TS EAMCET 2020 (Online) 14th September Evening Shift | TS EAMCET Year Wise Previous Years Questions

Chemistry

1. Given the ratio of kinetic energy of electron in two orbitals is $16: 9$. Calculate the ratio of wavelength of electron 2. Which of the following results is not true about photoelectric effect? 3. Trans uranium elements are 4. Arrange the following ions in the correct order with respect to their ionic radii. 5. What is the correct order of bond lengths in the following molecules? I. $\mathrm{O}_2$ II. $\mathrm{O}_2^{+}$ III. $\ma 6. Which one of the following compound is hypervalent? 7. What is the ratio of kinetic energy of 7 grams of nitrogen and 4 grams of oxygen at $T(\mathrm{~K})$ ? 8. Equal amount of gases are kept in two separate containers. If densities of the two gases are in $1: 2$ ratio and their t 9. Given the ratio of amounts of nitrogen and oxygen in a particular gaseous mixture is $4: 1$. Calculate the ratio of numb 10. Sulphuric acid reacts with sodium hydroxide as follows: $$ \mathrm{H}_2 \mathrm{SO}_4+2 \mathrm{NaOH} \longrightarrow \m 11. For the reactions, $$ \begin{aligned} 2 \mathrm{Cl}(g) & \longrightarrow \mathrm{Cl}_2(g) \\ \mathrm{CO}_2(g) & \longrig 12. Which of the following statement is correct? 13. For a given reaction, $2 A \rightleftharpoons B+C$, the equilibrium constant is $2 \times 10^{-3}$. If at any given time 14. At atmospheric pressure and very low temperature, water crystallises to 15. Which of the following statement(s) are correct, when alkali metals burn in the presence of oxygen? I. Lithium forms mon 16. Pick the correct statement. I. Borax is white crystalline solid containing $\left[\mathrm{B}_4 \mathrm{O}_5(\mathrm{OH}) 17. Which element does not show catenation property? 18. Acid rain is mainly caused by the emissions of which of the following gases? I. Sulphur dioxide II. Carbon dioxide III. 19. During the course of estimating nitrogen using Kjeldahl's method, the organic compound is heated with 20. An organic compound, ' $A$ ' with molecular formula $\mathrm{C}_8 \mathrm{H}_8 \mathrm{O}$ on reaction with $\mathrm{I}_ 21. The order of circled $\mathrm{C}-\mathrm{H}$ bond dissociation energy in the following compound is 22. Intercepts of a plane in crystal is given by $a, b / 2,3 c$ in a simple cubic unit cell. The miller indices are 23. Relative lowering of vapour pressure of a dilute solution is 0.5 . What is the mole fraction of the non-volatile solute? 24. The solubility product of a sparingly soluble $A B_2$ salt is $2.56 \times 10^{-4} \mathrm{M}^3$ at $25^{\circ} \mathrm{ 25. $\mathrm{Mg}^{2+}$ displaces hydrogen from acids but copper does not. A galvanic cell prepared by combining $\mathrm{Cu} 26. For a reversible reaction $A \rightleftharpoons B$, pre-exponential factor is same for both the forward and backward rea 27. Which of the following is true for spontaneous adsorption? 28. Which element does not exist in elemental state in the earth's crust? 29. Phosphine is prepared by the reaction of $\mathrm{P}_4$ with which of the following? 30. The most stable form of sulphur allotrope is 31. When $\left[\mathrm{Ti}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right] \mathrm{Cl}_3$ is heated at $250^{\circ} \mathrm{C} 32. Which compound is zero valent metal complex? 33. $$ \text { The structure given below is an example of } $$ I. A condensation and biodegradable polymer. II. A biodegrada 34. Which of the following statements support the cyclic form for glucose? (i) It doesn't give Schiff's test. (ii) It is f 35. $$ \text { The structure of paracetamol is } $$ 36. Arrange the following in the correct order of reactivity towards nucleophilic substitution reaction. I. 1-chloro-2-nitro 37. Reactions that produce $n$-butanol in the following are : I. $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}=\mathrm{CH}_2 \xri 38. $$ \text { What are } X \text { and } Y \text { in the following reaction sequence? } $$ 39. $$ \text { Predict } A \text { and } B \text { in the following reaction sequence : } $$ $$ \mathrm{CH}_3-\mathrm{CH}_2- 40. The major product formed by the reaction of benzylamine with nitrous acid is

