Chemistry
1. The kinetic energy of electrons emitted, when radiation of frequency $1.0 \times 10^{15} \mathrm{~Hz}$ hits a metal, is 2. In which of the following species, the ratio of $s$-electrons to $p$-electrons is same? 3. Identify the pair of elements in which the difference in atomic radii is maximum 4. Match the following.
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.tg td{border-color:black;border-style:solid;bor 5. Identify the pair in which difference in bond order value is maximum. 6. The pair of molecules/ions with same geometry but central atoms in them are in different states of hybridisation is 7. If the density of a mixture of nitrogen and oxygen gases at 400 K and l atm pressure is $0.920 \mathrm{gL}^{-1}$, what i 8. The incorrect rule regarding the determination of significant figures is 9. At 61 K , one mole of an ideal gas of 1.0 L volume expands isothermally and reversibly to a final volume of 10.0 L . Wha 10. At $T(\mathrm{~K}), K_C$ for the dissociation of $\mathrm{PCl}_5$ is $2 \times 10^{-2} \mathrm{~mol} \mathrm{~L}^{-1}$. 11. The dihedral angles in gaseous and solid phases of $\mathrm{H}_2 \mathrm{O}_2$ molecule respectively are 12. Identify the compound which gives $\mathrm{CO}_2$ more readily on heating? 13. The major components of cement are 14. Consider the following reactions (not balanced).
$$ \begin{array}{r} \mathrm{BF}_3+\mathrm{NaH} \xrightarrow{450 \mathrm 15. Which of the following does not exist? 16. Methemoglobinemia is due to 17. The IUPAC name of the following compound is
18. The functional groups present in the product ' $X$ ' of the reaction given below are
19. Identify the major product $(P)$ in the following reaction sequence.
$$ \left(\mathrm{CH}_3\right)_3 \mathrm{CBr} \xrigh 20. What is the percentage of carbon in the product ' $X$ ' formed in the given reaction?
$+\mathrm{C}_2 \mathrm{H}_5 \math 21. Identify the correct statement about the crystal defects in solids. 22. Dry air contains $79 \% \mathrm{~N}_2$ and $21 \% \mathrm{O}_2$. At $T(\mathrm{~K})$, if Henry's law constants for $\mat 23. If the degree of dissociation of formic acid is $11.0 \%$, the molar conductivity of 0.02 M solution of it is
(Given, $\ 24. Consider the gaseous reaction,
$$
A_2+B_2 \longrightarrow 2 A B
$$
The following data was obtained for the above reactio 25. Adsorption of a gas a solid adsorbent follows. Freundlich adsorption isotherm. If $x$ is the mass of the gas adsorbed on 26. Consider the following reactions.
$$ X+\mathrm{O}_2 \rightarrow \mathrm{Cu}_2 \mathrm{O}+\mathrm{SO}_2, \mathrm{Cu}_2 \m 27. $Y$ in the given sequence of reactions is
$$ \begin{gathered} \mathrm{P}_4+x \mathrm{NaOH}+y \mathrm{H}_2 \mathrm{O} \xr 28. In contact process of manufacture of $\mathrm{H}_2 \mathrm{SO}_4$, the arsenic purifier used in the industrial plant con 29. $\mathrm{Pt}+3: 1$ mixture of $\left(\right.$ Conc. $\mathrm{HCl}+$ conc. $\left.\mathrm{HNO}_3\right) \rightarrow[\math 30. In which of the following, ions are correctly arranged in the increasing order of oxidising power? 31. Which of the following will have a spin only magnetic moment of 2.86 BM ? 32. The monomer which is present in both bakelite and melamine polymers is 33. Cellulose is a polysaccharide and is made of 34. Match the following.
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.tg td{border-color:black;border-style:solid;bor 35. Which of the following is an example of allylic halide? 36. Identify the correct statements about $Z$.
$$ \mathrm{C}_2 \mathrm{H}_5 \mathrm{NH}_2 \xrightarrow[0^{\circ} \mathrm{C}] 37. Assertion (A) : Aldehydes are more reactive than ketones towards nucleophilic addition reactions
Reason (R) : In aldehyd 38. Arrange the following in the correct order of their boiling points.
39. What is the major product $Z$ in the given reaction sequence?
$$ \left(\mathrm{CH}_3\right)_2 \mathrm{C}=\mathrm{O} \xri 40. Match the following.
