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

Chemistry

1. The maximum number of possible electrons in a subshell with $n=3$ and $l=2$ is 2. The uncertainty in position and velocity of a particle in motion are $1 \times 10^{-8} \mathrm{~m}$ and $6.627 \times 10 3. The basic difference in approach between Mendeleev's periodic law and modern periodic law is the change on the basis of 4. Which of the following pairs shows diagonal relationship? 5. The correct set of symbols of the molecular orbitals given below is 6. Find out the correct order of repulsive interaction of electron pairs in the following systems. (I) Lone pair - lone pai 7. Equal amounts of two gases of molecular weights 4 and 40 are mixed. The pressure of the mixture is 1.1 atm . What will b 8. Which of the curve ( $Z v s p$ ) will be followed by a real gas? 9. How much volume of 1 N aqueous solution of $\mathrm{H}_2 \mathrm{SO}_4$ should be taken, which will contain 0.2 moles of 10. The weight of potassium dichromate (molecular weight $=294$ ) required to prepare 0.04 N of 250 mL solution is 11. Which of the following statements regarding the first law of thermodynamics is correct? 12. Aqueous solution of ferric nitrate when mixed with aqueous solution of potassium thiocyanate gives red colour solution. 13. The pH of the solution, when (i) sodium acetate is dissolved in water. (ii) ammonium chloride is dissolved in water. 14. Dihydrogen can be prepared by which of the following reactions. (I) Reaction of granulated Zn with dil. HCl (II) Reactio 15. The carbonates of alkaline earth metals decompose on heating to give I. $\mathrm{CO}_2$ II. Metal oxide III. $\mathrm{H} 16. Borax is converted into crystalline boron by the following steps : $$ \text { Borax } \xrightarrow[\mathrm{H}_2 \mathrm{ 17. Buckminister fullerene contains the following $X$ number of six and $Y$ number of five member rings. What is the value o 18. The average atmospheric residence time is lowest for which of the given the greenhouse gas? 19. Which one of the following methods is suitable to separate a mixture of $n$-pentane and toluene? 20. Product 6-oxoheptanal is formed by reductive ozonolysis of 21. The major products $P$ and $Q$ from the below reactions are : $$ \mathrm{CH}_3 \mathrm{CH}=\mathrm{CH}_2 \xrightarrow{\m 22. A compound can crystallise in two forms $\alpha$ and $\beta$ which are fcc and bcc, respectively. The $\alpha$-form has 23. A 1.17 % solution of solute $A$ is isotonic with 7.2 % solution of glucose. If the molecular weight of solute $A$ is 58. 24. A mixture of 3.0 moles of $\mathrm{Na}_2 \mathrm{O}$ and 1.5 mol of $\mathrm{KO}_2$ is dissolved in 1000 mL of water. Th 25. A solution of $\mathrm{Fe}^{2+}$ is titrated potentiometrically using $\mathrm{Ce}^{4+}$ solution. When $80 \% \mathrm{F 26. What is the unit for the zero order rate constant? 27. To resist the coagulation of 100 cc gold sol; 1 cc of $10 \% \mathrm{NaCl}$ is added to it in the presence of $10^{-4} \ 28. In the following reactions, identify $P, Q$ and $R$, respectively I. $3 \mathrm{Fe}_2 \mathrm{O}_3+\mathrm{CO} \longrigh 29. The number of dissociable protons in "orthophosphoric acid" is 30. The geometry of $\mathrm{XeOF}_4$ is 31. Which of the following ions will exhibit colour in aqueous solution? 32. Which of the following correctly represents the order of ligands in spectrochemical series? 33. $$ \text { Monomeric units of melamine polymer are } $$ 34. Xerophthalmia disease is caused by the deficiency of 35. Artificial sweetening agent from below is 36. $$ \text { The major product formed in the following reactions is } $$ 37. $$ \text { The major product in the following reaction is } $$ 38. An alkene $A\left(\mathrm{C}_4 \mathrm{H}_8\right)$ exhibits cis/trans isomerism. $A$ on ozonolysis gives $B$, which whe 39. $$ \text { The major product formed in the following reaction is } $$ 40. $$ \text { The major product in the following reactions, is } $$

