Chemistry
1. The wavelength of second line of Balmer series of hydrogen atom is $\lambda \mathrm{nm}$. What is the wavelength of firs 2. Consider the following.
I. The electron spin quantum number describes the orientation of the spin of the nucleus with re 3. In which of the following options, the elements are correctly arranged with respect to their negative electron gain enth 4. Identify the option in which the molecules are arranged in the correct order of their dipole moments 5. The bond order of $\mathrm{O}_2^{+}$is $x$. The bond orders of $\mathrm{O}_2^{-}$and $\mathrm{O}_2^{2+}$ are respectivel 6. Certain volume of oxygen gas diffuses through a porous pot in 20 seconds. Same volume of another gas, $X$ diffuses in $Y 7. Which of the following is only a redox reaction but not a disproportionation reaction? 8. The enthalpies of formation of gaseous $\mathrm{N}_2 \mathrm{O}$ and NO at 298 K are 82.0 and $90.0 \mathrm{~kJ} \mathrm 9. At 780 K and 10 atmosphere pressure the equilibrium constant for the reaction $2 A(g) \rightleftharpoons B(g)+C(g)$ is 3 10. The chemical name of calgon is 11. Which of the following set of metals have strong tendency to form super oxides? 12. Identify the correct statements with respect to compounds of beryllium.
I. Beryllium oxide is amphoteric in nature.
II. 13. In group 13 of the long form of periodic table an element $X$ has a boiling point of $T_2(\mathrm{~K})$ and melting poin 14. The dioxides and monoxides of elements $X$ and $Y$ are amphoteric in nature. $X$ and $Y$ are respectively 15. $$ \text { Identify ' } Z \text { ' in the following reaction sequence } $$
16. What is the major product ' $C$ ' in the following sequence of reactions?
17. $$ \text { The IUPAC name of the following compound is } $$
18. $$ \text { Consider the following three resonance structures } $$
The correct order of their stabilities is 19. Identify the crystal system in which primitive unit cell has edge lengths $a=b=200 \mathrm{pm}$ and $c=300 \mathrm{pm}$ 20. At 300 K , the osmotic pressure of a decinormal solution of sodium chloride is 4.82 atm . The degree of dissociation of 21. At 300 K , the conductivity of $0.01 \mathrm{~mol} \mathrm{dm}^{-3}$ aqueous solution of acetic acid is $19.5 \times 10^ 22. The graph obtained between $\ln k$ ( $k=$ rate constant) on $y$-axis and $1 / T$ on $x$-axis is a straight line. The slo 23. Consider the following about the tyndall effect.
(I) It is used to distinguish between a true and colloidal solution.
(I 24. $$ \text { Match the following. } $$$$ \begin{array}{llll} \hline & \begin{array}{c} \text { List-I } \\ \text { (Refini 25. Assertion (A) : In group 15 elements nitrogen does not form pentahalides.
Reason (R) : Nitrogen can exhibit +5 oxidation 26. In which of the following options, molecules are correctly arranged with respect to their bond angles. 27. Which of the following reaction represents Deacon's method? 28. The number of lone pair of electrons present in the valence shell of xenon $(\mathrm{Z}=54)$ in $\mathrm{XeOF}_4, \mathr 29. The order of melting points of $\mathrm{Cr}, \mathrm{Mo}$ and W is 30. Identify the incorrect match from the following. 31. $$ \text { Match the following } $$
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;borde 32. The functional group present in asparagine, a non-essential amino acid, are 33. The medicine used in controlling depression and hypertension is 34. Which of the following reaction represents swarts reaction? 35. Which of the following compound has no reaction with sodium metal? 36. Which of the following represents Gatterman-Koch reaction? 37. The major products of Reimer-Tiemann reaction and Kolbe's reaction are respectively 38.
