TS EAMCET 2023 (Online) 14th May Morning Shift | TS EAMCET Year Wise Previous Years Questions

Chemistry

1. The energy of second orbit of hydrogen atom is $-5.45 \times 10^{-19} \mathrm{~J}$. What is the energy of first orbit of 2. The number of electrons with $(n+l)$ values equal to 3,4 and 5 in an element with atomic number $(Z) 24$ are respectivel 3. $$ \text { Match the following. } $$ $$ \begin{array}{cccc} \hline & \begin{array}{c} \text { List-I } \\ \text { (Atomi 4. According to molecular orbital theory, the molecule which contains only $\pi$-bonds between the atoms is 5. In which of the following changes there is no change in hybridisation of the central atom? 6. The rate of diffusion of a gas $A$ is $\sqrt{5}$ times more than that of gas $B$. If the molar mass of $A$ is $x \mathrm 7. Which one of the following has the same number of atoms as are in 6 g of $\mathrm{H}_2 \mathrm{O}$ ? 8. For the reaction at $25^{\circ} \mathrm{C}, X_2 \mathrm{O}_4(l) \longrightarrow 2 \mathrm{XO}_2(g), \Delta U$ and $\Delt 9. Which of the following does not form a buffer solution? 10. The hydrides of which group elements of the periodic table form electron precise hydrides? 11. The alkali metal with lowest $E^{\circ}{ }_{M^{+} / M}(\mathrm{~V})$ is $X$ and the alkali metal with highest $E^{\circ} 12. Assertion (A) Be and Mg do not impart any colour to the flame. Reason (R) The electrons in them are strongly bound to ge 13. Aluminium reacts with dilute HCl and liberates a gas ' $A$ ' and with aqueous alkali liberates a gas ' $B$ '. $A$ and $B 14. Identify the incorrect statement about the oxidation states of group 14 elements. 15. $$ \text { The IUPAC name of the given compound is } $$ 16. The aromatic compound/species with maximum number of $\pi$-electrons is 17. $$ \text { In the conversion of } A \text { to } B \text {, the electrophile involved is } $$ 18. An alkene $X$ on ozonolysis gives a mixture of propan-2-one and methanal. What is $X$ ? 19. The formula of a metal oxide is $M_{0.96} \mathrm{O}_1$. The fractions of metal that exists as $M^{3+}$ and $M^{2+}$ ion 20. At $50^{\circ} \mathrm{C}$, the vapour pressure of pure benzene is 268 torr. The number of moles of non-volatile solute 21. The rate law for the decomposition of hydrogen iodide is $-\frac{d[\mathrm{HI}]}{d t}=k[\mathrm{HI}]^2$. The units of ra 22. A current of 15.0 A is passed through a solution of $\mathrm{CrCl}_2$ for 45 minutes. The volume of $\mathrm{Cl}_2$ (in 23. Which of the following can form ionic micelles in water? 24. The ore which is purified by leaching process is 25. $$ \begin{array}{r} \mathrm{P}_4+3 \mathrm{NaOH}+3 \mathrm{H}_2 \mathrm{O} \xrightarrow{\mathrm{CO}_2} 3 X+\mathrm{PH}_3 26. The ratio of lone pair of electrons to bond pair of electrons in ozone molecule is 27. Consider the following statements about the oxides of halogens. A. At room temperature, $\mathrm{OF}_2$ is thermally sta 28. $$ \begin{aligned} \mathrm{XeF}_4+\mathrm{O}_2 \mathrm{~F}_2 & \longrightarrow X+\mathrm{O}_2 \\ X+\underset{(1 \text { 29. Among the following the incorrect statement about transition metals is 30. $$ \text { Match the following. } $$ $$ \begin{array}{llll} \hline & \begin{array}{l} \text { List-I } \\ (\text { Compl 31. Ziegler-Natta catalyst is used in the manufacture of 32. The deficiency of which vitamin causes pernicious anaemia? 33. $$ \text { The following molecule with the structure acts as } $$ 34. Which of the following is least reactive towards $\mathrm{S}_{\mathrm{N}} 1$ reactions? 35. Consider the following sequence of reactions, $$ \mathrm{C}_2 \mathrm{H}_4 \xrightarrow[\text { (ii) } \mathrm{Zn} / \ma 36. The common name of benzene-1,3-diol is 37. Identify the major product $C$ in the given sequence of reactions 38. Arrange the following in the correct order of their reactivity towards nucleophilic addition reactions. 39. $R$ is one of the monomers for the formation of a polymer called 40. $$ \text { What is } B \text { in the given reaction? } $$

