TS EAMCET 2023 (Online) 13th May Morning Shift | TS EAMCET Year Wise Previous Years Questions

Chemistry

1. The radius of first Bohr orbit of hydrogen atom is same as that of orbit $(n)$ of hydrogen like species $X .(n)$ and $X$ 2. Identify the impossible quantum number set for the electron from the following. 3. Choose the correct order of second ionisation enthalpies of carbon, nitrogen, oxygen and fluorine. 4. From the following, identify the ions with same bond order. I. $\mathrm{CN}^{-} \quad$ II. $\quad \mathrm{N}_2^{+}$ III. 5. The hybridisations of the central atom in the molecules $\mathrm{BF}_3, \mathrm{BeF}_2, \mathrm{BrF}_3$ are respectively 6. The ratio of rates of diffusion of gases $X$ and $Y$ of molecular weights 36 and 64 is 7. The masses of carbondioxide and water (in g) respectively formed during complete combustion of 10 g of glucose at STP ar 8. Enthalpy of formation of $\mathrm{CO}(g), \mathrm{CO}_2(g)$ are -110 , $-393 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respective 9. At $T(\mathrm{~K})$ when one mol of $X$ and one mol of $Y$ are heated in a 1 L flask, 0.5 moles of $Z$ is formed at the 10. Identify the correct statements about the hydrides. I. In saline hydrides oxidation state of hydrogen is +1 . II. La H i 11. Assertion (A) Alkali metals and their salts impart characteristic flame colours. Reason (R) Alkali metals have low ionis 12. When compared with alkaline earth metals, the alkali metals have 13. Kernite and cryolite are the minerals of two elements $X$ and $Z$. Respectively $X$ and $Z$ are 14. Choose the correct statement from the following with reference to inert pair effect. 15. In the following reaction ' $C$ ' is an aromatic compound having substitutents $D$ and $E$. What are $D$ and $E$ ? 16. $$ \text { The correct IUPAC name of the given structure is } $$ 17. An alkene $(X)$ on ozonolysis gives propanal and ethanal. What is $X$ ? 18. Match the following. The correct answer is 19. A body centred cubic lattice is made up of two different types of atoms $X$ and $Y$. Atom $X$ occupies the body centre a 20. ' $x^{\prime} \mathrm{g}$ of urea (molar mass $60 \mathrm{gmol}^{-1}$ ) is completely dissolved in ' $y^{\prime} \mathrm 21. The conductivity of a solution of concentration $0.1 \mathrm{~mol} \mathrm{~L}^{-1}$ of a weak monobasic acid $(\mathrm{ 22. The rate of a first order reaction doubles when the temperature changes from 300 K to 310 K . The activation energy of t 23. The graph given below is showing the relation between the extent of adsorption $(x / \mathrm{m})$ and pressure at differ 24. Ellingham diagram is the plot of $X$ vs $Y$, what are $X$ and $Y$ ? 25. Identify the correct orders from the following with respect to the property associated with A. $\mathrm{NH}_3>\mathrm{PH 26. Which of the following is the strongest reducing agent? 27. $$ \text { Match the following. } $$ .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border- 28. Which one of the following compounds is having maximum 'lone pair-lone pair' electron repulsions? 29. $\mathrm{Cr}^{2+}$ and $\mathrm{Mn}^{3+}$ do possess $d^4$ electronic configuration. So, 30. According to Werner's theory, the number of groups bonded to the central metal atom/ion in a coordination complex repre 31. A polymer sample contains 3 molecules of molar mass $10^3, 3$ molecules of molar mass 500 and 4 molecules of molar mass 32. $$ \text { The Haworth projection shown below represents } $$ 33. Which one of the following will improve the lathering property of soap? 34. Choose the correct decreasing order of reactivity of alkyl halides towards $\mathrm{S}_{\mathrm{N}} 1$ reaction. 35. 1-propanol can be distinguished from 2-propanol by which test? 36. The product( $s$ ) formed when $m$-chlorobenzaldehyde is heated with concentrated NaOH is/are 37. Statement I Aldehyde on reaction with HCN gives cyanohydrin. Statement II Cyanohydrin is a compound which consists of hy 38. $$ \text { In the given reaction, what is } X \text { ? } $$ 39. Which of the following reactions are used in the preparation of aliphatic primary amines? I. Gabriel's phthalimide react 40. In the following sequence of reaction, identify the major product $B$.

