56 x^3+89 x^2-56 x+12=0$ such that $\alpha \bet 16. If all the letters of the word ACADEMICIAN are permuted in all possible ways, then the number of permutations in which n 17. The number of all possible three letter words that can be formed by choosing three letters from the letters of the word 18. The number of ways in which 6 boys and 4 girls can be arranged in a row such that between any two girls there must be ex 19. If $C_0, C_1, C_2, \ldots, C_n$ are the binomial coefficients in the expansion of $(1+x)^n$ then the value of $\Sigma r^ 20. The coefficient of $x^{12}$ in the expansion of $\left(x^2+2 x+2\right)^8$ is 21. If $\frac{x^2+1}{\left(x^2+2\right)\left(x^2+3\right)}=\frac{A x+B}{x^2+2}+\frac{C x+D}{x^2+3}$, then $A+B+C+D=$ 22. If $2 \sin \theta+3 \cos \theta=2$ and $\theta \neq(2 n+1) \frac{\pi}{2}$, then $\sin \theta+\cos \theta=$ 23. If $\sin A=-\frac{24}{25}, \cos B=\frac{15}{17}, A$ does not belong to 4th quadrant and $B$ does not belong to 1st quadr 24. $$ 4 \cos \frac{7 \theta}{2} \cos \frac{3 \theta}{2} \sin 5 \theta= $$ 25. If $x \in(-\pi, \pi)$, then the number of solutions of the equation $2 \sin x \sin 3 x \sin 5 x+\sin 5 x \cos 4 x=0$ is 26. The number of values of $x$ satisfying the equation, $\tan ^{-1}\left(x+\frac{\sqrt{2}}{x}\right)+\tan ^{-1}\left(x-\fra 27. $\cot h^2 x-\tanh ^2 x=$ 28. If $a=3, b=5, c=7$ are the sides of a $\triangle A B C$, then its circumradius is 29. Two ships leave a port at the same time. One of them move in the direction of $E 50^{\circ} \mathrm{N}$ with a speed of 30. In a $\triangle A B C$, if $\mathbf{B C}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and $\mathbf{C A}=6 \ha 31. $\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, a_1 \hat{\mathbf{i}}+b_1 \hat{\mathbf{j}}+c_1 \hat{\mathbf{k}}, a_2 32. If $\mathbf{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and $\mathbf{b}=9 \hat{\mathbf{i}}+6 \hat{\mathbf 33. Let $\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \mathbf{b}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}} 34. Let $\mathbf{a}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}-2 \ha 35. The mean deviation from the mean of the discrete data $2,3,5,7,11,13,17,19,22$ is 36. Out of the given 25 consecutive position integers, three integers are drawn. If the least integer among given 25 integer 37. If three dice are thrown at a time, then the probability of getting the sum of the numbers on them as a prime number is 38. Three companies $C_1, C_2, C_3$ produce car tyres. A car manufacturing company buys $40 \%$ of its requirement from $C_1 39. The probability distribution of a random variable $X$ is given below. Then, the standard deviation of $X$ is $$ \begin{a 40. If the mean and variance of a binomial distribution are $\frac{4}{3}$ and $\frac{10}{9}$ respectively, then $P(X \geq 6) 41. A straight line passing through a point $(3,2)$ cuts $X$ and $Y$ axes at the points $A$ and $B$ respectively. If a point 42. By shifting the origin to the point $(-1,2)$ through translation of axes, if $a x^2+2 h x y+b y^2+2 g x+2 f y+c=0$ is th 43. If a line $L$ passing through the point $A(-2,4)$ makes an angel of $60^{\circ}$ with the positive direction of $X$ - ax 44. If the perpendicular drawn from the point $(2,-3)$ to the straight line $4 x-3 y+8=0$ meets it at $M(a, b)$ and $a^3-b^3 45. Let $Q$ be the image of a point $P(1,2)$ with respect to the line $x+y+1=0$ and $R$ be the image of $Q$ with respect to 46. If the slopes of the lines represented by the equation $6 