TS EAMCET 2020 (Online) 10th September Evening Shift | TS EAMCET Year Wise Previous Years Questions

Chemistry

1. Which of the following statements is not true about Thomson's model of atom? 2. Which of the following statements is not the result of cathode ray discharge tube experiment with perforated anode? 3. The highest oxidation state observed in first row transition metals is 4. Based on the quantum numbers, what will be the maximum number of element for sixth period of the periodic table? 5. Let's assume the $\mathrm{C}_1 \equiv \mathrm{C}_2$ bond is acetylene is along $Z$-axis. Find out the correct combinatio 6. Which of the following molecules is not paramagnetic in nature? 7. Identify the correct observation with respect to the given graphs. 8. A gas is present at a pressure of 2 atm . What should be the increase in pressure, so that the volume of the gas can be 9. Identify the law for which the following statement is true. "Equal volume of all gases at same temperature and pressure 10. What is the equivalent weight of $\mathrm{KMnO}_4$ in acidic medium? (Molecular weight of $\mathrm{KMnO}_4=158 \mathrm{~ 11. What will be the $\Delta U$ value, when one mole of oxygen $\left(\mathrm{O}_2\right)$ is going from $-20^{\circ} \mathr 12. Calculate the molar solubility of calcium hydroxide $\mathrm{Ca}(\mathrm{OH})_2$ in 0.10 M NaOH solution. The ionic prod 13. Match the given ionisation constant values with the corresponding acids. $$ \begin{array}{lll} \hline \text { A. } & \ma 14. With reference to the redox properties of hydrogen peroxide $\left(\mathrm{H}_2 \mathrm{O}_2\right)$, which of these rea 15. Which halide of alkaline earth metals is covalent in nature and can be soluble in organic solvent, such as ethanol? 16. An aqueous solution of borax is 17. Which among the following is/are primary component(s) of the synthesis gas? 18. Which of the following is air pollutant? 19. $$ \text { Hybridisations of carbon-2 in } P \text { and } Q \text { are respectively. } $$ 20. A benzene derivative did not produce white precipitate with the ammonical silver nitrate solution but decolorised the co 21. Which of the following can be used as the test for unsaturation with regard to colour change of reaction? 22. In a bcc lattice having the edge length of 200 pm , the cation has the radius of 70 pm . The radius ratio of $\frac{r^{+ 23. An aqueous solution of $98 \%(w / w) \mathrm{H}_2 \mathrm{SO}_4$ has density of $1.02 \mathrm{~g} / \mathrm{cc}$. The mo 24. 25 mL of 0.1 N NaOH solution neutralises 12.5 mL of HCl solution. The amount of water needed to convert 500 mL of such H 25. The maximum work that can be obtained from the following cells is $$ X\left|X^{2+}(a q) \| Y^{+}(a q)\right| Y $$ Given, 26. The specific rate constant of decomposition of a compound is given by $\ln k=5.0-\frac{12000}{T}$. The activation energy 27. Which of the following statements is correct for chemisorption? 28. $$ \text { Match the following. } $$ $$ \begin{array}{llll} \hline & \text { Ores } & & \text { Composition } \\ \hline 29. The molecular formula of metaphosphoric acid is 30. The final acid product obtained during the synthesis of $\mathrm{H}_2 \mathrm{SO}_4$ by contact process is 31. Among the following series of transition metal ions, the one in which all the metal ions have $3 d^2, 3 p^6$ electronic 32. The correct match for complex with its magnetic behaviour in the following is 33. Which of the following are synthetic rubbers? (i) Terylene (ii) Buna-S (iii) Buna-N (iv) Neoprene (v) Polyacrylonitrile 34. $$ \text { Choose the correct Zwitter ionic form for aspartic acid. } $$ 35. Paracetamol is 36. The major products $P$ and $Q$ formed in the following reactions are respectively. 37. $$ \text { The major product formed in the following reactions is :} $$ 38. $$ \text { The major product formed in the following is } $$ 39. What is the product $R$ in the following reaction sequence? 40. $$ \text { The major product formed in the following reactions is } $$