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Mathematics
1. The domain of the real valued function $f(x)=\sqrt[3]{\frac{x-2}{2 x^2-7 x+5}}+\log \left(x^2-x-2\right)$ is 2. $f$ is a real valued function satisfying the relation $f\left(3 x+\frac{1}{2 x}\right)=9 x^2+\frac{1}{4 x^2}$. If $f\lef 3. $\frac{1}{3 \cdot 6}+\frac{1}{6 \cdot 9}+\frac{1}{9 \cdot 12}+\ldots \ldots .$. to 9 terms $=$ 4. If $\alpha, \beta$ and $\gamma$ are the roots of the equation $\left|\begin{array}{lll}x & 2 & 2 \\ 2 & x & 2 \\ 2 & 2 & 5. If $\mathrm{A}=\left[\begin{array}{lll}1 & 2 & 2 \\ 3 & 2 & 3 \\ 1 & 1 & 2\end{array}\right]$ and $\mathrm{A}^{-1}=\left 6. If $A X=D$ represents the system of linear equations $3 x-4 y+7 z+6=0,5 x+2 y-4 z+9=0$ and $8 x-6 y-z+5=0$, then 7. If $(x, y, z)=(\alpha, \beta, \gamma)$ is the unique solution of the system of simultaneous linear equations $3 x-4 y+z+ 8. If $\frac{(2-i) x+(1+i)}{2+i}+\frac{(1-2 i) y+(1-i)}{1+2 i}=1-2 i$, then $2 x+4 y=$ 9. If $z=1-\sqrt{3} i$, then $z^3-3 z^2+3 z=$ 10. The product of all the values of $(\sqrt{3}-i)^{\frac{2}{5}}$ is 11. The number of common roots among the 12 th and 30th roots of unity is 12. $\alpha$ is a root of the equation $\frac{x-1}{\sqrt{2 x^2-5 x+2}}=\frac{41}{60}$. If $-\frac{1}{2} 13. If $4+3 x-7 x^2$ attains its maximum value $M$ at $x=\alpha$ and $5 x^2-2 x+1$ attains its minimum value $m$ at $x=\beta 14. If $\alpha, \beta, \gamma$ are the roots of the equation $2 x^3-5 x^2+4 x-3=0$, then $\Sigma \alpha \beta(\alpha+\beta)= 15. $\alpha, \beta, \gamma, 2$ and $\varepsilon$ are the roots of the equation
$$ \begin{aligned} & \alpha, \beta, \gamma+4 16. Among the 4 -digit numbers that can be formed using the digits $1,2,3,4,5$ and 6 without repeating any digit, the number 17. If the number of circular permutations of 9 distinct things taken 5 at a time is $n_1$ and the number of linear permutat 18. The number of ways in which 4 different things can be distributed to 6 persons so that no person gets all the things is 19. If the coefficients of 3 consecutive terms in the expansion of $(1+x)^{23}$ are in arithmetic progression, then those te 20. The numerically greatest term in the expansion of $(3 x-16 y)^{15}$, when $x=\frac{2}{3}$ and $y=\frac{3}{2}$, is 21. If $\frac{3 x^4-2 x^2+1}{(x-2)^4}=A+\frac{B}{x-2}+\frac{C}{(x-2)^2}$ $+\frac{D}{(x-2)^3}+\frac{E}{(x-2)^4}$, then $2 A+3 22. The maximum value of the function $f(x)=3 \sin ^{12} x+4 \cos ^{16} x$ is 23. If $A+B+C=2 S$, then $\sin (S-A) \cos (S-B)-\sin (S-C) \cos S=$ 24. If $\cos x+\cos y=\frac{2}{3}$ and $\sin x-\sin y=\frac{3}{4}$, then $\sin (x-y)+\cos (x-y)=$ 25. The solution set of the equation $\cos ^2 2 x+\sin ^2 3 x=1$ i 26. If $2 \tan ^{-1} x=3 \sin ^{-1} x$ and $x \neq 0$, then $8 x^2+1=$ 27. Match the functions given in List I with their relevant characteristics from List II.