In the reaction sequence, conversion of $B$ to $C$ is known as
39. What is the major product ' $R$ ' in the following reaction sequence? 40. $$ \text { Identify what is } Y \text { in the following reaction sequence? } $$
Mathematics
1. The domain of the function $f(x)=\sin ^{-1}\left(\log _2\left(\frac{x^2}{2}\right)\right)$ is
2. The range of the function $f(x)=-\sqrt{-x^2-6 x-5}$ is
3. If $f: R \rightarrow R$ is defined by $f(x)=2 x+\sin x, x \in R$, then $f$ is 4. $$ \left|\begin{array}{ccc} \sqrt{3} & 2 \sqrt{5} & \sqrt{5} \\ \sqrt{15} & 5 & \sqrt{10} \\ 3 & \sqrt{15} & 5 \end{arra 5. If $A$ is a non-singular matrix such that $(A-2 I)$ $(A-3 I)=0$, then $\frac{1}{5} A+\frac{6}{5} A^{-1}=$ 6. Let $A$ be a matrix such that $A B$ is a scalar matrix, where $B=\left[\begin{array}{ll}1 & 2 \\ 0 & 3\end{array}\right] 7. If $A$ is a symmetric matrix with real entries, then 8. $\operatorname{Arg}\left(\sin \frac{6 \pi}{5}+i\left(1+\cos \frac{6 \pi}{5}\right)\right)=$ 9. $$ \text { If } x+i y=\sqrt{\frac{3+i}{1+3 i}}, \text { then }\left(x^2+y^2\right)^2= $$ 10. If the imaginary part of $\frac{2 z+1}{i z+1}$ is -2, then the locus of the point representing $z$ in the Argand plane i 11. $$ \begin{aligned} &\text { If } \omega \neq 1 \text { is a cube root of unity, then }\\ &\left|\begin{array}{ccc} \omeg 12. If $i=\sqrt{-1}$, then $(1+i)^{10}+(1-i)^{10}=$ 13. The set of all values of $x$ which satisfy both the inequations $x^2-1 \leq 0$ and $x^2-x-2 \geq 0$ simultaneously is 14. For all real values of $x$, the minimum value of $\frac{1-x+\lambda^2}{1+x+x^2}$ is 15. The quadratic equations $x^2-6 x+a=0$ and $x^2-c x+6=0$ have one root in common. If the other roots of the first and sec 16. If $\alpha$ and $\beta$ are the roots of the equation $x^2+2 x+2=0$, then $\alpha^{15}+\beta^{15}=$ 17. If the equation whose roots are $P$ times the roots of the equation $x^4-2 a x^3+4 b x^2+8 a x+16=0$ is a reciprocal equ 18. The total number of all those 3-digit numbers in which the sum of all the digits in each of them is 10 , is
19. All the letters of the word 'MOTHER' are written in all possible ways and the strings of letters (with or without meanin 20. A student is allowed to select at most $n$ books from a collection of ( $2 n+1$ ) books. If the total number of ways in 21. The number of integral terms in the expansion of $(\sqrt{3}+\sqrt[8]{5})^{256}$ is 22. The expansion of $\left(1+x+x^2\right)^{-3 / 2}$ in powers of $x$ is valid, if 23. If $(1+x)^n=c_0+c_1 x+c_2 x^2+\ldots \ldots+c_n x^n$ for $n \in N$, then $c_0+\frac{c_1}{2}+\frac{c_2}{3}+\ldots \ldots+ 24. If $\frac{x+1}{\left(x^2+1\right)(x-1)^2}=\frac{A x+B}{x^2+1}+\frac{C}{x-1}+\frac{D}{(x-1)^2}$, then $A+B+C+D=$ 25. $$ \text { If } \frac{2 \sin \theta}{1+\cos \theta+\sin \theta}=y, \text { then } \frac{1-\cos \theta+\sin \theta}{1+\si 26. If $\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{4 \pi}{7}=\frac{\sin \frac{8 \pi}{7}}{8 \sin \frac{\pi}{7}}$, the 27. If $f(\theta)=\cos ^3 \theta+\cos ^3\left(\frac{2 \pi}{3}+\theta\right)+\cos ^3\left(\theta-\frac{2 \pi}{3}\right)$, the 28. $$ \sinh (\log (3+\sqrt{8}))= $$ 29. $P Q R$ is an isosceles triangle with $P Q=P R$. If the radius of the circumcircle of $\triangle P Q R$ is equal to the 30. In $\triangle A B C$, if $\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos \cdot C}{c}$ and side $a=2$, then area of the $\t 31. If two vectors $\mathbf{a}$ and $\mathbf{b}$ which are perpendicular to each other are such that $|\mathbf{a}|=8$ and $| 32. Let $\mathbf{a}$ and $\mathbf{b}$ be non-collinear vectors. If the vectors $(\lambda-1) \mathbf{a}+2 \mathbf{b}$ and $3 33. If $M$ is the foot of the perpendicular drawn from $P($ -1,2,-1 ) to the plane passing through the point $A(3,-2,1)$ and 34. Vectors $\mathbf{p}=a \hat{\mathbf{i}}+b \hat{\mathbf{j}}+c \hat{\mathbf{k}}, \mathbf{q}=d \hat{\mathbf{i}}+3 \hat{\math 35. $\mathbf{b}$ and $\mathbf{c}$ are non-collinear vectors and $(\mathbf{c} \cdot \mathbf{c}) \mathbf{a}=\mathbf{c}$. If $( 36.