Mathematics

1. If $f: Z \rightarrow N$ is defined by $$ f(n)=\left\{\begin{array}{cll} 2 n, & \text { if } & n>0 \\ 1, & \text { if } & 2. Domain of $\cos ^{-1}\left[\log _5\left(x^2+7 x+15\right)\right]$ is 3. Let $f(n)=A(-2)^n+B(-3)^n \forall A, B \in \mathbf{R}$ and $n \in \mathbf{N}-\{1,2\}$. If $f(n)+a f(n-1)+b f(n-2)=0$, th 4. If $a$ and $b$ are any two real numbers, then $$ \left|\begin{array}{ccc} 2 a-2 b-4 & 4 a & 4 a \\ 4 & 2-b-a & 4 \\ 2 b 5. Let $A=\left[\begin{array}{ccc}2 & -2 & -4 \\ -1 & 3 & 4 \\ 1 & -2 & x\end{array}\right]$ and $A^2=A$. If $r$ is the ran 6. Let $a, b, c, d \in \mathbf{R}$ be such that $a d-b c \neq 0$ and $e$ be a positive number other than 1 . If $x^a y^b=e^ 7. Let $z$ be a complex number such that $|z|-z=2+i$, where $i=\sqrt{-1}$. Then, $|z|=$ 8. If the amplitude of $z-2-3 i$ is $\pi / 4$, then the locus of $z=x+i y$ is 9. If $1+\frac{\cos \theta}{2}+\frac{\cos 2 \theta}{4}+\frac{\cos 3 \theta}{8}+\ldots \ldots=\frac{a-2 \cos \theta}{5+b \co 10. For $n>1$ and $n \in \mathbf{N}$, if $z_1, z_2, \ldots, z_n$ are the roots of the equation $(z+1)^n=z^n$, then $\sum_{i= 11. If $x$ is real, then the maximum and minimum values of $\frac{x^2+14 x+9}{x^2+2 x+3}$ are respectively 12. When $\mathbf{R}$ is the set of all real numbers, $$ \left\{x \in \mathbf{R}: \frac{\sqrt{12-x-x^2}}{x+10} \leq \frac{\s 13. If $\alpha$ and $\beta$ are two complex roots of the equation $6 x^6-25 x^5+31 x^4-31 x^2+25 x-6=0$, then $\alpha+\beta= 14. If $\alpha$ is a root of multiplicity 3 of the equation $x^5-8 x^4+25 x^3-38 x^2+28 x-8=0$, then $\alpha^2-5 \alpha+6=$ 15. Consider the following statements: I. The number of positive integral solutions of $x_1+x_2+x_3+x_4=10$ is 286 . II. If 16. A student is allowed to select at least $(n+1)$ books but not all books from a collection of ( $2 n+1$ ) books. If the t 17. If $x$ is so small that all terms containing $x^2$ and higher powers of $x$ can be neglected, then the approximate value 18. The sum of the coefficients of $x^{-3 / 2}$ and $x^3$ in the expansion of $\sqrt{3+x}+\sqrt{5+x}$ when $3 19. If $\frac{x^5-5}{x^3+x^2}=f(x)+\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x+1}$, then the larger value of $K$ for which $f(K)+A+ 20. If $\cos x-\sin x=\sqrt{a} \sin x$, then $a \sin x+\cos x-\sin x=$ 21. $$ \text { Match the items of List-I to the items of List-II } $$ .tg {border-collapse:collapse;border-spacing:0;} .tg 22. If $\cot \left(\frac{A}{2}\right)=\sqrt{\frac{1+a}{1-a}} \cdot \cot \left(\frac{\theta}{2}\right)$, then $\cos \theta=$ 23. If $\sum\limits_{n=1}^k \tan ^{-1}\left(\frac{1}{n^2+3 n+3}\right)=\tan ^{-1} \alpha$, then $\alpha=$ 24. The set of values of $x$ such that $\tan ^{-1}\left(\frac{x}{x-2}\right)-\tan ^{-1}\left(\frac{x}{2 x-1}\right)=\tan ^{- 25. If $\sin \theta \cosh \alpha=\tan x, \cos \theta \sinh \alpha=\sec x$, then $\cos 2 \theta \cosh 2 \alpha=$ 26. If the sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one, then t 27. In $\triangle A B C, A D$ and $B E$ are medians drawn from $A$ and $B$. If $A D=\frac{7}{2}, \angle D A B=\frac{\pi}{8}$ 28. If the radius of the incircle of a