Mathematics

1. If $f(x)=x-\frac{1}{x}, x \neq 0$, then $3 f(x)=$ 2. Let $[\cdot]$ denote greatest integer function. If $f(x)=[x]$ and $g(x)=3\left[\frac{x}{3}\right]$, then the set of all 3. If $S_n$ is the sum of the first $n$ terms of the series $1^2+2 \times 2^2+3^2+2 \times 4^2+5^2+2 \times 6^2+\ldots \inf 4. Let $A=\left[\begin{array}{ccc}1 & 4 & 2 \\ 2 & -1 & 4 \\ -3 & 7 & -6\end{array}\right]$ and $B=\left[b_{i j}\right]_{3 5. A is a $m \times n$ matrix of rank 4 . If A contains an $m$ th order non singular sub matrix and $A^T A$ is a $7 \times 6. If $C$ and $D$ are two $n \times n$ non-singular matrices over the set of real number $\mathbf{R}$ such that $C D=-D C$, 7. If $z_1=x_1+i y_1, z_2=x_2+i y_2, z_3=x_1+\frac{i x_2}{2}, z_4=2 y_1+i y_2$ are complex numbers such that $\left|z_1\rig 8. Assertion (A) If $z$ is a complex number such that $|z| \geq 3$, then the least value of $\left|z+\frac{3}{z}\right|$ is 9. $$ \text { If }\left(\frac{\cos \theta+i \sin \theta}{\sin \theta+i \cos \theta}\right)^{2020}+\left(\frac{1+\cos \theta 10. If $\omega$ is a complex cube root of unity, then $\sum_{x=1}^{10}\left((\omega x+2)\left(\omega^2 x+2\right)-3\right)$ 11. If $\alpha$ and $\beta$ are the real roots of the equation $\sqrt{\frac{5 x}{x-2}}+\sqrt{\frac{x-2}{5 x}}=\frac{29}{10}$ 12. The minimum value of $\frac{9 \cdot 3^{2 x}+6 \cdot 3^x+4}{9 \cdot 3^{2 x}-6 \cdot 3^x+4}$ is 13. $p$ is non-zero real number. If the equation whose roots are the squares of the roots of the equation $x^3-p x^2+p x-1=0 14. If the roots of the equation, $8 x^3+6 p x^2+3 q x-27=0$ are in a geometric progression, then $q^2+9 p^2+6 p q+q / p=$ 15. If $x$ and $y$ represent the number of arrangements of the letters of word ATRAPATRAM such that (i) all A's are together 16. Numbers between 1 and 10,000 are formed using the digits 2 and 3 only once and the digit 4 twice. If the numbers thus fo 17. If the 9th and 10th terms are the numerically greatest terms in the expansion of $(5 x-6 y)^n$ when $x=2 / 5$ and $y=1 / 18. $$ 1-\frac{3}{16}+\frac{1 \cdot 4}{1 \cdot 2}\left(\frac{3}{16}\right)^2-\frac{1 \cdot 4 \cdot 7}{1 \cdot 2 \cdot 3}\lef 19. If $\frac{2 x+1}{(x-1)^2\left(x^2+1\right)}=\frac{A}{x-1}+\frac{B}{(x-1)^2}+\frac{C x+D}{x^2+1}$, then $A+B+C+D=$ 20. Let $a$ be maximum value of $(3 \cos \theta-4 \sin \theta)$ and $\theta \neq \frac{n \pi}{2}$. If $\alpha=a \sin ^2 \the 21. If $A$ does not belong to the first quadrant, $B$ does not belong to the second quadrant, $\sin A=\frac{11}{61}$ and $\c 22. If $\cos \left(\frac{\pi}{4}-x\right) \cos 2 x+\sin x \sin 2 x \sec x =\cos x \sin 2 x \sec x+\cos \left(\frac{\pi}{4}+x 23. The general solution of the equation $(\sqrt{3}-1) \sin \theta+(\sqrt{3}+1) \cos \theta=2$ is 24. If $\sin ^{-1}\left(\frac{12}{x}\right)+\sin ^{-1}\left(\frac{5}{x}\right)=\frac{\pi}{2}$, then $x=$ 25. $$ \log (9+3 \sqrt{2}(2+\sqrt{5})+4 \sqrt{5})= $$ 26. In a $\triangle A B C,\left(b^2-c^2\right) \cot A+\left(c^2-a^2\right) \cot B=$ 27. In a $\triangle A B C, \frac{\Delta^2}{a^2+b^2+c^2}\left(\frac{1}{r_1^2}+\frac{1}{r_2^2}+\frac{1}{r_3^2}+\frac{1}{r^2}\r 28. If $R: r_1: r=5: 12: 2$, then $r+r_3+r_2-r_1=$ 29. If $12 \hat{\mathbf{i}}-12 \hat{\mathbf{j}}-18 \hat{\mathbf{k}},-3 \hat{\mathbf{i}}-6 \hat{\mathbf{j}}-9 \hat{\mathbf{k} 30. Let $\Pi$ be a plane containing the points $(0,-5,-1),(1,-2,5),(-3,5,0)$ and $L$ be a line passing through the point $(0 31. For non-coplanar vectors $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$, if the point of intersection of the line $\mathbf{r} 32. If the orthocentre of the triangle whose vertices are $2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}, 5 \hat{ 33. If the vectors $\mathbf{A B}=p \hat{\mathbf{i}}+q \hat{\mathbf{j}}+r \hat{\mathbf{k}}, \mathbf{A C}=s \hat{\mathbf{i}}+3 34. Let $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ be three unit vectors such that $\mathbf{a} \times(\mathbf{b} \times \math 35. Assertion (A) Variance of $4 x_1, 4 x_2, \ldots, 4 x_n$ is 16 times the variance of $x_1, x_2, x_3, \ldots, x_n$ Reason 36. If $\alpha, \beta$ are respectively the mean deviation about the mean and variance of the first five prime numbers, then 37. If $A_1, A_2, \ldots, A_{15}$ are the events of a random experiment, then which one of the following is true? 38. In an examination there are four Yes/No type of questions. The probability that the answer by the student to a question 39. Four boxes $A, B, C$ and $D$ contain 5000, 3000, 2000 and 1000 fuses respectively. The percentages of defective fuses in 40. A die is thrown thrice. If getting 1 or 6 in a single throw is considered as success, then the variance of the number of 41. In a hospital, on an average if there are 35 births in a weak, then the probability that there will be less than 3 birth 42. Let $A(2,1)$ be a point and equation of the straight line $L$ be $x-y=0$. Let $a$ and $b$ respectively represent the dis 43. The point $(4,1)$ undergoes the following transformations successively : (i) Reflection is the line $x-y=0$ (ii) Shiftin 44. A function $f: \mathbf{R} \rightarrow \mathbf{R}$ is such that $f(\mathrm{l})=2$ and $f(x+y)=f(x) \cdot f(y) \forall x, 45. Two straight lines $3 x+4 y=5$ and $4 x-3 y=15$ intersect at the point $A$. The equations of the lines passing through $ 46. The equation of a line making an angle $60^{\circ}$ with the line $x+y-3=0$ and passing through the point $(1,1)$ is 47. Let $P$ be the pair of lines represented by $2 x^2-5 x y+2 y^2+6 x-3 y=0$ and consider the following independent stateme 48. The combined equation of the diagonals of the parallelogram formed by the lines $$ \left(7 x^2-4 x y+8 y^2\right)^2+(4 x 49. If the origin lies on a diameter of the circle $x^2+y^2-4 x-2 y-4=0$, then the equation of the circle passing through th 50. If $\alpha \neq-4$ and $(2, \alpha)$ is the mid-point of a chord of the circle $x^2+y^2-4 x+8 y+6=0$, then the values of 51. $C_1$ and $C_2$ are the external and internal centres of similitude of the circles $x^2+y^2-2 x+4 y+1=0$ and $x^2+y^2+4 52. Suppose the circle $S: x^2+y^2+2 g x+2 f y+c=0$ cuts orthogonally the two circles $S^{\prime}: x^2+y^2-4 x-6 y+11=0$ and 53. If the circle $S_1: x^2+y^2=16$ intersects another circle $S_2$ of radius 5 units such that the common chord is of maxim 54. For the parabola $y=\frac{h^3}{3} x^2+\frac{h^2}{2} x-h+\frac{3}{4 