Mathematics

1. The number of bijective functions $f: \mathbf{Z} \rightarrow \mathbf{Z}$ such that $f(x+y)=f(x)+f(y) \forall x, y \in \m 2. For each $n \in \mathbf{N}$, let $A_n=\{(n+1) k / k \in \mathbf{N}\}$ and $X=\bigcup_{n \in \mathbf{N}} A_n \cdot A$ map 3. For $n>2$ and $n \in \mathbf{N}$, the product of the roots of $(x-n)\left(\left(x^2-2 n x\right)^2+\left(2 n^2-5\right)\ 4. Let $I$ be a unit matrix of order 6 . Let $A=\left(a_{i j}\right)$ be a square matrix of order 6 such that $a_{i j}=\lef 5. Let $a, b, c \notin\{0,1\}$. If the system of equations $$ \begin{aligned} & \Pi_1 \equiv x+a y+a z=0 \\ & \Pi_2 \equiv 6. $A$ is a singular matrix of order five. $B$ is another matrix having the rank $\rho(B)$ equal to the $\operatorname{rank 7. The number of points $z$ on the Argand plane which satisfy the conditions $\operatorname{Re}\left(\frac{z-2}{z-4 i}\righ 8. Let $a=1+i$ and $z=x+i y$. If the curve $z \bar{z}+a z+\bar{a} \bar{z}-4=0$ is cut by the straight line $(z+\bar{z})-i(z 9. If $(\sqrt{3}+i)^{10}=a+b i, a, b \in \mathbf{R}$, then the values of $a$ and $b$ are respectively 10. If $z$ is a complex number such that $z^2+z+1=0$, then $\left(z+\frac{1}{z}\right)^3+\left(z^2+\frac{1}{z^2}\right)^3+\l 11. If $\alpha, \beta$ are the roots of $a x^2+b x+c=0$ then $\left(\frac{\alpha}{a \beta+b}\right)^3-\left(\frac{\beta}{a \ 12. The maximum value of $\left\{x \in \mathbf{R} / \sqrt{x+2}>\sqrt{8-x^2}\right\}=$ 13. Let the roots of the equation $E_1 \equiv x^3+x^2+l x+n=0$ be $x_i,(i=1,2,3)$ and the roots of $E_2 \equiv x^3+a x^2+b x 14. If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $x^4+x^2+1=0$, then $\frac{\alpha^3+\beta^3+\gamma^3+\d 15. For $n=1,2,3, \ldots .50$, let $$ A=\left\{a_n / a_n=\left\{\begin{array}{ll} (-1)^{\frac{n}{2}}\left(\frac{n}{2}\right) 16. If $\alpha$ represents the number of arrangements of $p$ men and $q$ women in a row such that all men are together and $ 17. If ${ }^n C_0,{ }^n C_1,{ }^n C_2, \ldots,{ }^n C_n$ respectively are the binomial coefficients in the expansion of $(1+ 18. If sum of the coefficients of $x^r(r=0,1,2, \ldots, 2 n)$ in the expansion of $\left(1+3 x-2 x^2\right)^n$ is 128 , then 19. If the partial fractions decomposition of $\frac{x^4+24 x^2+28}{\left(x^2+1\right)^3}$ is $\frac{A}{x^2+1}+\frac{B}{\lef 20. $$ \text { Match the items of List-I with those of List-II } $$ .tg {border-collapse:collapse;border-spacing:0;} .tg 21. The period of $\cos (3 x+5)+7$ is 22. If $\cos \left(\frac{\alpha-\beta}{2}\right)=2 \cos \left(\frac{\alpha+\beta}{2}\right)$, then $\tan \frac{\alpha}{2} \t 23. For the least possible value of $n \in \mathbf{Z}$ the solution $(x, y)$ of the equations $\cos ^{-1} x+\left(\sin ^{-1} 24. If $x=\left(\tan ^{-1} \frac{1}{5}+\tan ^{-1} \frac{1}{8}\right)$, then $\frac{\sin x+\cos x}{\tan x}=$ 25. If for $|x|>1, \tanh ^{-1}\left(\frac{1}{x}\right)+\operatorname{coth}^{-1}(x)=\log _e(f(x))$, then $f(-5)=$ 26. In a triangle $A B C$, if $a 27. In a triangle $A B C$, if $c=9, s=10$ and $\Delta=10 \sqrt{2}$ then $b\left[1+\sqrt{2} \tan \left(\frac{A-B}{2}\right)\r 28. In a $\triangle