Assertion (A) The variance of the first $n$ odd natural numbers is $\frac{n^2-1}{3}$.
Reason (R) The sum of the first 37. If $A$ and $B$ are two events of a random experiment such that $P(A \cup B)=P(A \cap B)$, then which one amongst the fol 38. If a group of six students including two particular students $A$ and $B$ stand in a row, then the probability of getting 39. $A, B, C, D$ cut a pack of 52 well shuffled playing cards successively in the same order. If the person who cuts a spade 40. Two bad eggs are mixed accidentally with 10 good ones. If three eggs are drawn at random from this lot in succession wit 41. The locus of the mid-points of the intercepted portion of the tangents by the coordinate axes, which are drawn to the el 42. A line $L$ has intercepts $a$ and $b$ on the coordinate axes. When the coordinate axes are rotated through an angle $\al 43. Two lines $L_1$ and $L_2$ passing through the point $P(1,2)$ cut the line $x+y=4$ at a distance of $\frac{\sqrt{6}}{3}$ 44. A pair of straight lines drawn though the origin forms. an isosceles triangle right angled at the origin with the line $ 45. The equation of the straight line passing through the point $(3,2)$ and inclined at an angle of $60^{\circ}$ with the li 46. An equilateral triangle is constructed between the lines $\sqrt{3} x+y-6=0$ and $\sqrt{3} x+y+9=0$ with base on one line 47. If $\theta$ is the acute angle between the lines joining the origin to the points of intersection of the curve $x^2+x y+ 48. If a circle passing through $(1,-2)$ has $x-y=2$ and $2 x+3 y=14$ as its diameters, then the radius of the circle is 49. The equation of the circle whose diameter is the common chord of the circles $x^2+y^2+2 x+3 y+1=0$ and $x^2+y^2+4 x+3 y+ 50. The number of common tangents to the circles $x^2+y^2-2 x-6 y+9=0$ and $x^2+y^2+6 x-2 y+1=0$ is
51. The pole of the straight line $9 x+y-28=0$ with respect to the circle $2 x^2+2 y^2-3 x+5 y-7=0$ is 52. The equation of the line perpendicular to the radical axis of two circles $x^2+y^2-5 x+6 y+12=0$, $x^2+y^2+6 x-4 y-14=0$ 53. If the angle between the circles
$$ x^2+y^2-2 x-4 y+c=0 \text { and } x^2+y^2-4 x-2 y+4=0 $$
is $60^{\circ}$, then $c=$ 54. The normal at a point on the parabola $y^2=4 x$ passes through $(5,0)$. If there are two more normals to this parabola p 55. The equations of common tangents to the parabola $y^2=16 x$ and the circle $x^2+y^2=8$ are 56. The product of the lengths of the perpendiculars drawn from the two foci of the ellipse $\frac{x^2}{9}+\frac{y^2}{25}=1$ 57. Tangents are drawn to the ellipse $\frac{x^2}{9}+\frac{y^2}{5}=1$ at all the ends of its latus recta. The area of the qu 58. $P(a \sec \theta, b \tan \theta)$ and $Q(a \sec \phi, b \tan \phi)$ are two points on the hyperbola $\frac{x^2}{a^2}-\fr 59. If $A=(1,-1,2), B=(3,4,-2), C=(0,3,2)$ and $D=(3$, $5,6)$, then the angle between the lines $\mathbf{A B}$ and $\mathbf{ 60. Consider the following statements:
Assertion (A) : The direction ratios of a line $L_1$ are 2,5, 7 and the direction rat 61. A line $L$ is parallel to both the planes $2 x+3 y+z=1$ and $x+3 y+2 z=2$. If line $L$ makes an angle $\alpha$ with the 62. $$ \lim\limits_{x \rightarrow 1}(1-x) \tan \left(\frac{\pi}{2} x\right)= $$ 63. If $f(9)=9$ and $f^{\prime}(9)=4$, then $\lim\limits_{x \rightarrow 9} \frac{\sqrt{f(x)}-3}{\sqrt{x}-3}=$ 64. If $\sec \left(\log _2 y^2\right)=\operatorname{cosec}\left(\log _2 x^2\right)$, then $\frac{d y}{d x}=$ 65. If $e^x=y+\sqrt{y^2-1}$, then $\frac{d y}{d x}=$ 66. If $x=\log p$ and $y=\frac{1}{p}$, then $\frac{d y}{d x}=$ 67. Electric current $(I)$ is measured by galvanometer, the current being proportional to the tangent of the angle ( $\theta 68. If the equation of a tangent drawn to the curve $y=\cos (x+y),-1 \leq x \leq 1+\pi$ is $x+2 y=k$, then $k=$ 69. $f: R \rightarrow R$ is a function defined by $f(x)=\frac{1}{e^x+2 e^{-x}}$
Assertion (A) : $f(c)=\frac{1}{3}$ for some 70. $$
\text { Match the following items from List I into List II }
$$
List-I
List-II
1.
