TS EAMCET 2023 (Online) 12th May Evening Shift | TS EAMCET Year Wise Previous Years Questions

Chemistry

Mathematics

1. The domain of the function $f(x)=\sin ^{-1}\left(\log _2\left(\frac{x^2}{2}\right)\right)$ is 2. The range of the function $f(x)=-\sqrt{-x^2-6 x-5}$ is 3. If $f: R \rightarrow R$ is defined by $f(x)=2 x+\sin x, x \in R$, then $f$ is 4. $$ \left|\begin{array}{ccc} \sqrt{3} & 2 \sqrt{5} & \sqrt{5} \\ \sqrt{15} & 5 & \sqrt{10} \\ 3 & \sqrt{15} & 5 \end{arra 5. If $A$ is a non-singular matrix such that $(A-2 I)$ $(A-3 I)=0$, then $\frac{1}{5} A+\frac{6}{5} A^{-1}=$ 6. Let $A$ be a matrix such that $A B$ is a scalar matrix, where $B=\left[\begin{array}{ll}1 & 2 \\ 0 & 3\end{array}\right] 7. If $A$ is a symmetric matrix with real entries, then 8. $\operatorname{Arg}\left(\sin \frac{6 \pi}{5}+i\left(1+\cos \frac{6 \pi}{5}\right)\right)=$ 9. $$ \text { If } x+i y=\sqrt{\frac{3+i}{1+3 i}}, \text { then }\left(x^2+y^2\right)^2= $$ 10. If the imaginary part of $\frac{2 z+1}{i z+1}$ is -2, then the locus of the point representing $z$ in the Argand plane i 11. $$ \begin{aligned} &\text { If } \omega \neq 1 \text { is a cube root of unity, then }\\ &\left|\begin{array}{ccc} \omeg 12. If $i=\sqrt{-1}$, then $(1+i)^{10}+(1-i)^{10}=$ 13. The set of all values of $x$ which satisfy both the inequations $x^2-1 \leq 0$ and $x^2-x-2 \geq 0$ simultaneously is 14. For all real values of $x$, the minimum value of $\frac{1-x+\lambda^2}{1+x+x^2}$ is 15. The quadratic equations $x^2-6 x+a=0$ and $x^2-c x+6=0$ have one root in common. If the other roots of the first and sec 16. If $\alpha$ and $\beta$ are the roots of the equation $x^2+2 x+2=0$, then $\alpha^{15}+\beta^{15}=$ 17. If the equation whose roots are $P$ times the roots of the equation $x^4-2 a x^3+4 b x^2+8 a x+16=0$ is a reciprocal equ 18. The total number of all those 3-digit numbers in which the sum of all the digits in each of them is 10 , is 19. All the letters of the word 'MOTHER' are written in all possible ways and the strings of letters (with or without meanin 20. A student is allowed to select at most $n$ books from a collection of ( $2 n+1$ ) books. If the total number of ways in 21. The number of integral terms in the expansion of $(\sqrt{3}+\sqrt[8]{5})^{256}$ is 22. The expansion of $\left(1+x+x^2\right)^{-3 / 2}$ in powers of $x$ is valid, if 23. If $(1+x)^n=c_0+c_1 x+c_2 x^2+\ldots \ldots+c_n x^n$ for $n \in N$, then $c_0+\frac{c_1}{2}+\frac{c_2}{3}+\ldots \ldots+ 24. If $\frac{x+1}{\left(x^2+1\right)(x-1)^2}=\frac{A x+B}{x^2+1}+\frac{C}{x-1}+\frac{D}{(x-1)^2}$, then $A+B+C+D=$ 25. $$ \text { If } \frac{2 \sin \theta}{1+\cos \theta+\sin \theta}=y, \text { then } \frac{1-\cos \theta+\sin \theta}{1+\si 26. If $\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{4 \pi}{7}=\frac{\sin \frac{8 \pi}{7}}{8 \sin \frac{\pi}{7}}$, the 27. If $f(\theta)=\cos ^3 \theta+\cos ^3\left(\frac{2 \pi}{3}+\theta\right)+\cos ^3\left(\theta-\frac{2 \pi}{3}\right)$, the 28. $$ \sinh (\log (3+\sqrt{8}))= $$ 29. $P Q R$ is an isosceles triangle with $P Q=P R$. If the radius of the circumcircle of $\triangle P Q R$ is equal to the 30. In $\triangle A B C$, if $\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos \cdot C}{c}$ and side $a=2$, then area of the $\t 31. If two vectors $\mathbf{a}$ and $\mathbf{b}$ which are perpendicular to each other are such that $|\mathbf{a}|=8$ and $| 32. Let $\mathbf{a}$ and $\mathbf{b}$ be non-collinear vectors. If the vectors $(\lambda-1) \mathbf{a}+2 \mathbf{b}$ and $3 33. If $M$ is the foot of the perpendicular drawn from $P($ -1,2,-1 ) to the plane passing through the point $A(3,-2,1)$ and 34. Vectors $\mathbf{p}=a \hat{\mathbf{i}}+b \hat{\mathbf{j}}+c \hat{\mathbf{k}}, \mathbf{q}=d \hat{\mathbf{i}}+3 \hat{\math 35. $\mathbf{b}$ and $\mathbf{c}$ are non-collinear vectors and $(\mathbf{c} \cdot \mathbf{c}) \mathbf{a}=\mathbf{c}$. If $( 36. Assertion (A) The variance of the first $n$ odd natural numbers is $\frac{n^2-1}{3}$. Reason (R) The sum of the first 37. If $A$ and $B$ are two events of a random experiment such that $P(A \cup B)=P(A \cap B)$, then which one amongst the fol 38. If a group of six students including two particular students $A$ and $B$ stand in a row, then the probability of getting 39. $A, B, C, D$ cut a pack of 52 well shuffled playing cards successively in the same order. If the person who cuts a spade 40. Two bad eggs are mixed accidentally with 10 good ones. If three eggs are drawn at random from this lot in succession wit 41. The locus of the mid-points of the intercepted portion of the tangents by the coordinate axes, which are drawn to the el 42. A line $L$ has intercepts $a$ and $b$ on the coordinate axes. When the coordinate axes are rotated through an angle $\al 43. Two lines $L_1$ and $L_2$ passing through the point $P(1,2)$ cut the line $x+y=4$ at a distance of $\frac{\sqrt{6}}{3}$ 44. A pair of straight lines drawn though the origin forms. an isosceles triangle right angled at the origin with the line $ 45. The equation of the straight line passing through the point $(3,2)$ and inclined at an angle of $60^{\circ}$ with the li 46. An equilateral triangle is constructed between the lines $\sqrt{3} x+y-6=0$ and $\sqrt{3} x+y+9=0$ with base on one line 47. If $\theta$ is the acute angle between the lines joining the origin to the points of intersection of the curve $x^2+x y+ 48. If a circle passing through $(1,-2)$ has $x-y=2$ and $2 x+3 y=14$ as its diameters, then the radius of the circle is 49. The equation of the circle whose diameter is the common chord of the circles $x^2+y^2+2 x+3 y+1=0$ and $x^2+y^2+4 x+3 y+ 50. The number of common tangents to the circles $x^2+y^2-2 x-6 y+9=0$ and $x^2+y^2+6 x-2 y+1=0$ is 51. The pole of the straight line $9 x+y-28=0$ with respect to the circle $2 x^2+2 y^2-3 x+5 y-7=0$ is 52. The equation of the line perpendicular to the radical axis of two circles $x^2+y^2-5 x+6 y+12=0$, $x^2+y^2+6 x-4 y-14=0$ 53. If the angle between the circles $$ x^2+y^2-2 x-4 y+c=0 \text { and } x^2+y^2-4 x-2 y+4=0 $$ is $60^{\circ}$, then $c=$ 54. The normal at a point on the parabola $y^2=4 x$ passes through $(5,0)$. If there are two more normals to this parabola p 55. The equations of common tangents to the parabola $y^2=16 x$ and the circle $x^2+y^2=8$ are 56. The product of the lengths of the perpendiculars drawn from the two foci of the ellipse $\frac{x^2}{9}+\frac{y^2}{25}=1$ 57. Tangents are drawn to the ellipse $\frac{x^2}{9}+\frac{y^2}{5}=1$ at all the ends of its latus recta. The area of the qu 58. $P(a \sec \theta, b \tan \theta)$ and $Q(a \sec \phi, b \tan \phi)$ are two points on the hyperbola $\frac{x^2}{a^2}-\fr 59. If $A=(1,-1,2), B=(3,4,-2), C=(0,3,2)$ and $D=(3$, $5,6)$, then the angle between the lines $\mathbf{A B}$ and $\mathbf{ 60. Consider the following statements: Assertion (A) : The direction ratios of a line $L_1$ are 2,5, 7 and the direction rat 61. A line $L$ is parallel to both the planes $2 x+3 y+z=1$ and $x+3 y+2 z=2$. If line $L$ makes an angle $\alpha$ with the 62. $$ \lim\limits_{x \rightarrow 1}(1-x) \tan \left(\frac{\pi}{2} x\right)= $$ 63. If $f(9)=9$ and $f^{\prime}(9)=4$, then $\lim\limits_{x \rightarrow 9} \frac{\sqrt{f(x)}-3}{\sqrt{x}-3}=$ 64. If $\sec \left(\log _2 y^2\right)=\operatorname{cosec}\left(\log _2 x^2\right)$, then $\frac{d y}{d x}=$ 65. If $e^x=y+\sqrt{y^2-1}$, then $\frac{d y}{d x}=$ 66. If $x=\log p$ and $y=\frac{1}{p}$, then $\frac{d y}{d x}=$ 67. Electric current $(I)$ is measured by galvanometer, the current being proportional to the tangent of the angle ( $\theta 68. If the equation of a tangent drawn to the curve $y=\cos (x+y),-1 \leq x \leq 1+\pi$ is $x+2 y=k$, then $k=$ 69. $f: R \rightarrow R$ is a function defined by $f(x)=\frac{1}{e^x+2 e^{-x}}$ Assertion (A) : $f(c)=\frac{1}{3}$ for some 70. $$ \text { Match the following items from List I into List II } $$ List-I List-II 1. ∫ 71. If $\int \frac{x}{(a+x)^5} d x=\frac{1}{k(a+x)^4}(f(x))+C$, then $\frac{f(-a)}{a k}=$ 72. $$ \int_0^{\pi / 4} \frac{\sec x}{1+2 \sin ^2 x} d x= $$ 73. If $\int x^4(\log x)^3 d x=x^5\left[A(\log x)^3\right]$ $\left.+B(\log x)^2+C \log x+D\right]+k$, then $A+B+C+5 D=$ 74. $$ \lim\limits_{n \rightarrow \infty}\left[\frac{1}{n^2} \sec ^2 \frac{1}{n^2}+\frac{2}{n^2} \sec ^2 \frac{4}{n^2}+\ldot 75. $$ \int\limits_2^5 \sqrt{\frac{5-x}{x-2}} d x= $$ 76. $$ \int\limits_0^{\frac{\pi}{2}} \sin ^6 x \cos ^4 x d x= $$ 77. The area (in sq units) bounded by the curve $y=2 x-x^2$ and the line $y=-x$ is 78. The degree and order of the differential equation of the family of parabolas whose axis is the $X$-axis, are respectivel 79. The general solution of the differential equation $\left(x \sin \frac{y}{x}\right) d y=\left(y \sin \frac{y}{x}-x\right) 80. The general solution of the differential equation $\left(2 x-10 y^3\right) d y+y d x=0, y \neq 0$ is