A B C, \cot A+\cot B+\cot C=$ 29. If $A(4,7,8), B(2,3,4)$ and $C(2,5,7)$ are the vertices of $\triangle A B C$, then the length of the internal bisector o 30. For scalars $\lambda, \mu$ if the vector equation of a plane is $\mathbf{r}=(2+3 \lambda-\mu) \hat{\mathbf{i}}+(1-2 \lam 31. The equation of the plane in normal form passing through the point $A(\bar{a})$, parallel to a vector $\bar{b}$ and cont 32. The position vectors of the points $A$ and $B$ are respectively $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}$ and $2 \hat{\mathb 33. $\mathbf{x}, \mathbf{y}, \mathbf{z}$ are three vectors each of magnitude $\sqrt{2}$ and each making an angle $60^{\circ} 34. Let $\mathbf{a}=2 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=-\hat{\mathbf{j}}+\hat{\mathbf{k}}$. 35. If $S_1$ and $S_2$ are the variances of the first $2 k$ and $k(k>1)$ natural numbers respectively, then ( $S_1 / S_2$ ) 36. The standard deviations of two sets of observations $X=\left\{x_i\right\}$ and $Y=\left\{y_i\right\}(i=1,2, \ldots, 100) 37. 4-digit numbers are formed using the digits 4, 5, 6, 7, 8, 9 allowing repetition of the given digits. If a number is cho 38. If $E_1, E_2 \ldots, E_n$ are an independent events such that $P\left(E_r\right)=\frac{1}{1+r},(r=1,2, \ldots, n)$, then 39. An urn contains five balls. Two balls are drawn at random and they are found to be white. The probability that all the b 40. If the probability function of a random variable $X$ is given by $P(X=n)=\frac{k(n+1)}{3 n}$ for $n \in \mathbf{N} \cup\ 41. An observer counts 240 vehicles per hour at a specific location on a highway. Assuming that the arrival of vehicles at t 42. A point $P$ moves so that distance from $(0,2)$ to $P$ is $\frac{1}{\sqrt{2}}$ times the distance of $P$ from $(-1,0)$. 43. When the coordinate axes are rotated through an angle $\theta$ in anti clockwise direction, if the transformed equation 44. If the lines $3 x+y-4=0, x-a y-10=0, b x+2 y+9=0$ form three successive sides of a rectangle in that order and the fourt 45. The points $A(2,1), B(3,-2)$ and $C(a, b)$ are vertices of the rectangle $A B C D$. If the point $P(3,4)$ lies on $C D$ 46. If $\left|\begin{array}{lll}a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{array}\right|=0$, then the lines $ 47. For integer $k$, if the area of the triangle formed by the pair of lines $S=3 x^2-2 k x y+y^2=0$ with the line $L=2 x-y- 48. If the sides of a triangle $A B C$ are $2 x^2-y^2=0$, $x+y-1=0$ and the sides of another triangle $P Q R$ are $2 x^2-5 x 49. If $x^2+y^2-a^2+\lambda(x \cos \alpha+y \sin \alpha-p)=0$ is the smallest circle through the points of intersection of $ 50. If $P A$ and $P B$ are the tangents drawn from the point $P(1,1)$ to the circle $x^2+y^2+g x+g y-2=0$ with $C$ as the ce 51. The point/points of intersection of the common tangents of the two circles $x^2+y^2-8 x-6 y+21=0$ and $x^2+y^2-2 y-15=0$ 52. $L_1$ and $L_2$ are two common tangents to two circles. If $L_1$ touches the two circles at $A(1,1)$ and $B(0,1)$ and $L 53. The centre of the smallest circle which cuts the circles $x^2+y^2-2 x-4 