x^2+2 h x y+4 y^2=0$ are in the ratio $2: 3$, then the value o 47. If $(3,-2)$ is the centre of the circle $S \equiv x^2+y^2+2 g x+2 f y-23=0$ and $A$ is a point on the circle $S=0$ such 48. Two circles which touch both the coordinate axes intersect at the points $A$ and $B$. If $A=(1,2)$, then $A B=$ 49. The lines $4 x-3 y+2=0$ intersects the circle $x^2+y^2-2 x+6 y+c=0$ at two points $A, B$ and $A B=8$. If $(1, k)$ is a p 50. If $2 x-3 y+5=0$ and $4 x-5 y+7=0$ are the equations of the normals drawn to a circle and $(2,5)$ is a point on the give 51. If $(\alpha, \beta)$ is the centre of the circle which passes through the point $(1,-1)$ and cuts the circles $$ x^2+y^2 52. The centre of the circle touching the circles $x^2+y^2-4 x-6 y-12=0$ $x^2+y^2+6 x+18 y+26=0$ at their point of contact a 53. The number of normals that can be drawn through the point $(2,0)$ to the parabola $y^2=7 x$ is 54. If $m_1$ and $m_2$ are the slopes of the tangents drawn from the point $(1,4)$ to the parabola $y^2=11 x$, then $2\left( 55. If the perpendicular distance from the focus of an ellipse $\frac{x^2}{9}+\frac{y^2}{b^2}=1(b 56. The length of the chord of the ellipse $\frac{x^2}{4}+y^2=1$ formed on the line $y=x+1$ is 57. Let $P, Q, R, S$ be the points of intersection of the circle $x^2+y^2=4$ and the hyperbola $x y=\sqrt{3}$. If $P=(\alpha 58. The number of values of ' $k$ ' for which the points $(-4,9, k),(-1,6, k),(0,7,10)$ from right-angled isosceles triangle 59. A line makes angles $60^{\circ}, 45^{\circ}, \theta$ with positive $X, Y, Z$ axes respectively. If $\theta$ is an acute 60. If the foot of the perpendicular drawn from the point $(2,0,-3)$ to the plane $\pi$ is $(1,-2,0)$ and the equation of th 61. If $[t]$ represents the greatest integer $\leq t$, then the value of $\lim\limits_{x \rightarrow 3} \frac{11-[2-x]}{[x+1 62. If the real valued function $$ f(x)=\left\{\begin{array}{ccc} \frac{\cos 3 x-\cos x}{x \sin x}, & \text { if } & x0 \end 63. If $y=\sqrt{\log \left(x^2+1\right)+\sqrt{\log \left(x^2+1\right)+\sqrt{\log \left(x^2+1\right)+\ldots+\infty}}, \text { 64. If $x=\sqrt{1-\tan y}$, then $\frac{d y}{d x}=$ 65. If $y=\sec ^{-1} x$, then $\frac{d^2 y}{d x^2}=$ 66. If $x=\sin 2 \theta \cos 3 \theta, y=\sin 3 \theta \cos 2 \theta$, then $\frac{d y}{d x}=$ 67. If the tangent and the normal drawn to the curve $x y^2+x^2 y=12$ at the point $(1,3)$ meet the X -axis in $T$ and $N$ r 68. A man of 5 feet height is walking away from a light fixed at a height of 15 feet at the rate of of $K$ miles/hour. If th 69. There is a possible error of 0.03 cm in a scale of length 1 foot with which the height of a closed right circular cylind 70. For a real number ' $a$ ', if a real valued function $f(x)=4 x^3+a x^2+3 x-2$ is monotonic in its domain, then the range 71. If the point $P\left(x_1, y_1\right)$ lying on the curve $y=x^2-x+1$ is the closest point to the line $y=x-3$, then the 72. $$ \int \frac{3^x(x \log 3-1)}{x^2} d x= $$ 73. If $\frac{5 \pi}{4} 74. $$ \int x \tan ^{-1} \sqrt{\frac{1+x^2}{1-x^2}} d x= $$ 75. $$ \int \frac{1}{(2 \cos x+\sin x)^2} d x= $$ 76. $$ \int_{-1}^1 \frac{\log 2-\log (1+x)}{\sqrt{1-x^2}} d x= $$ 77. $$ \int_0^{\frac{\pi}{4}} \frac{\sec x}{3 \cos x+4 \sin x} d x= $$ 78. $$ \int_{-2}^4\left|2-x^2\right| d x= $$ 79. The general solution of the differential equation $\frac{d y}{d x}+(\sec x \operatorname{cosec} x) y=\cos ^2 x$ 80. If the differential equation having $y=A e^x+B \sin x$ as its general solution is $f(x) \frac{d^2 y}{d x^2}+g(x) \frac{d