∫
71. If $\int \frac{x}{(a+x)^5} d x=\frac{1}{k(a+x)^4}(f(x))+C$, then $\frac{f(-a)}{a k}=$
72. $$ \int_0^{\pi / 4} \frac{\sec x}{1+2 \sin ^2 x} d x= $$ 73. If $\int x^4(\log x)^3 d x=x^5\left[A(\log x)^3\right]$ $\left.+B(\log x)^2+C \log x+D\right]+k$, then $A+B+C+5 D=$ 74. $$ \lim\limits_{n \rightarrow \infty}\left[\frac{1}{n^2} \sec ^2 \frac{1}{n^2}+\frac{2}{n^2} \sec ^2 \frac{4}{n^2}+\ldot 75. $$ \int\limits_2^5 \sqrt{\frac{5-x}{x-2}} d x= $$ 76. $$ \int\limits_0^{\frac{\pi}{2}} \sin ^6 x \cos ^4 x d x= $$ 77. The area (in sq units) bounded by the curve $y=2 x-x^2$ and the line $y=-x$ is 78. The degree and order of the differential equation of the family of parabolas whose axis is the $X$-axis, are respectivel 79. The general solution of the differential equation $\left(x \sin \frac{y}{x}\right) d y=\left(y \sin \frac{y}{x}-x\right) 80. The general solution of the differential equation $\left(2 x-10 y^3\right) d y+y d x=0, y \neq 0$ is
Physics
1. If $F_1$ and $F_2$ are the relative strengths of the gravitational and weak nuclear forces respectively, then $F_2 / F_1 2. The number of significant figures in $3.78 \times 10^{22} \mathrm{~kg}$ is 3. The ratio of the displacements of a freely falling body during first, second and third seconds of its motion is 4. A person walks in such a way that he covers equal distance in each step. The person takes 2 steps forwards towards east, 5. A person initially at rest, starts walking towards east without slipping or skidding. What is the type of friction actin 6. While a person climbs stairs, the gravitational potential energy of the person increases. The source of this energy is 7. Moon revolves around the earth in an orbit of radius $R$ with time period of revolution $T$. It also rotates about its o 8. The spinning of the Diwali cracker 'ground chakkar' involves the concept of 9. A clock is designed based on the oscillation of a spring-block system suspended vertically in the absence of air-resista 10. A body of mass 6 kg is moving with a uniform velocity $4 \mathrm{~ms}^{-1}$. Its velocity changes to $6 \mathrm{~ms}^{-1 11. The ratio of the radii of two planets is $r$ and the ratio of accelerations due to gravity on the planets is $x$. Then t 12. Two wires $A$ and $B$ of same length, same radius and same Young's modulus are heated to same range of temperatures. If 13. If the work done in blowing a soap bubble of radius $R$ is $W$, then the work done in blowing the soap bubble of radius 14. Three identical vessels are filled with three liquids ${ }_{A, B}$ and $C$ with equal masses but having densities $\rho_ 15. Two rod of same area of cross-section have lengths $L$ and $2 L$ and coefficients of linear expansions $2 \alpha$ and $a 16. For a given mass of a gas at constant temperature, the volume and the pressure are $V$ and $p$ respectively. Then the sl 17. An ideal gas at $127^{\circ} \mathrm{C}$ is compressed suddenly to $8 / 27 \mathrm{}$of its initial volume. If $\gamma=5 18. An insulating cylinder contains 4 moles of an ideal diatomic gas. When a heat $Q$ is supplied to it, 2 moles of the gas 19. A rod of length $L$ and negligible mass is suspended by two identical strings $A B$ and $C D$ as shown in the figure A m 20. An observer moves towards a stationary source of sound with a speed $\frac{1}{5}$ th that of sound. The frequency of ${ 21. The angles of incidence and emergence of a light ray passing through a prism of angle $A$ are $i$ and $e$ respectively. 