Physics

1. If $F_1$ and $F_2$ are the relative strengths of the gravitational and weak nuclear forces respectively, then $F_2 / F_1 2. The number of significant figures in $3.78 \times 10^{22} \mathrm{~kg}$ is 3. The ratio of the displacements of a freely falling body during first, second and third seconds of its motion is 4. A person walks in such a way that he covers equal distance in each step. The person takes 2 steps forwards towards east, 5. A person initially at rest, starts walking towards east without slipping or skidding. What is the type of friction actin 6. While a person climbs stairs, the gravitational potential energy of the person increases. The source of this energy is 7. Moon revolves around the earth in an orbit of radius $R$ with time period of revolution $T$. It also rotates about its o 8. The spinning of the Diwali cracker 'ground chakkar' involves the concept of 9. A clock is designed based on the oscillation of a spring-block system suspended vertically in the absence of air-resista 10. A body of mass 6 kg is moving with a uniform velocity $4 \mathrm{~ms}^{-1}$. Its velocity changes to $6 \mathrm{~ms}^{-1 11. The ratio of the radii of two planets is $r$ and the ratio of accelerations due to gravity on the planets is $x$. Then t 12. Two wires $A$ and $B$ of same length, same radius and same Young's modulus are heated to same range of temperatures. If 13. If the work done in blowing a soap bubble of radius $R$ is $W$, then the work done in blowing the soap bubble of radius 14. Three identical vessels are filled with three liquids ${ }_{A, B}$ and $C$ with equal masses but having densities $\rho_ 15. Two rod of same area of cross-section have lengths $L$ and $2 L$ and coefficients of linear expansions $2 \alpha$ and $a 16. For a given mass of a gas at constant temperature, the volume and the pressure are $V$ and $p$ respectively. Then the sl 17. An ideal gas at $127^{\circ} \mathrm{C}$ is compressed suddenly to $8 / 27 \mathrm{}$of its initial volume. If $\gamma=5 18. An insulating cylinder contains 4 moles of an ideal diatomic gas. When a heat $Q$ is supplied to it, 2 moles of the gas 19. A rod of length $L$ and negligible mass is suspended by two identical strings $A B$ and $C D$ as shown in the figure A m 20. An observer moves towards a stationary source of sound with a speed $\frac{1}{5}$ th that of sound. The frequency of ${ 21. The angles of incidence and emergence of a light ray passing through a prism of angle $A$ are $i$ and $e$ respectively. 22. If the slit width is 2 mm and wavelength of light used is $4000\mathop {\rm{A}}\limits^{\rm{o}}$, then Fresnel distance 23. The electric field and electric potential at a point due to a point charge are $500 \mathrm{NC}^{-1}$ and 30 V respectiv 24. If a capacitor of capacitance $100 \mu \mathrm{~F}$ is charged at a steady rate of $100 \mu \mathrm{C} \mathrm{s}^{-1}$, 25. A potentiometer balances at 44 cm when a cell of internal resistance $1 \Omega$ is in the secondary circuit. To obtains 26. Two wires made of the same material have lengths in the ratio $2: 3$ and radii in the ratio $8: 9$. If the same potentia 27. The magnetic field at a perpendicular distance of one metre from a wire carrying current of 1 A is 28. A circular coil of area $2 \mathrm{~cm}^2$ has 1000 turns. If the current through the coil is 1 A , then its magnetic mo 29. The magnetic susceptibility of ferromagnetic materials is 30. If the vertical component of earth's magnetic field is $0.5 \times 10^{-4} \mathrm{~T}$ at a point. When an aeroplane of 31. A boy is playing with the empty rim of a cycle wheel of radius 40 cm by rolling it along a horizontal road towards north 32. In an ideal step up transformer, if the input voltage and input power are $V_1$ and $R_1$ respectively and the output vo 33. The correct statement among the following is 34. The additional energy that should be given to an electron to reduce its de-Broglie wavelength from 1 nm to 0.5 nm is 35. The ratio of the energies of the electron in the hydrogen atom in the first and second excited states is 36. In the following nuclear reaction $X$ is $$ { }_{13} \mathrm{Al}^{27}+{ }_2 \mathrm{He}^4 \longrightarrow{ }_0 n^1+X $$ 37. Nuclear fission and fusion can be explained on the basis of 38. If the ratio of electron and hole currents in a semiconductor is $7 / 4$ and the ratio of drift velocities of electrons 39. When a semiconductor is doped with donor impurity 40. The need for modulation is

TS EAMCET 2023 (Online) 12th May Evening Shift

MCQ (Single Correct Answer)

-0

If $\frac{x+1}{\left(x^2+1\right)(x-1)^2}=\frac{A x+B}{x^2+1}+\frac{C}{x-1}+\frac{D}{(x-1)^2}$, then $A+B+C+D=$

$-\frac{1}{2}$

$\frac{1}{2}$

$\frac{3}{2}$

TS EAMCET 2023 (Online) 12th May Evening Shift

MCQ (Single Correct Answer)

-0

$$ \text { If } \frac{2 \sin \theta}{1+\cos \theta+\sin \theta}=y, \text { then } \frac{1-\cos \theta+\sin \theta}{1+\sin \theta}= $$

$y$

$\frac{1}{y}$

$1-y$

$1+y$

TS EAMCET 2023 (Online) 12th May Evening Shift

MCQ (Single Correct Answer)

-0

If $\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{4 \pi}{7}=\frac{\sin \frac{8 \pi}{7}}{8 \sin \frac{\pi}{7}}$, then $\sin \frac{\pi}{14} \sin \frac{3 \pi}{14} \sin \frac{5 \pi}{14} \sin \frac{7 \pi}{14} \sin \frac{9 \pi}{14} \sin \frac{11 \pi}{14} \sin \frac{13 \pi}{14}=$

$\frac{1}{16}$

$\frac{1}{32}$

$\frac{1}{64}$

$\frac{1}{128}$

TS EAMCET 2023 (Online) 12th May Evening Shift

MCQ (Single Correct Answer)

-0

If $f(\theta)=\cos ^3 \theta+\cos ^3\left(\frac{2 \pi}{3}+\theta\right)+\cos ^3\left(\theta-\frac{2 \pi}{3}\right)$, then $f\left(\frac{\pi}{5}\right)=$

$\frac{3(\sqrt{5}-1)}{16}$

$\frac{3 \sqrt{10-2 \sqrt{5}}}{8}$

$\frac{3 \cdot \sqrt{10+2 \sqrt{5}}}{8}$

$\frac{3(\sqrt{5}+1)}{16}$

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