Chemistry
1. The radius of third orbit of hydrogen atom is $R \mathrm{pm}$. The radius of second orbit of $\mathrm{He}^{+}$ion (in pm 2. The threshold frequency of a metal is $10^{15} \mathrm{~s}^{-1}$. The ratio of maximum kinetic energies of the photoelec 3. Consider the following.
(I) The order of first ionisation enthalpy of first three elements of 3rd period is $\mathrm{Mg} 4. In which of the following set of molecules the hybridisation of central atoms is different?
5. At 300 K and 760 torr pressure, the density of a mixture of He and $\mathrm{O}_2$ gases is $0.543 \mathrm{gL}^{-1}$. The 6. The equivalent weight of which of the following is maximum?
(Given : atomic weights $\mathrm{Na}=23, \mathrm{Mn}=55$,
$ 7. If 2.5 moles of an ideal gas at a certain temperature are allowed to expand isothermally and reversibly from an initial 8. A solution is prepared by mixing 10 mL of 1.0 M acetic acid and 20 mL of 0.5 M sodium acetate and diluted to 100 mL . If 9. Consider the following statements about the hydrides.
(I) Sodium hydride with water liberates oxygen gas.
(II) Methane, 10. The nitrate of which of the following metals does mot liberate $\mathrm{NO}_2$ gas on heating?
11. Match the following.
The correct answer is
12. What are the correct statements about the elements of group 13 given below?
(I) The stability of +1 oxidation state foll 13. Assertion (A) Graphite is used as a dry lubricant in machines which run at high temperatures.
Reason ( $\mathbf{R}$ ) Th 14. The correct IUPAC name of the compound given under is 15. At $T(\mathrm{~K})$, copper (atomic mass $=63.5 \mathrm{u}$ ) has fce structure with an edge length of $x \AA$. The dens 16. The vapour pressure of a pure liquid $A$ is 70 torr at 300 K . It forms an ideal solution with another liquid $B$. The m 17. The electrode potential of chlorine electrode is maximum, when the concentration of chloride ion in the solution (in $\m 18. If benzene diazonium chloride undergoes first order decomposition at $T(\mathrm{~K})$ with a rate constant of $6.93 \tim 19. Identify the factors which favour the physical adsorption from the following
(I) High surface area
(II) Low temperatures 20. Sphalerite, siderite and malachite are the ores of metals $X, Y$ and $Z$. The atomic numbers of them are respectively
21. Consider the reaction,
$$ \mathrm{P}_4+3 \mathrm{NaOH}+3 \mathrm{H}_2 \mathrm{O} \longrightarrow Q+3 \mathrm{NaH}_2 \mat 22. The oxidation state of sulphur atoms and numbers of $\mathrm{S}-\mathrm{OH}$ bonds in peroxydisulphuric acid are respect 23. Identify the correct statements from the following.
(I) Au is soluble in aqua regia but not Pt .
(II) Among the oxoacids 24. $$
\underset{(1: 20)}{\mathrm{Xe}(g)+\mathrm{F}_2(\mathrm{~g}) \xrightarrow[60-70 \text { bar }]{573 \mathrm{~K}} X(\mat 25. The number $f$-electrons in +3 oxidation state of gadolinium $(Z=64)$ is $x$ and in +2 oxidation state of ytterbium $(Z= 26. Table
Match the following.
The correct answer is
27. Amongst the following, how many of them come under the category of elastomers?
Natural rubber, polyethene, vulcanized ru 28. Which of the following is the incorrect statement about maltose?