22. If the slit width is 2 mm and wavelength of light used is $4000\mathop {\rm{A}}\limits^{\rm{o}}$, then Fresnel distance 23. The electric field and electric potential at a point due to a point charge are $500 \mathrm{NC}^{-1}$ and 30 V respectiv 24. If a capacitor of capacitance $100 \mu \mathrm{~F}$ is charged at a steady rate of $100 \mu \mathrm{C} \mathrm{s}^{-1}$, 25. A potentiometer balances at 44 cm when a cell of internal resistance $1 \Omega$ is in the secondary circuit. To obtains 26. Two wires made of the same material have lengths in the ratio $2: 3$ and radii in the ratio $8: 9$. If the same potentia 27. The magnetic field at a perpendicular distance of one metre from a wire carrying current of 1 A is 28. A circular coil of area $2 \mathrm{~cm}^2$ has 1000 turns. If the current through the coil is 1 A , then its magnetic mo 29. The magnetic susceptibility of ferromagnetic materials is 30. If the vertical component of earth's magnetic field is $0.5 \times 10^{-4} \mathrm{~T}$ at a point. When an aeroplane of 31. A boy is playing with the empty rim of a cycle wheel of radius 40 cm by rolling it along a horizontal road towards north 32. In an ideal step up transformer, if the input voltage and input power are $V_1$ and $R_1$ respectively and the output vo 33. The correct statement among the following is 34. The additional energy that should be given to an electron to reduce its de-Broglie wavelength from 1 nm to 0.5 nm is 35. The ratio of the energies of the electron in the hydrogen atom in the first and second excited states is
36. In the following nuclear reaction $X$ is
$$ { }_{13} \mathrm{Al}^{27}+{ }_2 \mathrm{He}^4 \longrightarrow{ }_0 n^1+X $$ 37. Nuclear fission and fusion can be explained on the basis of
38. If the ratio of electron and hole currents in a semiconductor is $7 / 4$ and the ratio of drift velocities of electrons 39. When a semiconductor is doped with donor impurity 40. The need for modulation is
1
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $\int x^4(\log x)^3 d x=x^5\left[A(\log x)^3\right]$ $\left.+B(\log x)^2+C \log x+D\right]+k$, then $A+B+C+5 D=$
A
$\frac{2}{25}$
B
$\frac{8}{25}$
C
$\frac{12}{125}$
D
$\frac{16}{125}$
2
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$$ \lim\limits_{n \rightarrow \infty}\left[\frac{1}{n^2} \sec ^2 \frac{1}{n^2}+\frac{2}{n^2} \sec ^2 \frac{4}{n^2}+\ldots \ldots+\frac{1}{n} \sec ^2 1\right]= $$
A
$\frac{1}{2} \sec (1)$
B
$\frac{1}{2} \operatorname{cosec}(1)$
C
$\tan (1)$
D
$\frac{1}{2} \tan (1)$
3
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$$ \int\limits_2^5 \sqrt{\frac{5-x}{x-2}} d x= $$
A
$\pi$
B
$\frac{\pi}{2}$
C
$\frac{3 \pi}{2}$
D
$\frac{\pi}{4}$
4
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$$ \int\limits_0^{\frac{\pi}{2}} \sin ^6 x \cos ^4 x d x= $$
A
$\frac{\pi}{256}$
B
$\frac{\pi}{512}$
C
$\frac{3 \pi}{512}$
D
$\frac{5 \pi}{512}$
Paper analysis
Total Questions
Chemistry
40
Mathematics
80
Physics
40
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