y-4=0$ and $x^2+y^2-10 x+12 y+52=0$ orthogonally 54. If all the vertices of an equilateral triangle lie on the parabola $y^2=16 x$ and one of them coincides with the vertex 55. If $m x-y+c=0$ is a normal at a point $P$ on the parabola $y^2=16 x$ and the focal distance of $P$ is 40 units, then $|c 56. If $\pi / 3, \theta$ are the eccentric angles of the ends of a focal chord of the ellipse $\frac{x^2}{16}+\frac{y^2}{12} 57. If $x+2 y+k=0, k>0$ is a tangent to the ellipse $2 x^2+y^2=2$, then the equation of the normal to the given ellipse at $ 58. If $(8,2)$ is a point on the hyperbola whose length of the transverse axis is 12 and conjugate axis is $x=0$, then the e 59. If $A(4,3,2), B(5,4,6), C(-1,-1,5)$ are the vertices of a triangle, then the coordinates of the point in which the bisec 60. Assertion (A) The direction ratios of line $L_1$ are 2, 5, 7 and those of line $L_2$ are $\frac{4}{\sqrt{19}}, \frac{10} 61. If $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-7}{2}$ lies in the plane $a x+b y+z=7$, then $a+b=$ 62. $$\mathop {\lim }\limits_{x \to 0} \frac{1-\cos (1-\cos x)}{\sin ^4 x}= $$ 63. At $x=0, f(x)=\left\{\begin{array}{l}\frac{x}{|x|+2 x^2}, x \neq 0 \\ k, \quad x=0\end{array}\right.$ is 64. Match the functions of List-I with derivates given in List-II .tg {border-collapse:collapse;border-spacing:0;} .tg td{b 65. If $f(x)=\frac{x-1}{e^x}$, then $f^{\prime}(0)+f^{\prime \prime}(0)=$ 66. $$ \begin{aligned} & \text { If }\left(\frac{d y}{d x}\right)=\frac{1}{\left(\frac{d x}{d y}\right)} \text { and } \frac 67. The approximate value of $\left(3 \sqrt{126}+\sin 61^{\circ}\right)$ correct to three decimal places, obtained by taking 68. The radius of a sphere is changing. At an instant of time the rate of change in its volume and its surface area are equa 69. The volume of a sphere is increasing at the rate of $4 \pi \mathrm{cc} / \mathrm{sec}$. When its volume is $288 \pi \mat 70. Assertion (A) The function $f(x)=x-\log \left(\frac{1+x}{x}\right), x>0$ has no maximum. Reason (R) If a function $f(x)$ 71. $$ \int \frac{x^2}{\left(\sqrt{4-x^2}\right)^3} d x= $$ 72. $$ \int \frac{d x}{x \ln (x) \ln ^2(x) \ln ^3(x) \ldots \ln ^m(x)}=\frac{(\ln (x))^K}{K}+C \Rightarrow 2 K= $$ 73. If $I_m=\int x^m \cos n x d x=g(x)-\frac{m(m-1)}{n^2} I_{m-2}$, then $g(x)=$ 74. Let $I_n=\int \sec ^n x d x$. If $5 I_6-4 I_4=f(x)$, then $f\left(\frac{\pi}{4}\right)$ is equal to 75. If $$ f(x)=\left|\begin{array}{ccc} 1+\sin x+\sin 2 x+\sin 3 x & \frac{3+\sin 2 x}{2} & \frac{-2+\sin 3 x}{3} \\ 3+4 \si 76. $$ \lim\limits_{n \rightarrow \infty} \frac{1}{n}\left[\frac{1}{n} \sin ^{-1} \frac{1}{n}+\frac{2}{n} \sin ^{-1} \frac{2 77. The area (in sq. units) enclosed by the curves $y=2 x-x^2$ and $y=x^2-2 x-6$ is 78. If $\alpha$ and $\beta$ are respectively the order and degree of the differential equation for which $a x^2+b y^2=1$ is 79. The solution of the differential equation $x d y-y d x=\sqrt{x^2+y^2} d x$, given that $y=1$ when $x=\sqrt{3}$, is 80. If the solution $y(x)$ of the differential equation $\sin x \frac{d y}{d x}+y \cos x=e^{2 x}, x \in(0, \pi)$ satisfies $

