TS EAMCET 2020 (Online) 11th September Morning Shift | TS EAMCET Year Wise Previous Years Questions

Chemistry

1. In the two elements, ${ }_{Z_1} A^{M_1}$ and ${ }_{Z_2} B^{M_2}$, the following relations are true. $M_1 \neq M_2$ and $ 2. The correct order of decreasing energy for the electrons whose quantum numbers $n$ and $l$ are given below, is A. $n=5$ 3. Find the correct set with isoelectronic species? 4. Among the following, the pair of elements having same electronegativity values are I. H and $\mathrm{P} \quad$ II. Be an 5. The correct order of $\mathrm{H}-\mathrm{N}-\mathrm{H}$ bond angles of ammonia, ammonium ion and amide are 6. Find out the correct hybridisation of the central atom in $\mathrm{BCl}_3, \mathrm{PCl}_5, \mathrm{NH}_3$ and $\mathrm{S 7. Which among the following graphs, correctly represents the Boyle's Law? 8. A vessel of volume 24.6 L contains 1.5 moles of $\mathrm{H}_2$ and 2.5 moles of $\mathrm{N}_2$ at 300 K . Calculate the 9. For a given unbalanced reaction, $\mathrm{MnO}_2+\mathrm{HCl} \longrightarrow \mathrm{MnCl}_2+\mathrm{H}_2 \mathrm{O}$, 10. The emperical formula of a compound is $\mathrm{C}_2 \mathrm{H}_5 \mathrm{O}$ and its vapour density is 45 . What is the 11. Find the value of the equilibrium constant $(K)$ of a reaction at 300 K , when standard Gibbs free energy change is $-25 12. What is the pH of 10 L of a buffer solution containing $0.01 \mathrm{M} \mathrm{NH}_4 \mathrm{Cl}$ and $0.1 \mathrm{M} \ 13. Decreasing order of number of ionisable hydrogen atoms in the following molecules is I. $\mathrm{H}_3 \mathrm{PO}_4$ II. 14. What will be the organic compound formed, when aluminium carbide react with deuterated water? 15. What is the increasing order of hydration enthalpies of alkali metal ions? 16. When orthoboric acid $\left(\mathrm{H}_3 \mathrm{BO}_3\right)$ is subjected to strong heating, the residue left is 17. When graphite is heated at $300^{\circ} \mathrm{C}$ with potassium vapour, it forms $\mathrm{C}_8 \mathrm{~K}$ compound 18. Which of the following molecules is present in photochemical smog? 19. The correct order of the relative stability of the following carbanions is I. $\mathrm{HC} \equiv \mathrm{C}^{-}$ II. $\ 20. Which of the following sets of functional groups is meta-directing group? 21. The correct order of reactivity of hydrogen halides with propene is 22. The angle between (100) and (110) planes of FCC lattice is 23. $15 \%$ aqueous solution of glucose (molecular weight $=180 \mathrm{~g} / \mathrm{mol}$ ) is isotonic with $8 \%$ aqueou 24. The vapour pressure of pure water is 23 mmHg . The vapour pressure of an aqueous solution, which contains 10 mass per ce 25. What is the standard cell potential for the reaction with $K=1$ (equilibrium constant) 26. For a first order reaction ( $A \rightarrow B$ ), the temperature ( $T$ ) dependent rate constant $(k)$ in $\mathrm{s}^{ 27. The method, which is based on the principle that "different components of a mixture are differently adsorbed on an adsor 28. The solubilities of the impurities in the melt and solid states is not same. This principle is applied during the extrac 29. How many bridging oxygen atoms are present in $\mathrm{P}_4 \mathrm{O}_{10}$ ? 30. Ozone is obtained from oxygen 31. What is the oxidation state of Cr , when the pH of the aqueous solution of potassium dichromate changes from acidic to b 32. Coordination number of Fe in the complexes $\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{4-},\left(\mathrm{Fe}(\mathrm{CN})_ 33. Type of reaction involved in the initial step in the formation of bakelite 34. Which of the following are reducing sugars? I. Sucrose III. Lactose II. Ribose IV. Fructose 35. The number of six and five membered rings present in norethindrone (a synthetic progesterone) are respectively 36. 4-Nitrotoluene (para-nitrotoluene) on reduction with $\mathrm{Fe} / \mathrm{HCl}$ and then electrophilic bromination wit 37. $$ \text { What are } X \text { and } Y \text { in the following reaction? } $$ 38. The major products $P$ and $Q$ in the following reaction sequences are 39. $$ \text { Identify the correct decreasing order of acidic strength. } $$ 40. $$ \text { Identify } X \text { in the following. } $$