h^3}$, if the equation of directrix is $y=k$, then $k 55. The equation of the common tangent of the parabolas $x^2=108 y$ and $y^2=32 x$ is 56. The ellipse having its foci $(0, \pm 1)$ and major axis of length $\sqrt{5}$ is 57. An ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ with eccentricity $\frac{2 \sqrt{2}}{3}$ is inscribed in a circle $x^2+y^ 58. If the circle $x^2+y^2=a^2$ intersects the hyperbola $x y=b^2$ at four points $\left(x_1, y_1\right),\left(x_2, y_2\righ 59. If the line passing through the points $(a, 2,-4)$ and $(5,3, b)$ crosses the $Z X$-plane at the point $(-a+2 b, 0, a+b) 60. The direction cosines of the normal to the plane containing the lines having direction ratios $1,2,1$ and 4,5, -3 are 61. The foot of the perpendicular drawn from the point $(1,1,1)$ to the plane $\pi_1$ is $(1,3,5)$. If $(2,2,-1),(3,4,2)$, $ 62. $$ \mathop {\lim }\limits_{x \to 0} \frac{1-\cos \left(x^2+\pi(x+2)\right)}{x^2}= $$ 63. The value of ' $a$ ' for which the function $f(x)=\left\{\begin{array}{cl}\frac{1-\cos 4 x}{x^2}, & x 64. $$ \begin{aligned} & \text { If } f(x)=\tan ^{-1}\left(\frac{1}{\sin ^2 x+\sin x+1}\right) \\ & \quad+\tan ^{-1}\left(\f 65. If $\alpha$ is such a minimum value for which the inverse of $f(x)=x^2+3 x-3$ exists in $[\alpha, \infty)$ and $g$ is th 66. If $y=e^{a x}(\cos b x+\sin b x)$ satisfies the equation $\frac{d^2 y}{d x^2}-K \frac{d y}{d x}+L y=0$, then $L+b K=$ 67. If $\frac{k}{\alpha^3}$ is the length of the sub normal at any point $P(\alpha, y)$ on the curve $x^2-a^2=\frac{x^2 y^2} 68. A tank in the shape of a rectangular parallelopiped has volume 27 cubic meters. This tank is filled with water such that 69. Let $f:[2,5] \rightarrow \mathbf{R}$ be a differentiatiable function and $\frac{f(5)}{f(2)}=1$. If there is a $c \in(2,5 70. Let $f:[2,5] \rightarrow \mathbf{R}$ be a differentiatiable function and $\frac{f(5)}{f(2)}=1$. If there is a $c \in(2,5 71. $$ \text { Match the functions of List I with the items of List II. } $$ List I List II A. 3 x 4 72. For $x \in\left(\frac{3 \pi}{4}, \pi\right), \int(\sqrt{1+\sin 2 x}+\sqrt{1-\sin 2 x}) d x=$ 73. $$ \begin{aligned} & \text { If } \int \frac{x^2\left(x \sec ^2 x+\tan x\right)}{(x \tan x+1)^2} d x=A \log (|x \sin x+\ 74. $$ \text { If } \begin{aligned} & \int x^3(\log x)^2 d x=x^4\left[A(\log x)^2+B(\log x)\right. \\ &+C \log e]+K, \text { 75. $$ \begin{aligned} & \text { If } \int \frac{9 x+15}{x^3-6 x-9} d x=A \log |g(x)| \\ & \quad+B \log |f(x)|+C, \text { th 76. $$\mathop {\lim }\limits_{x \to \infty } \frac{\pi}{2 n}\left[\sin \frac{\pi}{2 n}+\sin \frac{2 \pi}{2 n}+\ldots+\sin \f 77. $$ \int_0^{\pi / 2} \frac{d x}{4+5 \sin x} $$ 78. The area (in square units) of the region enclosed between the parabola $y^2=2 x$ and the line $y=4 x-1$ 79. The differential equation for which $y=a x^2+b x+c$ is the general solution is 80. The general solution of the differential equation $(3 y-7 x+7) d x+(7 y-3 x+3) d y=0$ is 81. The general solution of the differential equation $(3 y-7 x+7) d x+(7 y-3 x+3) d y=0$ is 82. The general solution of the differential equation $x \cos \frac{y}{x}(y d x+x d y)=y \sin \frac{y}{x}(x d y-y d x)$ is