Physics

1. The long range force experienced by a neutral particle with a finite mass 2. The dimension of angular momentum in mass $(M)$, length $(L)$ and time $(T)$ is 3. Consider that a truck is moving initially with $54 \mathrm{~km} / \mathrm{h}$. It has stopped by the driver after lookin 4. A ball is thrown vertically upwards with an initial velcoity $u$ reaches maximum height in 5 s . The ratio of distance t 5. A particle of mass $m=1 \mathrm{~kg}$ moves in the $x y$-plane. The force on it at time $t$ is $F(t)=[2 \sin (\alpha t) 6. A particle aimed at a target, projected with an angle $15^{\circ}$ with the horizontal is short of the target by 10 m . 7. A circular freeway entrance and exit are commonly banked to control a moving car at $14 \mathrm{~m} / \mathrm{s}$. To de 8. A cyclist leans with the horizontal at angle $30^{\circ}$, while negotiating round a circular road of radius $20 \sqrt{3 9. The block starts from rest as shown in the figure. Find the work done by force of 10 N and friction in the time 0 to 4 s 10. Under action of force, a 2 kg body moves such that its position $x$ as function of time $t$ is given by $x=\alpha t^2 / 11. Consider a thin metal strip of mass l kg and length 5 m . Calculate its moment of inertia about an axis perpendicular to 12. A solid cylinder is released from rest from the top of an inclined plane of inclination $30^{\circ}$ and length 60 cm . 13. A stiff spring having spring constant $k=400 \mathrm{~N} / \mathrm{m}$ is attached to the floor vertically. A mass $m=10 14. If the radius of the earth shrinks by $1 \%$, its mass remaining the same, then the acceleration due to gravity on the e 15. Young's modulus is proportionality constant that relates the force per unit area applied perpendicularly at the surface 16. The change in surface energy when a big spherical drop fo radius $R$ is split into $n$ spherical droplets of radius $r$ 17. A sheet of steel at $20^{\circ} \mathrm{C}$ has size as shown in figure below. If the co-efficient of linear expansion f 18. Different material of two identical long bars $A$ and $B$ are coated with wax and have their one end immersed in a hot o 19. A gas is at constant pressure $4 \times 10^5 \mathrm{~N} / \mathrm{m}^2$. When a heat energy of 2000 J is supplied to th 20. Certain amount of heat supplied to an ideal gas under isothermal condition will result in 21. Two trucks heading in opposite directions each with speed $0.1 u$, approach each other. The speed of the sound is $u$. T 22. A prism is made of a glass having refractive index $\sqrt{2}$. If the angle of minimum deviation is equal to angle of th 23. A thin glass prism of angle $9^{\circ}$ with refractive index 1.4 is combined with another glass prism of refractive ind 24. Wavelength of light used in an optical instruments are $\lambda_1=4000 \mathop {\rm{A}}\limits^{\rm{o}}$ and $\lambda_2= 25. The electric flux from a cube of edge $l$ is $\phi$ in an enclosed charge. If the edge of the cube is made $\frac{2}{3} 26. If the dielectric constant of a substance $K=\frac{4}{3}$, then the electric susceptibility $\chi$ in terms of vacuum p 27. Find potential difference points $A \& F$ and $F \& B$. 28. Four $4 \Omega$ resistors are connected together along the edges of a square. A 12 V battery with internal resistance of 29. A straight wire of mass 0.2 kg and length 1.5 m carries a current 2A is shown in the figure. It is suspended in mid-air 30. The ratio of the magnetic field inside a solenoid at an axial point well inside and at an axial end point is 31. A solenoid has a core of a material with relative permeability $\frac{800}{\pi}$. The windings of the solenoid are insul 32. An infinite long wire lying along the $Y$-axis, is carrying a current $I$ as shown in the figure. The magnetic flux thro 33. For an $R$ - $L-C$ circuit, driven with voltage of amplitude $V_m$ and frequency $\omega_0=\frac{1}{\sqrt{L C}}$, the cu 34. The typical wavelength of X-ray is 35. In a photoelectric effect experiment if the frequency of light is doubled, the stopping potential will 36. A monochromatic light of wavelength $\lambda$ ejects photoelectrons from a metal surface with work function ( $\phi) 2.4 37. The binding energy (BE) per nucleon for an element is 7.14 MeV . If the BE of element is 28.6 MeV , then the number of n 38. In $p-n-p$ transistor, the collector current is 39. The output of a NOR gate is HIGH when 40. The electromagnetic waves of frequency 6 GHz are used in