Mathematics

1. If ${ }^n C_r$ denotes the number of combinations of $n$ distinct things taken $r$ at a time, then the domain of the fun 2. Let $X=\left\{\left.\left[\begin{array}{ll}a & b \\ c & d\end{array}\right] \right\rvert\, a, b, c, d \in R\right\}$. If 3. If $f(x)$ is a function such that $f(x+y)=f(x)+f(y)$ and $f(1)=7$, then $\sum_{r=1}^n f(r)=$ 4. If $A$ is a square matrix of order $3, \operatorname{then}\left|\operatorname{Adj}\left(\operatorname{Adj} A^2\right)\ri 5. If $A$ and $B$ are two square matrices of the same order and $(A B+B A)^T+(A B-B A)^T=2 B A$, then 6. If $\operatorname{adj}\left[\begin{array}{ccc}1 & 0 & 2 \\ -1 & 1 & -2 \\ 0 & 2 & 1\end{array}\right]=\left[\begin{array 7. If $A=\left[\begin{array}{ll}0 & 3 \\ 0 & 0\end{array}\right]$ and $f(x)=x+x^2+x^3+\ldots \ldots+x^{2023}$, then $f(A)+I 8. If $i=\sqrt{-1}$, then $\sum_{n=0}^{\infty}\left(\frac{i}{3}\right)^n=$ 9. If $i=\sqrt{-1}$, then $\operatorname{Arg}\left[\frac{(1+i)^{2025}}{(1-i)^{2022}}\right]=$ 10. The locus of $z$ such that $\left|\frac{z-i}{z+i}\right|=2$, where $z=x+i y$, is 11. If $x_n=\cos \frac{\pi}{2^n}+i \sin \frac{\pi}{2^n}$, then $\prod_{n=1}^{\infty} x_n=$ 12. If the roots of the equation $z^2-i=0$ are $\alpha$ and $\beta$, then $|\arg \beta-\arg \alpha|=$ 13. If $x^2+2 p x-2 p+8>0$ for all real values of $x$, then the set of all possible values of $p$ is 14. If $R-(\alpha, \beta)$ is the range of $\frac{x+3}{(x-1)(x+2)}$, then the sum of the intercepts of the line $\alpha x+\b 15. The quadratic equation whose roots are $\sin ^2 18^{\circ}$ and $\cos ^2 36^{\circ}$ is 16. The roots of the equation $x^4+x^3-4 x^2+x+1=0$ are diminished by $h$ so that, the transformed equation does not contain 17. $\alpha, \beta, \gamma$ are the roots of the equation $x^3+2 x^2-x-2=0$, then $\alpha^6+\beta^6+\gamma^6=$ 18. The number of diagonals of a polygon is 35 . If $A$ and $B$ are two distinct vertices of this polygon, then the number o 19. There are 10 points in a plane, of which no three points are collinear except 4. Then, the number of distinct triangles 20. A student is asked to answer 10 out of 13 questions in an examination such that he must answer atleast four questions fr 21. If $(-c, c)$ is the set of all values of $x$ for which the expansion of $(7-5 x)^{\frac{-2}{3}}$ is valid, then $5 c+7=$ 22. If $n$ is a positive integer and $f(n)$ is the coefficient of $x^n$ in the expansion of $(1+x)(1-x)^n$, then $f(2023)=$ 23. If $y=\frac{3}{4}+\frac{3 \cdot 5}{4 \cdot 8}+\frac{3 \cdot 5 \cdot 7}{4 \cdot 8 \cdot 12}+\ldots$ to $\infty$, then 24. If $\frac{3 x+2}{(x+1)\left(2 x^2+3\right)}=\frac{A}{x+1}+\frac{B x+C}{2 x^2+3}$, then $A-B+C=$ 25. The period of the function $f(x)=e^{\log (\sin x)}+(\tan x)^3-\operatorname{cosec}(3 x-5)$ is 26. If $\cos \theta=\frac{-3}{5}$ and $\pi 27. If $\sin 2 \theta$ and $\cos 2 \theta$ are solutions of $x^2+a x-c=0$, then 28. If $x=\log \left(y+\sqrt{y^2+1}\right)$, then $y=$ 29. In $\triangle A B C$, if $a: b: c=4: 5: 6$, then the ratio of the circumradius to its inradius is 30. The perimeter of a $\triangle A B C$ is 6 times the arithmetic mean of the values of the sine of its angles. If its side 31. If $|\mathbf{a}|=4,|\mathbf{b}|=5$ and $|\mathbf{a}-\mathbf{b}|=3$ and $\theta$ is the angle between the vectors $\mathb 32. If $A(1,2,3), B(3,7,-2), C(6,7,7)$ and $D(-1,0,-1)$ are points in a plane, then the vector equation of the line passing 33. If $\mathbf{a}+\mathbf{b}+\mathbf{c}=0,|\mathbf{a}|=3,|\mathbf{b}|=5,|\mathbf{c}|=7$, then the angle between $\mathbf{a} 34. If $2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+3 \hat{\mathbf{k}},-12 \hat{\mathbf{i}}-\hat{\mathbf{j}}-3 \hat{\mathbf{k}},-\ha 35. Let $\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and $\mathbf{b}=2 \hat{\mathbf{i}}-\hat{\mathbf{ 36. The variance of 50 observations is 7 . Suppose that each observation in this data is multiplied by 6 and then 5 is subtr 37. A bag contains four balls. Two balls are drawn randomly and found them to be white. The probability that all the balls i 38. If the coefficients $a$ and $b$ of a quadratic expression $x^2+a x+b$ are chosen from the sets $A=\{3,4,5\}$ and $B=\{1, 39. A random variable $X$ has the following probability distribution $$ \begin{array}{|c|l|l|l|l|l|l|l|l|} \hline \boldsymbo 40. 5 persons entered a lift cabin in the cellar of a 7 floor building apart from cellar. If each of them independently and 41. If a point $P$ moves so that the distance from $(0,2)$ to $P$ is $\frac{1}{\sqrt{2}}$ times the distance of $P$ from $(- 42. Let $d$ be the distance between the parallel lines $3 x-2 y+5=0$ and $3 x-2 y+5+2 \sqrt{13}=0$. Let $L_1 \equiv 3 x-2 y+ 43. If $(h, k)$ is the image of the point $(3,-4)$ with respect to the line $2 x-3 y-5=0$ and $(l, m)$ is the foot of the pe 44. A straight line parallel to the line $y=\sqrt{3} x$ passes through $Q(2,3)$ and cuts the line $2 x+4 y-27=0$ at $P$. The 45. If a line $a x+2 y=k$ forms a triangle of area 3 sq. units with the coordinate axis and is perpendicular to the line $2 46. The orthocenter of the triangle whose sides are given by $x+y+10=0, x-y-2=0$ and $2 x+y-7=0$ is 47. For $l \in R$, the equation $(2 l-3) x^2+2 l x y-y^2=0$ represents a pair of distinct lines 48. If the parametric equations of the circle passing through the points $(3,4),(3,2)$ and $(1,4)$ is $x=a+r \cos \theta, y= 49. A tangent $P T$ is drawn to the circle $x^2+y^2=4$ at the point $P(\sqrt{3}, 1)$. If a straight line $L$ which is perpen 50. If the angle between the pair of tangents drawn to the circle $x^2+y^2-2 x+4 y+3=0$ from the point $(6,-5)$ is $\theta$, 51. If the angle between the circles $x^2+y^2-4 x-6 y+k=0$ and $x^2+y^2+8 x-4 y+11=0$ is $\frac{\pi}{2}$, then the value of 52. The radius of a circle touching all the four circles $(x \pm \lambda)^2+(y \pm \lambda)^2=\lambda^2$ is 53. If the radical centre of the given three circles $x^2+y^2=1, x^2+y^2-2 x-3=0$ and $x^2+y^2-2 y-3=0$ is $C(\alpha, \beta) 54. If $x-2 y+k=0$ is a tangent to the parabola $y^2-4 x-4 y+8=0$, then the value of $k$ is 55. If the points of intersection of the parabolas $y^2=5 x$ and $x^2=5 y$ lie on the line $L$, then the area of the triangl 56. If the line $x \cos \alpha+y \sin \alpha=2 \sqrt{3}$ is a tangent to the ellipse $\frac{x^2}{16}+\frac{y^2}{8}=1$ and $\ 57. If $x+\sqrt{3} y=3$ is the tangent to the ellipse $2 x^2+3 y^2=k$ at a point $P$, then the equation of the normal to thi 58. If the angle between the asymptotes of a hyperbola is $30^{\circ}$, then its eccentricity is 59. In a $\triangle A B C$, if the mid-points of sides $A B, B C$ and $C A$ are $(3,0,0),(0,4,0)$ and $(0,0,5)$ respectively 60. If $l, m, n$ and $a, b, c$ are direction cosines of two lines, then 61. If $(2,-1,3)$ is the foot of the perpendicular drawn from the origin to a plane, then the equation of that plane is 62. $$ \lim _{n \rightarrow \infty} \frac{1}{n^3} \sum_{k=1}^n\left(k^2 x\right)= $$ 63. The quadratic equation whose roots are $$ l=\lim _{\theta \rightarrow 0}\left(\frac{3 \sin \theta-4 \sin ^3 \theta}{\the 64. On differentiation if we get $f(x, y) d y-g(x, y) d x=0$ from $2 x^2-3 x y+y^2+x+2 y-8=0$, then $\frac{g(2,2)}{f(1,1)}=$ 65. If $f(x)=e^x, h(x)=(f \circ f)(x)$, then $\frac{h^{\prime}(x)}{h(x)}=$ 66. If $\sin y=\sin 3 t$ and $x=\sin t$, then $\frac{d y}{d x}=$ 67. If a line having slope 2 is a tangent to the curve $y=x^4-6 x^3+13 x^2-12 x+5$ at points $P\left(x_1, y_1\right)$ and $Q 68. Let $m$ be the slope of the normal $L$ drawn at $(1,2)$ to the curve $x=t^2-7 t+7, y=t^2-4 t-10$ and $a x+b y+c=0$ be th 69. If the function $f(x)=x e^{-x}, x \in R$ attains its maximum value $\beta$ at $x=\alpha$, then $(\alpha, \beta)=$ 70. If $\int \frac{x^{49} \tan ^{-1}\left(x^{50}\right)}{\left(1+x^{100}\right)} d x=k\left(\tan ^{-1}\left(x^{50}\right)\ri 71. If $\int(\log x)^3 x^5 d x=\frac{x^6}{A}\left[B(\log x)^3\right. \left.+C(\log x)^2+D(\log x)-1\right]+k$ and $A, B, C, 72. $$ \int \frac{d x}{\left(x^2+1\right)\left(x^2+4\right)}= $$ 73. $\int \frac{d x}{(x-1)^{\frac{3}{4}}(x+2)^{\frac{5}{4}}}=$ 74. $$ \int_{-1}^1 x|x| d x= $$ 75. $$ \int_{-\pi / 2}^{\pi / 2} \sin ^2 x \cos ^2 x(\sin x+\cos x) d x= $$ 76. The area (in sq units) of the region bounded by the curve $y=|\sin 2 x|$ and the $X$-axis in $[0,2 \pi]$ is 77. If $\int_0^3\left(3 x^2-4 x+2\right) d x=k$, then an integer root of $3 x^2-4 x+2=3 k / 5$ is 78. If the order and degree of the differential equation corresponding to the family of curves $y^2=4 a(x+a)(a$ is parameter 79. If the solution of the differential equation $\frac{d y}{d x}=\frac{2 x+3 y}{3 x-2 y}$ is $y=x \tan (f(x))+C$, then $f(x 80. The general solution of the differential equation $\left(x^2+2\right) d y+2 x y d x=e^x\left(x^2+2\right) d x$ is