Physics

1. In atomic scale the weakest force in nature is 2. In five successive measurements, the mass of a ball is measured to be $2.61 \mathrm{~g}, 2.58 \mathrm{~g}, 2.40 \mathrm{ 3. A particle is moving along the $Y$-axis. The position of the particle from the origin as a function of time $(t)$ is giv 4. Two cars $A$ and $B$ are moving with speeds $v_A=120 \mathrm{km} / \mathrm{h}$ and $v_B=50 \mathrm{~km} / \mathrm{h}$ re 5. Initial velocity with which a body is projected is $10 \mathrm{~m} / \mathrm{s}$ from the base of an inclined plane as s 6. A projectile is fired at an angle of $45^{\circ}$ with the horizontal. Elevation angle of the projectile at its highest 7. A point $P$ is moving in uniform circular motion with radius 3 m . Let at some instant the acceleration of the point is 8. A block of mass 3 kg is pressed against a vertical wall by applying a force $F$ at an angle $30^{\circ}$ to the horizont 9. A force $\mathbf{F}=(2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}) \mathrm{N}$ is applied on an object of mass $M$. What is the 10. A ball of mass $m=1 \mathrm{~kg}$ is thrown from the top of a building with initial velocity $\mathbf{v}=(20 \mathrm{~m} 11. A solid sphere and a solid cylinder, each of mass $M$ and radius $R$ are rolling with a linear speed on a flat surface w 12. An object of mass 2 kg is hanging from a rope that is wrapped around a pulley of radius 25 cm . The mass of pulley is 2 13. A point mass oscillates along the $X$-axis according to the law $x=x_0 \cos \left(\omega t-\frac{\pi}{4}\right)$. If the 14. The graph correctly represents the variation of acceleration due to gravity $(g)$ with radial distance from the centre o 15. The length of a metal wire is found to be $L_1$ and $L_2$ when the tension of $T_1$ and $T_2$ are applied to it respecti 16. A cubical block of wood having mass of 160 g has a metal piece fastened underneath as shown in the figure. Find the maxi 17. A solid of 2 kg mass absorbs 50 kJ when its temperature is raised from $20^{\circ} \mathrm{C}$ to $70^{\circ} \mathrm{C} 18. A solid cylinder of radius $r_1=2.5 \mathrm{~cm}$, length $l_1=5.0 \mathrm{~cm}$ and temperature $40^{\circ} \mathrm{C}$ 19. Five moles of an ideal gas has pressure $p_0$, volume $V_0$ and temperature $T_0$. The gas is expanded to volume $3 V_0$ 20. How many rotational degrees of freedom does a rigid diatomic molecule have? 21. The transverse displacement $y(x, t)$ of a wave on a string is given by $y(x, t)=e^{-\left(a x^2+b t^2+2 \sqrt{a b x} t\ 22. A telescope has an objective of focal length 100 cm and an eye-piece of focal length 5 cm . The magnifying power of the 23. A convex lens and a concave lens, each with focal length of 4 cm are separated by a distance of 6 cm along their axis. A 24. The limit of resolution of a telescope is $3.0 \times 10^{-7} \mathrm{rad}$. Assuming that it is used to see the light o 25. Two negative charges of equal magnitude are located in $x y$-plane as shown below in the figure. The direction of the el 26. An infinite non-conducting sheet has a surface charge density $2 \times 10^{-7} \mathrm{C} / \mathrm{m}^2$ on one side. 27. A cylindrical wire $P$ has resistance $10 \Omega$. A second wire $Q$ has length and diameter half that of $P$. If the ma 28. Find the current in the circuit. 29. Two tangent galvanometers $A$ and $B$ have coils of radii 8 cm and 16 cm respectively and having resistance of 8 $\Omega 30. A particle of charge $q$ and mass $m$ moves in a circular orbit of radius $r$ with angular speed $\omega$. The ratio of 31. Two short magnets of equal dipole moments $M$ are fastened perpendicularly at their centres which lies at origin. Let tw 32. A varying current in a coil changes from 10 A to zero in 1.5 s . If the average emf induced in the coil is 200 V , the s 33. An alternating voltage $\varepsilon=30 \sin 200 t$ (in volts) is applied to the circuit below. The amplitude of the curr 34. A parallel-plate capacitor with circular plates is being discharged. The radius of the circular plate is 10 cm . A circu 35. Let $v_1$ and $v_2$ be the maximum velocities of the emitted electrons when the surface of a metal is illuminated with l 36. The wavelength of a spectral line emitted by hydrogen atom in the Balmer series is $\frac{16}{3 R}$ ( $R$ is Rydberg con 37. The half-life of a radioactive sample is 5 s . If the initial mass of the sample is 60 g , then the time required to red 38. A Zener diode is connected to battery and a load resistance as shown below The currents $I, I_Z$ and $I_L$ respectively 39. A semiconductor is doped with phosphorous atoms as impurity. The impurity levels created in the semiconductor are close 40. Assertion (A) Television signals are received through sky-wave propagation. Reason (R) The ionosphere reflects electroma