29. Which of the following is not correctly matched?
30. Consider the following reaction sequence
The correct statements about $Z$ are
I. It gives yellow precipitate with $\math 31. Conversion of $A$ to $B$ is an example of the reaction 32. In which of the following hyperconjugation is not possible? 33. The functional groups in $X$ and $Y$ are respectively. 34. Identify the major product $B$ in the given sequence of reactions. 35. Match the following.The correct answer is Table
36. Which of the following is least reactive towards $\mathrm{S}_{\mathrm{N}} 2$ reaction? 37. Phenol is mainly manufactured from a compound $X$ by subjecting it to oxidation in air followed by treating with dilute 38. Identify $A$ and $B$ from the following reactions 39. What are the products $X$ and $Y$ respectively in the reactions I and II? 40. Identify the product ' $Y$ ' in the following sequence of reactions
Mathematics
1. The range of the function $f(x)=\log _{0.5}\left(x^4-2 x^2+3\right)$ is 2. If $P$ is a non-singular matrix such that $I+P+P^2+\ldots \ldots+P^n=0(0$ denotes the null matrix $)$, then $P^{-1}=$
3. If $z_1$ and $z_2$ are complex numbers such that $\left|z_1+z_2\right|=\left|z_1\right|+\left|z_2\right|$, then the diff 4. If $i=\sqrt{-1}$, then $1+i^2+i^4+i^6+\ldots \ldots+i^{2024}=$
5. If one root of the equation $4 x^2-2 x+k-4=0$ is the reciprocal of the other, then the value of $k$ is
6. If the expression $x^3+3 x^2-9 x+\lambda$ is of the form $(x-\alpha)^2(x-\beta)$, then the values of $\lambda$ are
7. The number of ways of arranging all the letters of the word "SUNITHA" so that the vowels always occupy the first, middle 8. If the term independent of $x$ in the expansion of $\left(\sqrt{x}-\frac{k}{x^2}\right)^{10}$ is 405 , then $k=$
9. If $\frac{x^4}{(x-1)(x-2)(x-3)}=p(x)+\frac{A}{x-1}+\frac{B}{x-2}+\frac{C}{x-3}$, then $p\left(\frac{3}{2}\right)+C=$
10. For $0 \leq x \leq \pi$, if $81^{\sin ^2 x}+81^{\cos ^2 x}=30$, then $x=$ 11. If $\sinh (\log x)=-2$, then $x=$
12. In an isosceles right angled triangle, a straight line is drawn from the mid-point of one of the equal sides to the oppo 13. If the position vectors of $\mathbf{P}$ and $\mathbf{Q}$ are $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-7 \hat{\mathbf{k}}$ an 14. $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are three-unit yectors such that $|\mathbf{a}+\mathbf{b}+\mathbf{c}|=1$ and $\mathb 15. Two numbers $b$ and $c$ are chosen at random in succession without replacement from the set $\{1,2,3, \ldots \ldots, 9\} 16. A student is given 6 questions in an examination with true or false type of answers. If he writes 4 or more correct answ 17. If $P(X=x)=c\left(\frac{2}{3}\right)^x ; x=1,2,3,4, \ldots$ is a probability distribution function of a random variable 18. If $t$ is a parameter, $A=(a \sec t, b \tan t)$, $B=(-a \tan t, b \sec t)$ and $O=(0,0)$, then the locus of the centroid 19. The angle, by which the coordinate axes are to be rotated about the origin so that the transformed equation of $\sqrt{3} 20. If the slope of a straight line passing through $A(3,2)$ is $3 / 4$, then the coordinates of the two points on the same 21. If a diameter of the circle $x^2+y^2-4 x+6 y-12=0$ is a chord of a circle $S$ whose centre is at $(-3,2)$, then the radi 22. If a circle passing through $A(1,1)$ touches the $X$-axis, then the locus of the other end of the diameter through $A$ i 23. If two circles $x^2+y^2-6 x-6 y+13=0$ and $x^2+y^2-8 y+9=0$ intersect at $A$ and $B$, then the focus of the parabola who 24. A particle is travelling in clockwise direction on the ellipse $\frac{x^2}{100}+\frac{y^2}{25}=1$. If the particle leave 25. If the equation of a hyperbola is $9 x^2-16 y^2+72 x-32 y-16=0$, then the equation of conjugate hyperbola is