Physics

1. The ratio of the relative strengths of strong and weak nuclear forces is 2. The number of significant figures in the measurement of a length 0.079000 m is 3. The acceleration of a vertically projected body at its highest reaching position is 4. A player can throw a ball to a maximum horizontal distance of 80 m . If he throws the ball vertically with the same velo 5. If a man of mass 50 kg is in a lift moving down with an acceleration equal to acceleration due to gravity, then the appa 6. An engine is dragging a mass of 5000 kg with a velocity of $5 \mathrm{~ms}^{-1}$ along a smooth inclined plane of inclin 7. A ball falls freely from a height $h$ on a rigid horizontal plane. If the coefficient of restitution is $e$, then the to 8. The velocity of a particle having magnitude of $10 \mathrm{~ms}^{-1}$ in the direction of $60^{\circ}$ with positive $X$ 9. The ratio of the radii of two solid spheres of same mass is $2: 3$. The ratio of the moments of inertia of the spheres a 10. The displacement of a particle executing simple harmonic motion is given by $x=2 \cos (t)$ where $t$ is the time in seco 11. A man weighing 75 kg is standing in a lift. The weight of the man standing on a weighing machine kept in the lift when t 12. The dimensions of four wires of the same material are given below. The increase in length is maximum in the wire of 13. A cylindrical vessel, open at the top, contains 15 litres of water. Water drains out through a small opening at the bott 14. A cylinder of mass $m$ and material density $\rho$ hanging from a string is lowered into a vessel of cross-sectional are 15. The Fahrenheit and Kelvin scales of temperature will have the same reading at a temperature of 16. If the ratio of densities of two substances is $5: 6$ and the ratio of their specific heat capacities is $3: 5$, then th 17. In a process, the work done by the system is equal to the decrease in its internal energy. The process that the system u 18. N molecules each of mass $m$ of gas $A$ and 2 N molecules each of mass 2 m of gas $B$ are contained in a vessel which is 19. Among the following statements, the correct statement for a wave is 20. A source and an observer move away from each other with same velocity of $10 \mathrm{~ms}^{-1}$ with respect to ground. 21. Two convex lenses of focal lengths 20 cm and 30 cm are placed in contact with each other co-axially. The focal length of 22. A point source of light is placed at the focus of a concave mirror. Consider only paraxial rays. The shapes of the wavef 23. If the electric potential at a point on the surface of a hollow conducting sphere of radius $R$ is $V$, then the electri 24. The effective capacitance between points $A$ and $B$ shown in the circuit is 25. The Wheatstone bridge shown in the diagram is balanced. If $P_3$ is the power dissipated by $R_3$ and $P_1$ is the power 26. A wire of resistance $2 R$ is stretched such that its length is doubled. Then the increase in its resistance is 27. It is found that a non-zero current element is unable to produce any magnetic field at a particular point. Then the angl 28. Three long, straight, parallel wires carrying different currents are arranged as shown in the diagram. In the given arra 29. If $\chi$ is the susceptibility and $\mu_r$ is the relative permeability of a ferromagnetic substance, then 30. Metal detector works on the principle of 31. A copper disc of radius 0.1 m rotates about an axis passing through its centre and perpendicular to its plane with 10 re 32. At very high frequencies, the current ( $i$ ) in the given circuit is 33. Electromagnetic radiation of intensity $0.6 \mathrm{Wm}^{-2}$ is falling on a black surface. The radiation pressure on t 34. Radiations of wavelength 400 nm incidents on a photosensitive material of work function 2.2 eV . The stopping potential 35. In a hypothetical Bohr hydrogen atom, if the mass of the electron is doubled then the energy of the electron in the firs 36. The half-life period of element $X$ is same as the mean life time of element $Y$. Assume initially $X$ and $Y$ have same 37. Heavy water is used as moderator in nuclear reactor because 38. Photodiodes are mostly operated in reverse biased condition because 39. Which of the following statements is true about LEDs? 40. An amplitude modulated wave is represented by $c_m(t)=10[1+0.6 \sin (1250 t)] \sin \left(10^8 t\right)$. Then modulation

TS EAMCET 2023 (Online) 14th May Morning Shift

MCQ (Single Correct Answer)

-0

If the function $f(x)=x e^{-x}, x \in R$ attains its maximum value $\beta$ at $x=\alpha$, then $(\alpha, \beta)=$

$\left(2, \frac{1}{e}\right)$

$\left(1, \frac{1}{e}\right)$

$\left(1, \frac{-1}{e}\right)$

$\left(\frac{1}{e}, 1\right)$

TS EAMCET 2023 (Online) 14th May Morning Shift

MCQ (Single Correct Answer)

-0

If $\int \frac{x^{49} \tan ^{-1}\left(x^{50}\right)}{\left(1+x^{100}\right)} d x=k\left(\tan ^{-1}\left(x^{50}\right)\right)^2+C$, then $k=$

$\frac{-1}{100}$

$\frac{1}{50}$

$\frac{-1}{50}$

$\frac{1}{100}$

TS EAMCET 2023 (Online) 14th May Morning Shift

MCQ (Single Correct Answer)

-0

If $\int(\log x)^3 x^5 d x=\frac{x^6}{A}\left[B(\log x)^3\right. \left.+C(\log x)^2+D(\log x)-1\right]+k$ and $A, B, C, D$ are integers, then $A-(B+C+D)=$

172

184

192

216

TS EAMCET 2023 (Online) 14th May Morning Shift

MCQ (Single Correct Answer)

-0

$$ \int \frac{d x}{\left(x^2+1\right)\left(x^2+4\right)}= $$

$\frac{1}{3} \tan ^{-1} x+\frac{1}{6} \tan ^{-1}\left(\frac{x}{2}\right)+C$

$\frac{1}{3} \tan ^{-1} x-\frac{1}{3} \tan ^{-1}\left(\frac{x}{2}\right)+C$

$\frac{1}{3} \tan ^{-1} x+\frac{1}{3} \tan ^{-1}\left(\frac{x}{2}\right)+C$

$\frac{1}{3} \tan ^{-1} x-\frac{1}{6} \tan ^{-1}\left(\frac{x}{2}\right)+C$

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