TS EAMCET 2020 (Online) 10th September Evening Shift

MCQ (Single Correct Answer)

-0

The foot of the perpendicular drawn from the point $(1,1,1)$ to the plane $\pi_1$ is $(1,3,5)$. If $(2,2,-1),(3,4,2)$, $(3,3,0)$ are three points on the plane $\pi_2$, then the angle between the planes $\pi_1$ and $\pi_2$ is

$\frac{\pi}{2}$

$\cos ^{-1}\left(\frac{1}{3}\right)$

$\frac{\pi}{6}$

$\cos ^{-1}\left(\frac{2}{5}\right)$

TS EAMCET 2020 (Online) 10th September Evening Shift

MCQ (Single Correct Answer)

-0

$$ \mathop {\lim }\limits_{x \to 0} \frac{1-\cos \left(x^2+\pi(x+2)\right)}{x^2}= $$

$\frac{\pi}{2}$

$\frac{\pi^2}{4}$

$\frac{\pi^2}{2}$

$\frac{\pi}{4}$

TS EAMCET 2020 (Online) 10th September Evening Shift

MCQ (Single Correct Answer)

-0

The value of ' $a$ ' for which the function

$f(x)=\left\{\begin{array}{cl}\frac{1-\cos 4 x}{x^2}, & x<0 \\ \frac{a}{\sqrt{x}}, & x=0 \text { is continuous at } x=0, \text { is } \\ \frac{\sqrt{16+\sqrt{x}}-4}{\sqrt{16+}} & \end{array}\right.$

$\frac{1}{2}$

TS EAMCET 2020 (Online) 10th September Evening Shift

MCQ (Single Correct Answer)

-0

$$ \begin{aligned} & \text { If } f(x)=\tan ^{-1}\left(\frac{1}{\sin ^2 x+\sin x+1}\right) \\ & \quad+\tan ^{-1}\left(\frac{1}{\sin ^2 x+3 \sin x+3}\right)+\tan ^{-1} \end{aligned} $$

$\left(\frac{1}{\sin ^2 x+5 \sin x+7}\right)+\ldots+$ upto 10 terms, then $f^{\prime}(0)=$

$\frac{-1}{101}$

$\frac{100}{101}$

$\frac{-100}{101}$

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