Mathematics

1. If the function $f: R \rightarrow R$ is defined by $$ f(x)= \begin{cases}2 x-3, & \text { if } x2\end{cases} $$ then $f$ 2. The domain of the real valued function $$ f(x)=\frac{\sqrt{\log _{10}\left(\frac{x}{x-2}\right)}}{\sqrt{[x]^2-5[x]+6}} \ 3. The range of the real valued function $f(x)=\frac{1}{x-|x|}$ is 4. If $A=\left[\begin{array}{ccc}1 & 2 & -1 \\ -1 & 0 & 2 \\ 1 & 2 & 0\end{array}\right]$ and $B=\left[\begin{array}{ccc}-3 5. $$ \left|\begin{array}{lll} 2 & 3 & 5 \\ 3 & 5 & 2 \\ 5 & 2 & 3 \end{array}\right|+\left|\begin{array}{ccc} 1 & 1 & 1 \\ 6. If $A=\left[\begin{array}{ccc}k & 5 & 2 \\ 2 & -k & 5 \\ 5 & 2 & -k\end{array}\right]$ and $\operatorname{det} A=190$, t 7. If the unique solution of the simultaneous linear equations $3 x-2 y+z=5 k, 2 x+3 y-2 z=-5 k$, $x+4 y+3 z=k$ is $x=\alph 8. If the value of $\sqrt{-5-12 i}+\sqrt{7+24 i}$ is a negative real number $k$, then $k=$ 9. Let $z=x+i y$ be a point in the argand plane. If the amplitude of $\left(\frac{z-3}{z+2 i}\right)$ is $\frac{\pi}{2}$, t 10. If a point $P$ denotes the complex number $z=x+i y$ in the argand plane and if $\frac{z-(2+i)}{z+(1-2 i)}$ is purely rea 11. If $i$ is the root of the equation $x^2+1=0$, then $$ (1+\sqrt{3} i)^{2023}+(1-\sqrt{3} i)^{2023}= $$ 12. One of the values of $(\sqrt{3}-i)^{\frac{1}{6}}$ is 13. If $x^2+3 x-2 k=0$ and $x^2-2 x-7 k=0$ have a non-zero common root, then the positive root of the equation $k x^2+(k+2) 14. The values of $\frac{x^2-2 x+1}{x^2+x-1}$ do not lie in the interval 15. If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+4 x^2-9 x-36=0$ and $\alpha 16. If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+4 x^2-9 x-36=0$ and $\alpha 17. If the sum of two particular roots of the equation $x^4-4 x^3-7 x^2+22 x+24=0$ is equal to the sum of the remaining two 18. If $n, r$ are two positive integers such that $1 \leq r 19. The number of ways in which $n$ boys and $n$ girls can be arranged in a row such that all the boys are together and all 20. Among the positive divisors of the number 12600 , if $n_1$ is the number of divisors which are multiples of 3 and $n_2$ 21. In the expansion of $(x-2 y+3 z)^5$, if the total number of terms is $p$ and the coefficient of $x^2 y z^2$ is $q$, then 22. Let $C_0, C_1, C_2, \ldots, C_n$ be the binomial coefficients in the expansion of $(1+x)^n$. If $S_{n+1}=5 \cdot C_0+8 \ 23. If $|x|$ is so small that $x^3$ and higher powers of $x$ can be neglected, then an approximate value of $\frac{1}{\sqrt{ 24. If $\frac{6 x^4+13 x^3+2 x^2-x+3}{2 x^2+3 x-2}=f(x)+\frac{A}{a x-1}+\frac{B}{x+b}$, then $f(\mathrm{l})+a \cdot B+b \cdo 25. If $\cot \theta=-\frac{2}{3}$ and $\theta$ does not lie in the 4 th quadrant, then $\frac{(5 \sin \theta+\cos \theta)^2} 26. If $540^{\circ} $$ \frac{\cos \frac{\theta}{2}-5 \sin \frac{\theta}{2}}{\sqrt{-(12 \sec \theta+5 \operatorname{cosec} \t 27. If $A+B+C+D=2 \pi$, then $\cos A-\cos B+\cos C-\cos D=$ 28. If $\cosh x=\frac{4}{3}$, then $3 \cosh x+3^2 \cosh 2 x+3^3 \cosh 3 x=$ 29. In $\triangle A B C$, if $A$ is an acute angle, $b=6, c=9$ and $\sin A=\frac{2 \sqrt{14}}{9}$, then $3 a(\cos B+\cos C)= 30. If the roots of the equation $x^3-11 x^2+36 x-36=0$ are the ex-radii of a $\triangle A B C$, then the perimeter of the $ 31. Let $\mathbf{O A}=\hat{\mathbf{i}}-3 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{O B}=\hat{\mathbf{i}}+3 \hat{\mathbf{j}} 32. The point of intersection of the line passing through the point $\hat{\mathbf{i}}-\hat{\mathbf{j}}, \hat{\mathbf{j}}-\ha 33. If the vectors $\mathbf{B C}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\mathbf{C D}=\hat{\mathbf{i}}+2 34. A plane $\pi$ passing through the point $3 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$ is parallel to the pl 35. Let $\mathbf{a}=\lambda \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}, \mathbf{b}=3 \hat{\mathbf{i}}-\hat{\math 36. If the variance of the data $2,3,5,8,12$ is $\sigma^2$ and the mean deviation from the median for this data is $M$, then 37. If two cards are drawn at random simultaneously from a pack of 52 playing cards, then the probability of getting a face 38. If three unbiased dice are rolled simultaneously, then the probability that all the three dice show distinct numbers is 39. Three persons $A, B$ and $C$ attended a recruitment test, The ratio of the chances of $A, B, C$ in getting through the t 40. Two cards are drawn at random one after the other with replacement from a pack of 52 playing cards. Then, the variance o 41. Let $A=(2,0)$ and $B=(0,-2)$. Let $P$ be any point such that the sum of the distance of $P$ from $A$ and $B$ is 4 . Then 42. Let $P$ be the point to which origin has to be shifted by the translation of axes, so as to remove the first degree term 43. If $\alpha$ is the angle made by the perpendicular drawn from origin to the line $3 x-4 y+5=0$ with positive $X$-axis in 44. If $L_1$ is a line passing through the point $P(4,-3)$ and perpendicular to the line $3 x-4 y+k=0$ then the distance of 45. Let the line $L_1$ passing through the point of intersection of the lines $2 x+3 y-5=0$ and $4 x-5 y+7=0$ divide the lin 46. Let $A B C$ be a triangle and $A=(1,2)$. If $x-3 y-5=0$ the and $x+5 y-9=0$ are the perpendicular bisectors of the sides 47. If $a x^2-x y-3 y^2-5 x+20 y+c=0$ represents a pair of lines passing through the point $(2,3)$, then $a-c=$ 48. Let a chord $A B$ subtend an angle of $60^{\circ}$ at the centre $C(2,3)$ of a circle $S$. If the equation of $A B$ is $ 49. Let 6,8 be the $X$ and $Y$-intercepts made by the circle $S \equiv x^2+y^2+2 g x+2 f y+c=0$, respectively. If $g x+f y+1 50. If $(3,1)$ and $(-2,4)$ are points on a circle $S$ whose centre lies on the line $x-y+1=0$, then the parametric equation 51. Let $S \equiv x^2+y^2-8 x+10 y+5=0$ be a circle. Let $P(1,1)$ and $Q(1,-1)$ be two points. Then, the point of intersecti 52. If the angle between the circles $x^2+y^2-2 x+2 y+1=0$ and $x^2+y^2+2 x-2 y+k=0$ is $\frac{\pi}{3}$, then 53. Let the line $x-y+1=0$ intersect the circle $x^2+y^2+2 x+2 y+1=0$ in two points $A$ and $B$. If $A B$ is the diameter of 54. If the focal distance of a point $P\left(2, y_1\right)$ on the parabola $y^2=k x$ is 3 , then the equation of the tangen 55. Normals are drawn from the point $P(8,0)$ to the parabola $y^2=12 x$. If $\theta$ is the acute angle between two non-hor 56. Let $S$ and $S^{\prime}$ be the foci of an ellipse $E$ and $B$ be one end of its minor axis. Let $\angle S^{\prime} S B= 57. If $4 x+2 y+n=0$ is a normal to the ellipse $\frac{x^2}{36}+\frac{y^2}{16}=1$ then $n=$ 58. If $y=m x+4(m>0)$ is a tangent to the hyperbola $\frac{x^2}{25}-\frac{y^2}{9}=1$, then the point of contact of this tang 59. Let $A(4,3,5), B(1,-2,1), C(3,2,1)$ be the vertices of a $\triangle A B C$. If the internal bisector of $\angle B A C$ m 60. Let the direction cosines of two lines satisfy the equations $3 l+2 m+n=0$ and $2 m n-3 n l+5 l m=0$. If $\theta$ is the 61. $(1,-2,1)$ is a point on a plane $\pi$ and $\pi$ is parallel to the plane $x-y-z=0$. If the equation of $\pi$ is $a x+b 62. $$\mathop {\lim }\limits_{x \to 2 + }\left([x]^2-[x]-2\right)+\mathop {\lim }\limits_{x \to- 3 - }\left([x]^2-4[x]+3\rig 63. $$ \lim _{x \rightarrow 0} \frac{\left(3^{2 x}-\sqrt{x+1}\right) \sin 5 x}{1-\cos 4 x}= $$ 64. If $f(x)=|x-1|+|x-2|$, then $$ f^{\prime}(-2023)+f^{\prime}\left(\frac{2024}{2023}\right)+f^{\prime}(2023)= $$ 65. If $f(x)=\frac{e^{2 x}-e^{-2 x}}{e^{3 x}+e^{-3 x}}$, then $f^{\prime}(0)=$ 66. If $f(x)=x^{\tan x}+(\tan x)^x$, then $f^{\prime}\left(\frac{\pi}{4}\right)=$ 67. The nearest approximate value of $\sqrt{2023}$ is (let $\Delta x=87$ ). 68. The slope of the normal drawn at a point $P$ to the curve $y=x^3-10 x^2+31 x-30$ is $-\frac{1}{14}$. If the co-ordinates 69. $x$ and $y$ are two positive integers such that $2 x+3 y=50$. If $x^2 y^3$ is maximum for $x=\alpha$ and $y=\beta$, then 70. $$ \int \frac{1}{16-7 \sin ^2 x} d x= $$ 71. $$ \int \frac{\sec ^2 x}{(\sec x+\tan x)^2} d x= $$ 72. $$ \int \frac{1}{3 \cos x-4 \sin x+5} d x= $$ 73. $$ \int \frac{1}{(x-2)\left(x^2+1\right)} d x= $$ 74. $$ \int_0^3\left|x^2-3 x+2\right| d x= $$ 75. $$ \int_{-\frac{\pi}{8092}}^{\frac{\pi}{8092}} \frac{\sec (2023 x)}{1+(2023)^{(2023 x)}} d x= $$ 76. $$ \int_0^2 x^{\frac{5}{2}} \sqrt{2-x} d x= $$ 77. Area of the region bounded by the curve $y=2-x-3 x^2$, the $X$-axis, the $Y$-axis and the line $x=-2$ is 78. If $A$ and $B$ are arbitrary constants, then the differential equation having $y=A e^x+B \sin 2 x$ as its general soluti 79. The general solution of the differential equation $\frac{d y}{d x}=\sin (x-y)+\cos (x-y)$ is 80. The general solution of the differential equation $x^2 d y-\left(x y-y^2\right) d x=0$ is