26. If the direction cosines $(l, m, n)$ of two lines are connected by the relations $l+m+n=0$ and $l m=0$, then the angle b 27. The sum of the squares of the perpendicular distances of a point $(x, y, z)$ from the coordinate axes is $k$ times the s 28. Equation of the plane through the mid-point of the line segment joining the points $A(4,5,-10)$ and $B(-1,2,1)$ and perp 29. $$
\lim \limits_{x \rightarrow 1} \frac{(2 x-3)(\sqrt{x}-1)}{2 x^2+x-3}=
$$
30. If $\mathbf{a}$ is a vector such that $\mathbf{a} \times \hat{\mathbf{i}}=\hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\mathb 31. The equation of the normal at $t=\frac{\pi}{2}$ to the curve $x=2 \sin t, y=2 \cos t$ is
32. $$
\int \frac{\sin ^8 x-\cos ^8 x}{1-2 \sin ^2 x \cos ^2 x} d x=
$$
33. $$
\int_{1 / 2}^2\left|\log _{10} x\right| d x=
$$
34. Two tangents are drawn from the point $(-1,-2)$ to the parabola $y^2=4 x$. If $\theta$ is the angle between these tangen 35. If $f:[2, \infty) \rightarrow R$ is defined by $f(x)=x^2-4 x+5$, then the range of $f$ is
36. If $A=\left[\begin{array}{ccc}5 & 5 \alpha & \alpha \\ 0 & \alpha & 5 \alpha \\ 0 & 0 & 5\end{array}\right]$ and $\opera 37. If $\frac{1+i \cos \theta}{1-2 i \cos \theta}$ is purely real, then $\cos ^3 \theta+\sin ^2 \theta+\cos \theta+1=$
38. If $\theta=\frac{\pi}{6}$, then the 10 th term of the series $1+(\cos \theta+i \sin \theta)^1+(\cos \theta+i \sin \theta 39. If $(x-2)$ is a common factor of the expressions $x^2+a x+b$ and $x^2+c x+d$, then $\frac{b-d}{c-a}=$
40. The roots of the equation $x^3-14 x^2+56 x-64=0$ are in
41. The number of all four digit numbers that can be formed with the digits $0,1,2,3,4,5$ when the repetition of the digits 42. The number of rational terms in the binomial expansion $(\sqrt[4]{5}+\sqrt[5]{4})^{100}$ is
43. $$
\frac{\left(1+\tan 32^{\circ}\right)}{\left(1-\tan 48^{\circ}\right)}=
$$
44. In a $\triangle A B C$, if $r_1=2 r_2=3 r_3$, then $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}=$
45. The position vectors of the point $A, B$ are $\mathbf{a}, \mathbf{b}$ respectively. If the position vector of the point 46. If $|\mathbf{a}|=1,|\mathbf{b}|=2,|\mathbf{a}-\mathbf{b}|^2+|\mathbf{a}+2 \mathbf{b}|^2=20$, then $(a, b)=$
47. In a non-leap year, the probability of getting 53 Sundays or 53 Tuesdays or 53 Thursdays is
48. If each of the points $(a, 4),(-2, b)$ lies on the line joining the points $(2,-1)$ and $(5,-3)$, then the point $(a, b) 49. If $C(\alpha, \beta)(a 50. The equations of the tangents to the circle $x^2+y^2=4$ drawn from the point $(4,0)$ are
51. The equation of the parabola with $x+2 y=1$ as directrix and $(1,0)$ as focus is
52. If an ellipse with foci at $(3,3)$ and $(-4,4)$ is passing through the origin, then the eccentricity of that ellipse is
53. If $a, b, c$ and $k$ are non-zero real numbers and $\lim \limits_{x \rightarrow \infty} x\left(a^{1 / x}+b^{1 / x}+c^{1 54. If $\tan y=\cot \left(\frac{\pi}{4}-x\right)$, then $\frac{d y}{d x}=$
55. If $x=3 \sqrt{2} \cos ^3 \theta$ and $y=4 \tan ^2 \theta$, then $\left(\frac{d y}{d x}\right)_{\theta=\pi / 4}=$
56. If $\int \frac{x^2\left(\sec ^2 x+\tan x\right)}{(x \tan x+1)^2} d x=\frac{-x^2}{x \tan x+1}+f(x)+C$, then
$$
f(x)=
$$
57. $$
\int_0^{\pi / 2} \frac{\sin ^2 x}{\sin x+\cos x} d x=
$$
58. If $m$ and $n$ are respectively the order and degree of the differential equation of the family of parabolas with origin 59. If $f(x)=-|x|$, then $($ fofof $)(x)+($ fofof $)(-x)=$
60. $P$ is a $3 \times 3$ square matrix and $\operatorname{Tr}(P) \neq 0$. If $\operatorname{Tr}\left(P-P^I\right)+$ $\opera 61. If $\alpha$ and $\beta$ are non-zero integers and $z=(\alpha+i \beta)(2+7 i)$ is a purely imaginary number, then minimum 62. The sum of the roots of the equation $e^{4 t}-10 e^{3 t}+29 e^{2 t}-20 e^t+4=0$ is
63. The number of four digit numbers that can be formed using the digits $1,2,3,4,5,6$ and 7 which are divisible by 4 , when 64. The coefficient of $x^{50}$ in the expansion of $(1+x)^{101}\left(1-x+x^2\right)^{100}$ is