triangle with sides $5 k, 6 k$ and $5 k$ is 6 , then the largest angle of that triang 29. If $\mathbf{a , b , c}$ are three independent vectors and there exists a non zero scalar traid $(l, m, n)$ such that $l( 30. If $\mathbf{a}$ and $\mathbf{b}$ represent two non collinear vectors, the equation $\mathbf{r}=t \mathbf{a}+(1-t) \mathb 31. Let $\mathbf{a , b , c}$ be three vectors such that the magnitude of $\mathbf{b}$ is twice that of $\mathbf{a}$ and magn 32. If $\mathbf{a , b , c}$ are three mutually perpendicular vectors such that the magnitudes of $\mathbf{b}$ and $\mathbf{c 33. The locus of the point $P(\mathbf{r})$ which encloses a triangle $A B P$ of area 1 sq. unit with the fixed points $A(\ha 34. The shortest distance between the skew-lines $\mathbf{r}=(-\hat{\mathbf{i}}+3 \hat{\mathbf{k}})+t(2 \hat{\mathbf{i}}+3 \ 35. In a discrete data $\frac{1 \text { th }}{4}$ of the observations are equal to $a$, another $\frac{1 \text { th }}{4}$ o 36. For the following distribution, the mean deviation about the median is $$ \begin{array}{cccccccc} \hline x_i & 6 & 12 & 37. If a man throws a die until he gets a number bigger than 3 , then the probability that he gets a 5 in his last throw is 38. A diagnostic test has the probability 0.95 of giving a positive result when applied to a person suffering from a certain 39. Consider the following statements Assertion (A) If $P_1, P_2, P_3$ are probability of happening of three independent eve 40. If probability function of a discrete random variable $X$ is $P(X=r)=r / k, r=1,2,3,4,5$, then $P\left(X=2\right.$ or $\ 41. If the probability that an individual will suffer a reaction from an injection of a drug is 0.001 , then the probability 42. Let $A=(2,3), B=(3,-5)$ be two vertices of $\triangle A B C$ such that $C$ is a point on the line $L \equiv 3 x+4 y-5=0$ 43. If $a \alpha^2+b \beta^2+c \alpha \beta+d=0$ is the transformed equation of $4 x^2+\sqrt{3} x y+5 y^2-4=0$ obtained by u 44. If the normal form of the equation of a straight line $4 x+3 y+2=0$ is $x \cos \alpha+y \sin \alpha=p$ and its intercept 45. For an integer $K$, if the point $P\left(K^2, K+1\right)$ and the origin $O(0,0)$ lie in the same region between the lin 46. The area (in square units) of the quadrilateral formed by the point of intersection of the lines $x+y-1=0$, $x-y+1=0$, t 47. The condition that the lines joining the origin to the points of intersection of the two curves $x^2+y^2+g x+c=0, x^2+y^ 48. If $\alpha$ represent the square of the distance between the origin and the point of intersection of the lines $x^2-y^2- 49. If the parametric equations of the circle passing through the points $(3,4),(3,2)$ and $(1,4)$ is $x=a+r \cos \theta$, $ 50. From a point $P$ on the circle $x^2+y^2-4 x-6 y+9=0$, a pair of tangents $P Q$ and $P R$ are drawn touching the circle $ 51. The equations of the tangents drawn from the origin to the circle $x^2+y^2+2 g x+2 f y+g^2=0$ are 52. If $2 x+y=0$ is the equation of a chord of the circle $x^2+y^2-2 x-6 y+3=0$, then the circle with this chord as diameter 53. If the radical axis of the circles $x^2+y^2+2 \alpha x+2 \beta