Physics

1. Gravitational forces operate among which of the following? 2. Velocities $(v)$ and accelerations (a) in two systems of units 1 and 2 are related as $v_2=\frac{n}{m^2} v_1$ and $a_2=\ 3. A body starts rest with uniform acceleration. If its velocity after $n^{\text {th }}$ second (last second) is $v$ then i 4. A stone projected from the ground with a velocity $50 \mathrm{~ms}^{-1}$ at an angle of $30^{\circ}$ with the horizontal 5. A body of weight 50 N is placed on a horizontal surface as shown in the figure. The minimum force required to move the b 6. A block of mass $M$ moving on a frictionless horizontal surface collides with a spring of spring constant $K$, as shown 7. A body falls freely from a height $h$ on a fixed horizontal plane and rebounds. If $e$ is the coefficient of restitution 8. Two blocks of equal masses are tied to the ends of a light string. The string passes over a mass less pulley fixed on fr 9. A body is rolling without slipping on a horizontal plane. If the rotational kinetic energy of the body is $50 \%$ of its 10. A pendulum has a time period $T$ in air. Whạt it is made to oscillate in water its time period is $\sqrt{2} T$. Then the 11. For an ideal gas at a temperature of $27^{\circ} \mathrm{C}$ and at constant pressure, the coefficient of volume expansi 12. The percentage increase in the energy for an artificial satellite to shift it from an orbit of radius $r$ to an orbit of 13. The length of four wires $A, B, C$ and $D$ made of same materials are $1 \mathrm{~m}, 2 \mathrm{~m}, 3 \mathrm{~m}$ and 14. A liquid is taken in a long vertical cylindrical vessel and the cylinder is rotated about its vertical axis as shown in 15. A vessel having small hole in the bottom has to hold water without leakage, if water is poured into if upto a height of 16. Air is filled at $60^{\circ} \mathrm{C}$ in a vessel of open mouth. The vessel is heated to a temperature $f^{\circ} \ma 17. The temperature of 100 g of water is to be raised from $24^{\circ} \mathrm{C}$ to $90^{\circ} \mathrm{C}$ by adding stea 18. Two identical containers $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and sa 19. If the seventh harmonic of a closed pipe is in unison with fourth harmonic of an open organ pipe, then the ratio of leng 20. An observer moves towards a stationary source of sound, with a speed of one fifth of the speed of sound. The apparent in 21. Refractive index of a medium is $\mu$. If the angle of incidence is twice that of the angle of refracation, then the ang 22. Two slits are made one millimetre apart and the screen is placed one metre away from the slits. The fringe width when li 23. The flux of the electric field $\mathbf{E}=24 \hat{\mathbf{i}}+30 \hat{\mathbf{j}}+28 \hat{\mathbf{k}} \mathrm{NC}^{-1}$ 24. The effective capacitance between points $A$ and $B$ shown in the figure is 25. The electric resistance of a certain wire of iron is $R$. If its length and radius are both doubled, then 26. In a meter bridge experiment the ratio of the left gap resistance to the right gap resistance is $2: 3$. The balance len 27. A charge $q$ moves with a velocity $2 \mathrm{~ms}^{-1}$ along $X$-axis in a uniform magnetic field $\mathbf{B}=(2 \hat{ 28. In a galvanometer, $5 \%$ of the total current in the circuit passes through it. If the resistance of the galvanometer i 29. materials suitable for permanent magnets, must have which of the following properties? 30. The expression for the magnetic energy stored in a solenoid of length $L$, in terms of magnetic field $B$ and area $A$ i 31. An aeroplane is travelling horizontally towards west with a speed of $540 \mathrm{kmh}^{-1}$. The wing span of the plane 32. A series $L-C-R$ circuit is connected to an AC source of voltage $150 \sin (80 \pi t)$ volt. If the resistance of the re 33. The displacement current through the plates of a parallel plate capacitor of capacitance $30 \mu \mathrm{~F}$ is $150 \m 34. The de-Broglie wavelength of a particle moving with a speed of $0.8 c$ is equal to the wavelength of a photon. If $c$ is 35. In hydrogen spectrum, the shortest and longest wavelengths of Balmer series are $\lambda_1$ and $\lambda_2$ respectively 36. $\alpha$-decay of a parent nucleus $X$ results in a daughter nucleus $Y$. If $m_x, m_y$ and $m_\alpha$ are the masses of 37. In the nuclear fission of one nucleus of $\mathrm{U}^{235}$ the energy released is 188 MeV . The energy released in the 38. The phase difference between the input voltage and the output voltage in a common emitter amplifier is 39. The built-in potential of a $p-n$ junction diode is 0.7 V . If the diode is forward biased and the applied voltage is 0. 40. The loss of strength of a signal while propagating through a medium is known as

TS EAMCET 2023 (Online) 13th May Morning Shift

MCQ (Single Correct Answer)

-0

The slope of the normal drawn at a point $P$ to the curve $y=x^3-10 x^2+31 x-30$ is $-\frac{1}{14}$. If the co-ordinates of $P$ are integers, then the $X$-intercept of the tangent drawn at $P$ to the given curve is

$\frac{-11}{7}$

$\frac{11}{7}$

-22

TS EAMCET 2023 (Online) 13th May Morning Shift

MCQ (Single Correct Answer)

-0

$x$ and $y$ are two positive integers such that $2 x+3 y=50$. If $x^2 y^3$ is maximum for $x=\alpha$ and $y=\beta$, then $\frac{\alpha}{2}+\frac{\beta}{5}=$

$10 / 3$

TS EAMCET 2023 (Online) 13th May Morning Shift

MCQ (Single Correct Answer)

-0

$$ \int \frac{1}{16-7 \sin ^2 x} d x= $$

$\frac{1}{12} \tan ^{-1}\left(\frac{3 \tan x}{4}\right)+C$

$\frac{1}{3} \sin ^{-1}\left(\frac{3 \sin x}{4}\right)+C$

$\frac{1}{12} \log \left(\frac{4-\sqrt{7} \sin x}{4+\sqrt{7} \sin x}\right)+C$

$\frac{1}{12} \log \left(\frac{4+\sqrt{7} \sin x}{4-\sqrt{7} \sin x}\right)+C$

TS EAMCET 2023 (Online) 13th May Morning Shift

MCQ (Single Correct Answer)

-0

$$ \int \frac{\sec ^2 x}{(\sec x+\tan x)^2} d x= $$

$\frac{3+(\sec x+\tan x)^2}{2(\sec x+\tan x)^3}+C$

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

$-\frac{3+(\sec x+\tan x)^2}{2(\sec x+\tan x)^3}+C$

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

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