65. $$
\sin \alpha+\cos \alpha=m \Rightarrow \sin ^6 \alpha+\cos ^6 \alpha=
$$
66. 7. If $\int \sin (101 x)(\sin x)^{99} d x$ $=\frac{\sin (100 x)(\sin x)^\lambda}{\mu}+C$ then, $\frac{\lambda}{\mu}=$
67. If $A$ and $B$ are two events in a random experiment such that $P(A)+P(B)=2 P(A \cap B)$, then
68. The image of every point lying on the curve $x^2+y^2=1$ in the line $x+y=1$ satisfies the equation
69. If the inverse of $P(-3,5)$ with respect to a circle is $(1,3)$ then polar of $P$ with respect to that circle is
70. The derivative of $\frac{1-x^2}{1+x^2}$ with respect to $\frac{2 x}{1+x^2}$ at $x=2$ is
71. If the function $f(x)=\frac{x}{5}+\frac{5}{x},(x \neq 0)$ attains its relative maximum value at $x=\alpha$, then $\sqrt{ 72. If $\int e^x\left(\sin ^2 2 x-8 \cos 4 x\right) d x=e^x f(x)+C$, then $f\left(\frac{\pi}{4}\right)=$
73. [.] is the greatest integer function, then
$$ \int_0^{2 \pi}[|\sin x|+|\cos x|] d x= $$ 74. The general solution of $\frac{d y}{d x}+y f^{\prime}(x)-f(x) f^{\prime}(x)=0$, $y \neq f(x)$ is
75. If the system of equations
$x+k y+3 z=-2$,
$4 x+3 y+k z=14,$
$2 x+y+2 z=3$ can be solved by matrix inversion method, 76. If the slope of the tangent drawn to the curve $y=e^{a+b x^2}$ at the point $P(1,1)$ is -2 , then the value of $2 a-3 b$ 77. If the tangent drawn at the point $P$ on the circle $x^2+y^2+6 x+6 y=2$ meets the straight line $5 x-2 y+6=0$ at a point 78. If $n$ is a positive integer greater than 1 and $I_n=\int \frac{\sin n x}{\sin x} d x$, then $I_{n+1}-I_{n-1}=$
79. If $f$ is defined on $R$ such that $f(x) f(-x)=9$, then
$$
\int_{-23}^{23} \frac{d x}{3+f(x)}=
$$
Physics
1. If $F_1, F_2$ and $F_3$ are the relative strengths of the gravitational, the weak nuclear and the electromagnetic forces 2. Which of the following pairs has same dimensions?
3. The relation between time $t$ and distance $x$ of a particle is $t=a x^2+b x$, where $a$ and $b$ are constants. If $v$ i 4. A bomb is dropped on an enemy post on the ground by an aeroplane flying horizontally with a velocity of $60 \mathrm{kmh} 5. The angular speed of a particle moving in a circular path is doubled. Then, the centripetal acceleration of the particle 6. Two bodies of masses of 1 g and 4 g are moving with equal kinetic energies. The ratio of the magnitudes of their linear 7. The displacement $s$ of a body of mass 3 kg under the action of a force is given by $s=\frac{t^3}{3}$, where $s$ is in m 8. A system consists of two particles of masses $m_1$ and $m_2$. If the particle of mass $m_1$ is moved towards the centre 9. If the radius of the earth becomes $x$ times its present value, the new period of rotation in hours is 10. For a particle executing simple harmonic motion, the kinetic energy of the particle at a distance of 4 cm from the mean 11. A wire of length 40 cm is stretched by 0.1 cm . The strain on the wire is 12. A straw of circular cross-section of radius $R$ and negligible thickness is dipped vertically into a liquid of surface t 13. A solid metal sphere released in a vertical liquid column has attained terminal velocity in the downward direction. The 14. Two objects made of the same material have masses $m$ and $2 m$ and are at temperatures $2 T$ and $T$ respectively. When 15. On a new temperature scale, the melting point of ice is $20^{\circ} \mathrm{X}$ and the boiling point of water is $110^{ 16. The percentage of heat supplied to a diatomic ideal gas that is converted into work in an isobaric process is
17. Ratio of translational degrees of freedom to rotational degrees of freedom of a polyatomic linear gas molecule is