Mathematics

1. If $f:[-3,2] \rightarrow[0, \sqrt[3]{x}]$ is an onto function defined by $f(n)=\left\{\begin{array}{cc}2+\sqrt[3]{n}, & 2. Let $[x]$ denote the greatest integer not more than $x$. If $A$ and $B$ are the domains of the functions $f(x)=\frac{x-[ 3. $n^5-5 n^3+4 n$ is divisible by 120 is true for 4. A value of $\theta$ in $\left(0, \frac{\pi}{2}\right)$ and satisfying $\left|\begin{array}{ccc}1+\sin ^2 \theta & \cos ^ 5. Let $[A]_{3 \times 3}$ be a non-singular matrix such that $$ A^{-1}=\frac{1}{3}\left(A^2-5 A+7 I\right) . $$ Then $17 A^ 6. If $\left[\begin{array}{ccc}2 & 1 & 1 \\ 0 & 3 & -1 \\ 1 & -1 & 1\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end 7. For some $a, b, c \in \mathbf{R}$, if $\sin 5 \theta=a \cos ^4 \theta \sin \theta+b \cos ^2 \theta \sin ^3 \theta+c \sin 8. $A\left(z_1=2+2 i\right), B\left(z_2\right), C\left(z_3\right)$ are three points on the Argand plane satisfying $\left|z 9. For $n \in \mathbf{N}$, If $A_n=\cos \left(\frac{\pi}{2^n}\right)+i \sin \left(\frac{\pi}{2^n}\right)$, then $\left(A_1 10. Let $A_r=\left(x+\frac{1}{x}\right)^3 \cdot\left(x^2+\frac{1}{x^2}\right)^3 \cdot\left(x^3+\frac{1}{x^3}\right)^3 \cdots 11. $p$ and $q$ are two roots of the equation $x^2+7 x+3=0$. If $\frac{3 p}{1-2 p}, \frac{3 q}{1-2 q}$ are the roots of $l x 12. If the quadratic equations $3 x^2-7 x+2=0$ and $k x^2+7 x-3=0$ have a common root then the positive value of $k$ is 13. If the roots of $x^3+a x^2+b x+c=0$ are in arithmetic progression with common difference 1 , then 14. If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+3 x^2-x-3=0$, then $\left(1+\alpha^2\right)\left(1+\beta^2 15. The number of integers $x, y, z, w$ satisfying $x+y+z+w=25$ and $x, y, z \geq-1, w \geq 1$, is 16. If 3 sisters and 8 other girls are together playing a game, then the number of ways in which all the girls are seated ar 17. Suppose $1, m, n$ respectively represent the coefficient of $x^{10}$, the constant term and the coefficient of $x^{-10}$ 18. For $z \in \mathbf{C}$, if $(1+z)^n=1+{ }^n C_1 z+{ }^n C_2 z^2+\ldots{ }^n C_n z^n$ and $\sum_{r=0}^{100} 100 c_r(\sin 19. If $\frac{1}{x^4+x^2+1}=\frac{A x+B}{x^2+x+1}+\frac{C x+D}{x^2-x+1}$, then $\cos ^{-1}(A+B+C+D)=$ 20. The period of $\frac{\sin x}{\cos 3 x}+\frac{\sin 3 x}{\cos 9 x}+\frac{\sin 9 x}{\cos 27 x}+\frac{\sin 27 x}{\cos 81 x}$ 21. If $\alpha=\frac{\sin ^3 x}{\cos ^2 x}, \beta=\frac{\cos ^3 x}{\sin ^2 x}$ and $\sin x+\cos x=k$, then $\alpha \sin x+\b 22. If $A+B+C=60^{\circ}$, then $\cos \left(30^{\circ}-A\right)+\cos \left(30^{\circ}-B\right)+\cos \left(30^{\circ}-C\right 23. If $\left|\sin x-\cos ^2 x\right| \geq\left|3-3 \sin x+\sin ^2 x\right|+4|\sin x-1|$, then $x=$ 24. The number of real roots of the equation $\sin \left[2 \cos ^{-1}\left\{\cot \left(2 \tan ^{-1} x\right)\right\}\right]= 25. If $\operatorname{sech}^{-1}(1 / 2)-\operatorname{cosech}^{-1}(3 / 4)=\log _e k$, then 26. The perimeter of a $\triangle A B C$ is 6 times the arithmetic mean of the sine of its angles. If its side $B C$ is of u 27. In a $\triangle A B C$, with usual notation, if $r=r_1-r_2-r_3$, then $2 R=$ 28. In a $\triangle A B C$, let $a, b, c, s, r, R, I, S, r_1, r_2, r_3$ stand for their usual meaning. Then Match the items 29. If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are the position vectors of the points $A, B, C$ respectively, then match the it 30. If the point of intersection of the lines $\mathbf{r}=\hat{\mathbf{i}}-6 \hat{\mathbf{j}}+(p \sec \alpha) \hat{\mathbf{k 31. $\mathbf{1}, \mathbf{m}, \mathbf{n}$ are three unit vectors in a right handed system and $L$ is a line through the point 32. Let $\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and $\mathbf{b}=2 \hat{\mathbf{i}}-\hat{\mathbf{ 33. Let $\mathbf{p}, \mathbf{q}, \mathbf{r}$ be three non-coplanar vectors and $\left[\begin{array}{lll}\mathbf{p} & \mathbf 34. If $\mathbf{b}, \mathbf{c}$ are non collinear vectors, $|\mathbf{c}| \neq 0$, $\mathbf{a} \times(\mathbf{b} \times \math 35. $$ \text { The variance of the following frequency distribution is } $$ $$ \begin{array}{ccccccc} \hline \text { Classes 36. The mean deviation about the mean of the following data is nearly $$ \begin{array}{ccccccccc} \hline \text { Size }(x) & 37. If the roots of each of the equations $2 x^2+x-1=0$, $3 x^2-10 x+3=0$ and $6 x^2+11 x-2=0$ corresponds to probabilities 38. Cards are drawn one after the other without replacement from a well shuffled pack of cards until and ace card appears. I 39. A number is selected at random from the set $\{1,2, \ldots \ldots ., 100\}$. Given that the number selected is divisible 40. A target is to be destroyed in a bombing exercise and there is a $75 \%$ chance that a bomb will hit the target. Assumin 41. Let $X \sim B(n, p)$ with mean $\mu$ and variance $\sigma^2$. If $\mu=2 \sigma^2$ and $\mu+\sigma^2=3$, then $P(X \leq 3 42. If $A=(1,2), B=(2,1)$ and $P$ is any point satisfying the condition $P A+P B=3$, then the equation of the locus of $P$ i 43. Let $C$ be a curvea $x^2+2 h x y+b y^2+2 g x+2 f y+c=0$ in a cartesian plane. By rotating the coordinate axes through an 44. If the straight line passing through the point $P(3,4)$ makes an angle $\frac{\pi}{6}$ with the positive direction of $X 45. If the equation of the straight line passing through the point of intersection of $x+2 y-19=0, x-2 y-3=0$ and which is a 46. If two equal sides of an isosceles triangle are given by the equations $7 x-y+3=0$ and $x+y-3=0$, then the equation of i 47. Suppose $O(0,0)$ is the origin and the line $L=x+y-\lambda=0$ meets the curve $x^2+y^2-2 x-4 y+2=0$ at $A$ and $B$. If $ 48. Let $P$ be the point of intersection of the lines $L_1 \equiv x-y-7=0$ and $L_2 \equiv x+y-5=0 . A\left(x_1, y_1\right)$ 49. If the poles of the line $x-y=0$ with respect to the circles $x^2+y^2-2 g_i x+c_i^2=0(i=1,2,3)$ are ( $\alpha_i, \beta_i 50. If the circles $x^2+y^2-4 x+6 y+13-a^2=0$ and $x^2+y^2-10 x-2 y+17=0$ intersect in two distinct points, then ' $a$ ' is 51. If a circle of radius $r$ touches the positive coordinate axes and also the circle $x^2+y^2-12 x-10 y+52=0$ externally, 52. If the circles $x^2+y^2-2 x-2 y+k=0$ and $x^2+y^2+4 x+6 y+4=0$ touch each other externally, then the point of contact of 53. The centre of the circle passing through the points of intersection of the circles $(x+3)^2+(y+2)^2=25$ and $(x-2)^2+(y- 54. If a circle with its centre at the focus of the parabola $y^2=2 p x$ is such that it touches the directrix of the parabo 55. If the tangent drawn at the point $P(4,8)$ to the parabola $y^2=16 x$ meets the parabola $y^2=16 x+80$ at $A$ and $B$, t 56. If the sum of the distances from the foci to the centre $O(0,0)$ of an ellipse is $8 \sqrt{6}$ units and the area of the 57. The equation of the ellipse with directrix $3 x+4 y-5=0$, focus $(1,2)$ and eccentricity $1 / 2$, is 58. A rectangular hyperbola passing through $(3,2)$ has its asymptotes parallel to the coordinate axes. If $(1,1)$ is the po 59. $E(1,0,0), F(0,2,0), G(0,0,3)$ are respectively the mid-points of the sides $A B, B C, C A$ of $\triangle A B C$. If $a_ 60. If the direction ratios $a, b, c$ of a line $L$ satisfy the relations $a b+b c+c a=0$ and $6 a b+9 b c+8 c a=0$, then th 61. The equation of the plane passing through the line of intersection of planes $\pi_1=2 x+6 y+4 z-7=0$, $\pi_2=x-y-2 z-2=0 62. $$\mathop {\lim }\limits_{x \to 0} \frac{x \tan 4 x-2 x \tan 2 x}{(1-\cos 4 x)^2}= $$ 63. Assertion (A) $f(x)=|x-a|+|x-b|$, is continuous on $\mathbf{R}$ Reason (R) $\frac{|x-\alpha|}{x-\alpha}$ is continuous a 64. If $x \sqrt{1+y}+y \sqrt{1+x}=0$, then $\frac{d y}{d x}=$ 65. If $p(x)$ be a polynomial satisfying $p(2 x)=p^{\prime}(x) \cdot p^{\prime \prime}(x)$, then $\sum_{x=1}^5 p(x)=$ 66. If $2^x+2^y=2^{x+y}$, then $\frac{d y}{d x}=$ 67. If the tangent and normal drawn to the curve $x=a(\theta+\sin \theta), y=a(1-\cos \theta)$ at $P\left(\theta=\frac{\pi}{ 68. $x_1, x_2 \in \mathbf{N}$. If a line having slope 2 is a tangent to the curve $y=x^4-6 x^3+13 x^2-10 x+5$ at points $P\l 69. Consider the following statements Statement I If $a_0+\frac{a_1}{2}+\frac{a_2}{3}+\ldots .+\frac{a_n}{n+1}=0$, where $a_ 70. A function $y=f(x)$ with $f(-1)=-249$ has no maximum and has only one minimum at $x=5$ with $f(5)=75$. Which one of the 71. If $\int e^{\sin ^2 x}\left(\sin x \cos x+\cos ^3 x \sin x\right) d x=e^{\sin ^2 x}(1+f(x))+c$, then $f^{\prime}(x)=$ 72. $$ \int \frac{25 x^2+8}{\sqrt{25 x^2+9}} d x= $$ 73. $$ I_{m, n}=\int x^m(\log x)^n d x= $$ 74. The positive integer $n \leq 5$ for which $\int_0^1 e^x(x-1)^n d x=16-6 e$ is 75. If $f(x)=\sin ^6 x+\cos ^6 x+2 \sin ^3 x \cos ^3 x$, then $\int_0^{\pi / 4} \frac{\sin ^2 2 x}{f(x)} d x=$ 76. $$ \int_3^5(x-3)^3(5-x)^5 d x= $$ 77. The area (in sq. units) of the portion lying above the $X$-axis and enclosed between the curves $y^2=2 a x-x^2$ and $y^2 78. The differential equation for which $l x^2+m y^2=x+y$ is the general solution is 79. The general solution of the differential equation $(x-2 y+1) d y-(3 x-6 y+2) d x=0$ is 80. The general solution of the differential equation $\left(1+y^2\right) d x=\left(\tan ^{-1} y-x\right) d y$ is