y+c=0$ and $x^2+y^2+\frac{3}{2} x+4 y+c=0$ touches the ci 54. If $P Q$ is a focal chord of the parabola $y^2=4 x$ with focus $S$ and $P=(4,4)$, then $S Q=$ 55. If the parabola $x^2=4 a y,(a>0)$ makes an intercept of length $\sqrt{40}$ units on the line $y=1+2 x$ then $4 a=$ 56. If tangents are drawn to the ellipse $x^2+2 y^2=2$, then the locus of the mid-points of the intercepts made by those tan 57. The area (in sq. units) of the quadrilateral formed by the tangents drawn at the end points of the latus rectum to the e 58. If $p, q$ are the eccentricities of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ and its conjugate hyperbola respec 59. $\Pi_1, \Pi_2, \Pi_3$ are three planes which are respectively parallel to the $Y Z, Z X$ and $X Y$ planes at distances $ 60. The obtuse angle between the lines whose direction ratios are determined by the equations $a+b+c=0$, $2 a b+2 a c-b c=0$ 61. A plane meets the coordinate axes at $A, B, C$ respectively such that the centroid of the $\triangle A B C$ is $(2,3,5)$ 62. Let $[x]$ denote the greatest integer less than or equal to $x$ and $k \geq 2$ be an integer. Then $$ \mathop {Lt}\limit 63. Define $f(x)=\left\{\begin{array}{ll}1+x, & 0 \leq x \leq 2 \\ 3-x, & 2 If $f \circ f(x)$ is discontinuous at $a$ and $ 64. $$ \frac{d}{d x}\left[\operatorname{cosech}^{-1}(\tan 2 x)\right]= $$ 65. If $f(x)=\frac{1}{x^3} \int_5^x\left(2 u^2-u f^{\prime}(u) d u\right.$, then $f^{\prime}(5)=$ 66. Let $f: R \rightarrow R$ be defined by $f\left(\frac{x+y}{2}\right)=\frac{f(x)+f(y)}{2}$ for all $x$ and $y$. If $f^{\pr 67. The angle $A$ of $\triangle A B C$ is found by measurement to be $67 \frac{1^{\circ}}{2}$ and the area of $\triangle A B 68. Let $f: R \rightarrow R$ be a bijection. A curve represented by $y=f(x)$ is such that $f^{\prime}(x)>0 \forall x \in \ma 69. The $x$-coordinate changes on the curve $y=3 x^5+15 x-8$ at the rate of $\frac{1}{5}$ units/sec. $A\left(x_1, y_1\right) 70. In $\triangle A B C, \angle B=90^{\circ}$ and $(b+a)$ is always a constant. In order that $\triangle A B C$ encloses the 71. If $\int \frac{(x-1) d x}{(x+1) \sqrt{x^3+x^2+x}}=A \cdot \tan ^{-1} \sqrt{f(x)}+$ constant, then the ordered pair $(A, 72. If $f\left(\frac{2 x+3}{3 x+5}\right)=x+4, x \neq \frac{-5}{3}, \frac{2}{3}$ and $\int f(x) d x=A x+B \ln |3 x-2|+C$, th 73. If $\int e^x\left(\frac{x^2-8 x+19}{(x-1)^5}\right) d x=\frac{e^x(l x+m)}{(x-1)^4}+C$, then $4 l+m=$ 74. $$ \int \frac{d x}{(x-2) \sqrt{x^2-3 x+5}}= $$ 75. Assertion (A) $\int\limits_{-a}^a f(x) d x=\int_0^a(f(x)+f(-x)) d x$ Reason (R) $\int\limits_a^b f(x) d x=\int_{g(a)}^{g 76. If $\cos x+\cos 2 x+\ldots+\cos n x=\frac{A(x)}{2 \sin x / 2}$, then $\int\limits_0^\pi A(x) d x=$ 77. The area (in sq. units) bounded by the parabola $y=x^2+3$, the tangent to the parabola at $(3,12)$ and the coordinate ax 78. The order and degree of the differential equation $\frac{d^2 y}{d x^2}+y+\left(\frac{d y}{d x}-\frac{d^3 y}{d x^3}\right 79. The general solution of the differential equation $\frac{d y}{d x}=\frac{2 x-3 y+4}{3 x+2 y-7}$ is 80. The general solution of $\frac{d y}{d x}=\frac{x+y+1}{y-x+1}$ is