Physics

1. The range of weak nuclear force is of the order of 2. A piece of length 3.532 m is cut from a rod of length 43.4 m . The length of the remaining rod in metre is (up to correc 3. A person wearing a parachute jumps off a plane from a height of 2 km from the ground and falls freely for 20 m before hi 4. A ball projected at an angle of $45^{\circ}$ with the horizontal crosses two points at equal heights separated by a dist 5. A truck of mass 8 ton is carrying a block of mass 2 ton. If a breaking force of 25 kN is applied on the truck, then the 6. The work done in displacing a particle from $y=a$ to $y=2 a$ by a force $-\frac{K}{y^2}$ acting along $Y$-axis is 7. Due to the presence of air resistance, if a body dropped from a height of 20 m reaches the ground with a speed of $18 \m 8. A balance is made using a uniform metre scale of mass 100 g and two plates each of mass 200 g fixed at the two ends of t 9. The ratio of radii of gyration of a thin circular ring and a circular disc of same radius about a tangential axis in the 10. At a given place, to increase the number of oscillations made by a simple pendulum in one minute from 72 to 90 , the len 11. If the orbital speed of a body revolving in a circular path near the surface of the Earth is $8 \mathrm{kms}^{-1}$, then 12. The Young's modulus and Poisson's ratio of a material are respectively $Y$ and $\sigma$. The force required to decrease 13. A thin film of water is formed between two straight parallel wires each of length 8 cm separated by distance of 0.6 cm . 14. A rain drop of diameter 1 mm falls with a terminal velocity of $0.7 \mathrm{~ms}^{-1}$ in air. If the coefficient of vis 15. The temperature at which the reading on Fahrenheit scale becomes $90 \%$ more than the reading on Celsius scale is 16. A rectangular ice box of total surface area of $1000 \mathrm{~cm}^2$ initially contains 1.5 kg of ice at $0^{\circ} \mat 17. At constant pressure, equal amounts of heat are supplied to a monoatomic gas and a diatomic gas separately. The ratio of 18. If the rms speed of the molecules of a gas at a temperature of $77^{\circ} \mathrm{C}$ is $50 \mathrm{~ms}^{-1}$, then t 19. Two tuning forks of frequencies 320 Hz and 323 Hz are vibrated together. The time interval between a maximum sound and i 20. The frequency of sound heard by an observer moving towards a stationary source with certain speed is $n_1$ and if the ob 21. A cassegrain telescope uses two mirrors of radii of curvature 25 cm and 16 cm separated by a distance of 2.5 cm . The po 22. A convex lens of radii of curvature 6 cm and 12 cm is immersed in a liquid of refractive index 1.3. If the refractive in 23. When unpolarised light from air incidents on the surface of a medium of refractive index $\sqrt{3}$, then the reflected 24. An alpha particle and a proton are accelerated from rest in a uniform electric field. The ratio of the times taken by pr 25. A parallel plate capacitor with air as dielectric has a capacitance of $4 \mu \mathrm{~F}$. The space between the plates 26. The potential difference between the terminals of a cell is 20 V when a current of 2 A flows through the circuit. When t 27. A straight uniform wire of resistance $36 \Omega$ is bent in the form of a semi-circular loop. The effective resistance 28. An alpha particle moving with certain speed towards east enters a uniform magnetic field directed vertically up. The alp 29. The ratios of the voltage sensitivities, resistances and areas of the coils of two moving coil galvanometers $A$ and $B$ 30. A solenoid of 1000 turns per metre has a core of material with relative permeability 400 . The windings of the solenoid 31. An emf of 2.8 mV is induced in a rectangular loop of area $150 \mathrm{~cm}^2$ when the current in the loop changes from 32. A capacitor and a resistor of resistance $100 \sqrt{3} \Omega$ are connected in series to an AC source of voltage $100 \ 33. The amplitude of the electric field associated with a light beam of intensity $\frac{15}{\pi} \mathrm{Wm}^{-2}$ is 34. When photons incident on a photosensitive material of work function 1.5 eV , the maximum velocity of the emitted photoel 35. The potential energy of an electron in an orbit of hydrogen atom is -6.8 eV . The de-Broglie wavelength of the electron 36. If a radioactive substance decays $10 \%$ in every 16 hours, then the percentage of the radioactive substance that remai 37. If a nucleus $P$ converts into a nucleus $Q$ by the decay of one alpha particle and two $\beta^{-}$particles, then the n 38. The graph between the input voltage $\left(V_i\right)$ and the output voltage ( $V_o$ ) of a transistor connected in com 39. Which of the following logic gates is a universal gate? 40. The layer of the atmosphere which efficiently reflects high frequency waves particularly at night is

TG EAPCET 2025 (Online) 3rd May Evening Shift

MCQ (Single Correct Answer)

-0

If $x \in(-\pi, \pi)$, then the number of solutions of the equation $2 \sin x \sin 3 x \sin 5 x+\sin 5 x \cos 4 x=0$ is

TG EAPCET 2025 (Online) 3rd May Evening Shift

MCQ (Single Correct Answer)

-0

The number of values of $x$ satisfying the equation, $\tan ^{-1}\left(x+\frac{\sqrt{2}}{x}\right)+\tan ^{-1}\left(x-\frac{\sqrt{2}}{x}\right)=\tan ^{-1}(x)$ is

TG EAPCET 2025 (Online) 3rd May Evening Shift

MCQ (Single Correct Answer)

-0

$\cot h^2 x-\tanh ^2 x=$

$4 \operatorname{cosech} 2 x \tanh 2 x$

$4 \operatorname{sech} 2 x \operatorname{coth} 2 x$

$4 \operatorname{sech} 2 x \tanh 2 x$

$4 \cosh 2 x(\operatorname{cosech} 2 x)^2$

TG EAPCET 2025 (Online) 3rd May Evening Shift

MCQ (Single Correct Answer)

-0

If $a=3, b=5, c=7$ are the sides of a $\triangle A B C$, then its circumradius is

$\frac{7}{\sqrt{3}}$

$\frac{15}{2}$

$\frac{15 \sqrt{3}}{4}$

$\frac{\sqrt{3}}{2}$

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