Physics

1. Let $G, W, E$ and $S$ be relative strength of gravitational, weak-nuclear, electromagnetic and strong-nuclear forces, re 2. What is the dimension of $\frac{1}{\mu_0 \varepsilon_0}$ ? ( $\mu_0=$ magnetic permeability and $\varepsilon_0=$ permitt 3. A person moves 30 m North and then 20 m towards East and finally $30 \sqrt{2} \mathrm{~m}$ in South-West direction. The 4. A particle moving along $X$-axis has acceleration $f$ at time $t$ given by $f=f_0\left(1-\frac{t}{T}\right)$, where $f_0 5. Consider the following vectors. Choose the correct statement. 6. A river 200 m wide is flowing at a rate of $3.0 \mathrm{~m} / \mathrm{s}$. A boat is sailing at a velocity of $15 \mathr 7. An infinite number of masses are placed on a frictionless table and they are connected via massless strings. Their masse 8. A block of mass $m=2 \mathrm{~kg}$ is initially at rest on a horizontal surface. A horizontal force $\mathbf{F}_1=(6 \ma 9. A force of 4 N acts on a 10 kg body initially at rest. Let $W_1$ is work done by force during $0 \leq t \leq \mathrm{ls} 10. An elevator of mass 500 kg is ascending upwards with a constant acceleration $a=2 \mathrm{~m} / \mathrm{s}^2$. What is t 11. A solid sphere of mass 2 kg rolls on a smooth horizontal surface at $10 \mathrm{~m} / \mathrm{s}$. It then rolls up a sm 12. A rod of length $L$ revolves in a horizontal plane about the axis passing through its centre and perpendicular to its le 13. Consider a simple harmonic motion (SHM). Let $K$ and $U$ be kinetic energy and potential energy when the displacement in 14. A planet is moving in an elliptical orbit around the sun. The work done on the planet by the gravitational force of the 15. A steel rod has a radius of 10 mm and a length of 1 m . A 80 kN force stretches it along its length. If the Young's modu 16. A block of iron contains a hollow cavity as shown below. The block weighs 6000 N in air and 4000 N in water. If the dens 17. A heating element of mass 100 g and having specific heat of $1 \mathrm{~J} /\left(\mathrm{g}^{\circ} \mathrm{C}\right)$ 18. An ideal gas at temperature $T$, pressure $p$ occupies a volume $V$. If its temperature is halved and pressure doubled, 19. A Carnot engine whose efficiency is $40 \%$, receives heat at 500 K . If the efficiency is to be $50 \%$, the source tem 20. A system goes from $A$ and $B$ via two processes I and II as shown in figure. If $\Delta U_1$ and $\Delta U_2$ are the c 21. An organ pipe with both ends open has a length $L=25$ cm . An extra hole is created at position $L / 2$. The lowest freq 22. The magnifications produced by a convex lens for two position of an object are 4 and 3, respectively. If the distance of 23. What minimum separation between two objects a human eye would be able to resolve, if the eye pupil diameter is 2 mm and 24. The shape of wavefront of light diverging from point source 25. A cube of side $L$ has point charges $+q$ located at its seven vertices and $-q$ at remaining one vertex. The electric f 26. A capacitor is fully charged with a battery and then disconnected. A dielectric is then inserted into the capacitor. How 27. A conducting wire of cross-sectional area $1 \mathrm{~cm}^2$ has $3 \times 10^{23}$ charge carriers per $\mathrm{m}^3$. 28. The total current supplied to the following circuit by the battery is 29. A conducting wire is in the shape of a regular hexagon which is inscribed inside an imaginary circle of radius $R$. If a 30. A coil having 100 turns is wound tightly in the form of a spiral with inner and outer radii 1 cm and 2 cm , respectively 31. Let $m$ and $r$ are the dipole moment and radius of earth respectively. Then, the earth's magnetic field at the equator 32. A circular coil consists 70 closely wound turns and has a radius of 10 cm . An externally produced magnetic field of mag 33. The $L-C-R$ circuit shown below is driven by an ideal AC voltage source. At frequency $f=\frac{1}{2 \pi \sqrt{L C}}$, ch 34. At an instant, a plane electromagnetic wave has its magnetic field in the direction of the vector $\hat{\mathbf{i}}-\hat 35. When the energy of incident radiation is increased by $20 \%$, the kinetic energy of the photoelectrons emitted from a m 36. In the Bohr model an electron of mass $m$ moves in a circular orbit around the proton. Considering the orbiting electron 37. A radioactive element which can decay by two processes, has half-life $t_1$ for first process and half-life $t_2$ for se 38. A $p-n$ junction diode can withstand upto 20 mA current under forward bias. The diode has a potential difference of 0.5 39. In a Zener diode, 40. A message signal is super-imposed with a carrier signal. The resulting modulating signal $C_m(t)$ is given by $C_m(t)=A_

TS EAMCET 2020 (Online) 11th September Morning Shift

MCQ (Single Correct Answer)

-0

For $z \in \mathbf{C}$, if $(1+z)^n=1+{ }^n C_1 z+{ }^n C_2 z^2+\ldots{ }^n C_n z^n$ and $\sum_{r=0}^{100} 100 c_r(\sin r x)=\left(2 \cos \frac{x}{2}\right)^{100} \sin k x$, then $k=$

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