18. A ring has a mass $M$ and radius $R$. The distance of the point on its geometric axis from its centre at which the gravi 19. A heavy uniform rope is suspended vertically from a ceiling and is in equilibrium. A pulse is generated at the bottom en 20. A wave is given by the equation $y=(0.02) \sin (\pi x-8 \pi /$ then the velocity of the wave is $(y$ and $x$ are in metr 21. An empty tank has concave murror as its bottom. When sunlight falls normally on the mirror, it is focussed $\mathrm{a}_2 22. When Young's double slit experiment is performed in air, the $Y$-coordinates of central maxima and 10 th maxima are 2 cm 23. A clock dial has point charges $-q,-2 q,-3 q, \ldots \ldots \ldots,-12 q$ at the positions of the corresponding numbers 24. The electric potential at a place is varying as $V=\frac{1}{2}\left(y^2-4 x\right) \mathrm{V}$. Then, the electric field 25. When a potentiometer is connected between the points $A$ and $B$ as shown in the circuit, balance point is obtained at 6 26. In the given part of a circuit, the potential at point $B$ is zero. Then, the potentials at $A$ and $C$ respectively, ar 27. A contjucting wire $P Q$ carries a current 10 A as shown in the figure. ft is placed in a uniform magnetic field 5 T whi 28. A long straight wire carries a current of 18 A . The magnitude of the magnetic field at a point 12 cm from it is
29. A bar magnet has coercivity $4 \times 10^3 \mathrm{Am}^{-1}$. It is placed inside a solenoid of 12 cm length and 60 turn 30. When a current $i$ through a solenoid is increasing at a constant rate, then the induced current is
31. In a pair of adjacent coils, if the current in one coil changes from 10 A to 2 A in a time 0.2 s , an emf of 120 V is in 32. The power factor of an AC circuit containing peak current 2 A and peak voltage 1 V is $1 / 2$, then the angle between vo 33. If a plane electromagnetic wave has electric field oscillations of frequency 3 GHz , then the wavelength of the wave is 34. The de-Broglie wavelength of an electron accelerated between two plates having a potential difference of 900 V is nearly 35. If an electron is moving in the 4th orbit of the hydrogen atom, then the angular momentum of the electron in SI unit is
36. The energy equivalent to a mass of 1 kg is
37. If $S$ is the surface area of a nucleus of mass number $A$, then
38. In a transistor, the base current is $10 \mu \mathrm{~A}$ and the emitter current is 1 mA , then the collector current i 39. If the output of a NAND gate is given as input to a NOT gate, the resultant gate is
40. A message signal of frequency 10 kHz is used to modulate a carrier wave of frequency 6 MHz , then the side band frequenc
1
TS EAMCET 2023 (Online) 12th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\tan y=\cot \left(\frac{\pi}{4}-x\right)$, then $\frac{d y}{d x}=$
A
$\frac{\operatorname{cosec}^2\left(\frac{\pi}{4}-x\right)}{1+\cot ^2\left(\frac{\pi}{4}+x\right)}$
B
$\frac{-\operatorname{cosec}^2\left(\frac{\pi}{4}-x\right)}{\sec ^2 y}$
C
$\frac{\operatorname{cosec}^2\left(\frac{\pi}{4}-x\right)}{1+\tan ^2\left(\frac{\pi}{4}+x\right)}$
D
$\frac{\sec ^2\left(\frac{\pi}{4}+x\right)}{1+\tan ^2\left(\frac{\pi}{4}+x\right)}$
2
TS EAMCET 2023 (Online) 12th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $x=3 \sqrt{2} \cos ^3 \theta$ and $y=4 \tan ^2 \theta$, then $\left(\frac{d y}{d x}\right)_{\theta=\pi / 4}=$
A
$\frac{32 \sqrt{2}}{9}$
B
$\frac{16}{9}$
C
$-\frac{16}{9}$
D
$-\frac{32}{9}$
3
TS EAMCET 2023 (Online) 12th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\int \frac{x^2\left(\sec ^2 x+\tan x\right)}{(x \tan x+1)^2} d x=\frac{-x^2}{x \tan x+1}+f(x)+C$, then
$$
f(x)=
$$
A
$\log |x \sin x+\cos x|+C$
B
$\log |x \cos x+\sin x|+C$
C
$2 \log |x \sin x+\cos x|+C$
D
$2 \log |x \cos x+\sin x|+C$
4
TS EAMCET 2023 (Online) 12th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$$
\int_0^{\pi / 2} \frac{\sin ^2 x}{\sin x+\cos x} d x=
$$
A
$\sqrt{2} \log (\sqrt{2}+1)$
B
$\frac{1}{\sqrt{2}} \log (\sqrt{2}+1)$
C
$\log (\sqrt{2}+1)$
D
$\frac{1}{\sqrt{2}} \log (\sqrt{2}-1)$
Paper analysis
Total Questions
Chemistry
40
Mathematics
79
Physics
40
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