TS EAMCET 2020 (Online) 11th September Evening Shift

MCQ (Single Correct Answer)

-0

For $n>2$ and $n \in \mathbf{N}$, the product of the roots of $(x-n)\left(\left(x^2-2 n x\right)^2+\left(2 n^2-5\right)\left(x^2-2 n x\right)\right. \left.+\left(n^4-5 n^2+4\right)\right)=0$ is divisible by

625

120

TS EAMCET 2020 (Online) 11th September Evening Shift

MCQ (Single Correct Answer)

-0

Let $I$ be a unit matrix of order 6 . Let $A=\left(a_{i j}\right)$ be a square matrix of order 6 such that $a_{i j}=\left\{\begin{array}{l}1, \text { if } i+j=7 \\ 0, \text { if } i+j \neq 7\end{array}\right.$ then $\left(A(\operatorname{adj} A) A^{-1}\right) A^2=$

$/$

$A$

$-A$

$-/$

TS EAMCET 2020 (Online) 11th September Evening Shift

MCQ (Single Correct Answer)

-0

Let $a, b, c \notin\{0,1\}$. If the system of equations

$$ \begin{aligned} & \Pi_1 \equiv x+a y+a z=0 \\ & \Pi_2 \equiv b x+y+b z=0 \\ & \Pi_3 \equiv c x+c y+z=0 \end{aligned} $$

has a non-trivial solution, then the system of equations $\Pi_1=a, \Pi_2=b, \Pi_3=c$ has

unique solution

infinite number of solutions

no solution

unique solution only when $a=b=c$

TS EAMCET 2020 (Online) 11th September Evening Shift

MCQ (Single Correct Answer)

-0

$A$ is a singular matrix of order five. $B$ is another matrix having the rank $\rho(B)$ equal to the $\operatorname{rank} \rho(A)$ and $B$ has a non-zero minor of order 3. Then which one of the following is true?

$B$ is a $4 \times 4$ matrix

$\rho(A)=\rho(B)=4$, irrespective of the order of $B$

$\rho(A)=\rho(B)=3$, when all the fourth order minors of $A$ are zero

$|B|=0$

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