Physics

1. Identify the incorrect statement. 2. In an experiment the angles are required to be measured using an instrument in which 29 divisions of the main scale exac 3. A ball is thrown straight upward from ground with a speed of $20 \mathrm{~m} / \mathrm{s}$. The ball was caught on its w 4. A motor-bike starts from rest, attains a velocity of 10 $\mathrm{m} / \mathrm{s}$ with an acceleration of $0.5 \mathrm{~ 5. If $\mathbf{r}_1=2 \hat{\mathbf{x}}, \mathbf{r}_2=2 \hat{\mathbf{y}}$, where $\hat{\mathbf{x}}$ and $\hat{\mathbf{y}}$ a 6. Let $\mathbf{A}_1+\mathbf{A}_2=5 \mathbf{A}_3, \mathbf{A}_1-\mathbf{A}_2=3 \mathbf{A}_3, \mathbf{A}_3=2 \hat{\mathbf{i}} 7. The velocity of an object of mass 2 kg is given by $\mathbf{v}=\left(8 t \hat{\mathbf{i}}+3 t^2 \hat{\mathbf{j}}\right) 8. A box of mass $m$ is in equilibrium under the application of three forces as shown below. If the magnitude of $\mathbf{F 9. A moving body with a mass $m_1$ and velocity $u$ strikes a stationary body of mass $m_2$. The masses $m_1$ and $m_2$ sho 10. A force acts on a 30 g particle in such a way that the position of the particle as a function of time is given by $x=\al 11. A straight rod of length $L$ is made of a material having mass per unit length $m(x)=\lambda|x|$, where $x$ is measured 12. Consider a uniform horizontal solid cylinder of mass 10 kg such that its length is 9 times its radius. Let the radius be 13. A particle is executing simple harmonic motion in one-dimension. If the amplitude of oscillations is 0.2 cm and if its v 14. A mass $M$ is split into two parts $m_0$ and $M-m_0$. These two masses are then separated by a distance $D$. If the grav 15. Two metal wires $A$ and $B$ have length $L$ and $3 L$ respectively. The radius of cross-sectional circular area of wire 16. A hydraulic lift as shown in the figure is used to lift a mass of 1000 kg , which is placed on a piston $\left(P_1\right 17. If $\alpha_V$ and $T$ are the coefficient of volume expansion and temperature for an ideal gas respectively, then 18. If $\lambda$ denotes the wavelength at which the radiative emission from a black body at a temperature $T$ is maximum, t 19. A Carnot engine $C_1$ operates between temperature $T_1$ and $T_2\left(T_1>T_2\right)$. A second Carnot engine $C_2$ use 20. All gases deviate from gas laws at 21. A body is oscillating in simple harmonic motion according to the equation $x=6 \cos \left(2 \pi t+\frac{\pi}{3}\right) \ 22. A short straight object of length $l$ lies along the central axis of a spherical concave mirror, at a distance $X$ from 23. Consider a glass prism immersed in a liquid as shown below. The refractive index of glass and liquid is 1.5 and 1.2, res 24. If in a Young's double slit experiment the slit separation is doubled and the distance of the screen from the slits is r 25. In a uniformly charged sphere of total charge $Q$ and radius $R$, the electric field $E$ is plotted as function of dista 26. Electric charges $+q$ and $-q$ are placed at points $A$ and $B$ respectively which are at a distance of $2 L$ apart. If 27. Find the equivalent resistance between point $A$ and $B$ in the following circuit. (The resistance of each resistor is $ 28. In a meter bridge the balancing length from the left end is found to be 25 cm . The value of the unknown resistance is ( 29. Two infinite wires carrying opposite electrical currents $I$ and $i$ are placed a distance $x$ apart. A point $P$ at a d 30. A solenoid of length 2 m carries a current of 20 A . The diameter of the solenoid is 3 cm . If the magnetic field inside 31. Which of the following is desirable for making permanent magnets? 32. Consider two solenoids $X$ and $Y$ such that the area and length of $Y$ are twice that of $X$ respectively and the magne 33. Which one of the following curves represents the variation of impedance ( $Z$ ) with frequency $f$ in a series $L-C-R$ c 34. The radiation energy emitted per second by a point source is 100 W . If the efficiency of the source is $4 \%$, then the 35. A light of wavelength 310 nm is used in a photoelectric experiment. The metal electrode of work function of 2.5 eV is us 36. If the first line in the Lyman series has wavelength $\lambda$, then the first line in Balmer series has the wavelength 37. The half-life of a radiocative isotope is 30 h . How long will it take to get reduced to $12.5 \%$ of its initial amount 38. Which of the following circuits satisfies the logic condition $A=1, B=1$ and $D=1$ ? 39. In an $n-p-n$ transistor, $95 \%$ of emitted electrons reach the collector. If the base current is 2 mA , then collector 40. A message signal of frequency $50 / \pi \mathrm{kHz}$ and peak voltage of 5 V is used to modulate a carrier of frequency

TS EAMCET 2020 (Online) 14th September Evening Shift

MCQ (Single Correct Answer)

-0

For $n>1$ and $n \in \mathbf{N}$, if $z_1, z_2, \ldots, z_n$ are the roots of the equation $(z+1)^n=z^n$, then $\sum_{i=1}^n \frac{\cot ^{-1}\left(2\left|\operatorname{Im} z_i\right|\right)-1}{2 \operatorname{Re} z_i}=$

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