.tg {border-collapse:collapse;bo 28. In a $\triangle A B C$, if $\tan \frac{A}{2}: \tan \frac{B}{2}: \tan \frac{C}{2}=15: 10: 6$, then $\frac{a}{b-c}=$ 29. In a $\triangle A B C, \frac{a\left(r_1+r_2 r_3\right)}{r_1-r+r_2+r_3}=$ 30. $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are non-coplanar vectors. If the three points $\lambda a-2 b+c, 2 a+\lambda b-2 \ma 31. If $\hat{\mathbf{i}}+\hat{\mathbf{j}}, \hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{k}}+\hat{\mathbf{i}}, \hat{\mathb 32. If $\mathrm{a}, \mathrm{b}$ are two vectors such that $|\mathrm{a}|=3,|\mathrm{~b}|=4$, $|\mathbf{a}+\mathbf{b}|=\sqrt{3 33. $r$ is a vector perpendicular to the planet, determined by the vectors $2 \hat{\mathbf{i}}-\hat{\mathbf{j}}$ and $\hat{\ 34. $\mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \mathbf{k}, \quad \mathbf{c}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\m 35. The variance of the following continuous frequency distribution is
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36. Among the 5 married couples, if the names of 5 men are matched with the names of their wives randomly, then the probabil 37. If 3 dice are thrown, the probability of getting 10 as the sum of the three numbers that appeared on the top faces of th 38. Three similar urns $A, B, C$ contain 2 red and 3 white balls; 3 red and 2 white balls; 1 red and 4 white balls respectiv 39. If a random variable X has the following probability distribution, then the mean of $X$ is
$$
\begin{array}{c|c|c|c|c}
40. A A fair coin is tossed a fixed number of times. If the probability of getting 5 heads is equal to the probability of ge 41. If the ratio of the distances of a variable point $P$ from the point $(1,1)$ and the line $x-y+2=0$ is $1: \sqrt{2}$, th 42. If the origin is shifted to the point $\left(\frac{3}{2},-2\right)$ by the translation of axes, then the transformed equ 43. $L \equiv x \cos \alpha+y \sin \alpha-p=0$ represents a line perpendicular to the line $x+y+1=0$. If $p$ is positive, $\ 44. $(-2,-1),(2,5)$ are two vertices of a triangle and $\left(2, \frac{5}{3}\right)$ is its orthocenter. If $(m, n)$ is the 45. $L_1 \equiv 2 x+y-3=0$ and $L_2 \equiv a x+b y+c=0$ are two equal sides of an isosceles triangle. If $L_3 \equiv x+2 y+1 46. The slope of one of the pair of lines $2 x^2+h x y+6 y^2=0$ is thrice the slope of the other line, then $h=$ 47. If $P\left(\frac{\pi}{4}\right), Q\left(\frac{\pi}{3}\right)$ are two points on the circle $x^2+y^2-2 x-2 y-1=0$, then t 48. The power of a point $(2,0)$ with respect to a circle $S$ is -4 and the length of the tangent drawn from the point $(1,1 49. The pole of the line $x-5 y-7=0$ with respect to the circle $S \equiv x^2+y^2-2 x+4 y+1=0$ is $P(a, b)$. If $C$ is the c 50. The equation of the pair of transverse common tangents drawn to the circles $x^2+y^2+2 x+2 y+1=0$ and $x^2+y^2-2 x-2 y+1 51. If a circle passing through the point $(1,1)$ cuts the circles $x^2+y^2+4 x-5=0$ and $x^2+y^2-4 y+3=0$ orthogonally, the 52. Length of the common chord of the circles $x^2+y^2-6 x+5=0$ and $x^2+y^2+4 y-5=0$ is 53. $P$ and $Q$ are the extremities of a focal chord of the parabola $y^2=4 a x$. If $P=(9,9)$ and $Q=(p, q)$, then $p-q=$ 54. The number of normals that can be drawn through the point $(9,6)$ to the parabola $y^2=4 x$ is 55. The equations of the directrices of the elmpse $9 x^2+4 y^2-18 x-16 y-11=0$ are 56. $L_1^{\prime}$ is the end of a latus rectum of the ellipse $3x=2 \pm \frac{\sqrt{5}}{\sqrt{5}}$ $3 x^2+4 y^2=12$ which i 57. $(p, q)$ is the point of intersection of a latus rectum and an asymptote of the hyperbola $9 x^2-16 y^2=144$. If $p>0$ a 58. $A(3,2,-1), B(4,1,0), C(2,1,4)$ are the vertices of a $\triangle A B C$. If the bisector of $B A C$ ! intersects the sid 59. $(3,0,2)$ and $(0,2, k)$ are the direction ratios of two lines and $\theta$ is the angle between them. If $|\cos \theta| 60. A plane $(\pi)$ passing through the point $(1,2,-3)$ is perpendicular to the planes $x+y-z+4=0$ and $2 x-y+z+1=0$. If th 61. $\lim _{\theta \rightarrow \frac{\pi^{-}}{2}} \frac{8 \tan ^4 \theta+4 \tan ^2 \theta+5}{(3-2 \tan \theta)^4}=$ 62. Define $ f: R \rightarrow R $ by $ f(x)=\left\{\begin{array}{cl}\frac{1-\cos 4 x}{x^{2}}, & x 0\end{array}\right. $
The 63. If $y=\frac{\tan x \cos ^{-1} x}{\sqrt{1-x^2}}$, then the value of $\frac{d y}{d x}$, when $x=0$ is 64. If $y(\cos x)^{\sin x}=(\sin x)^{\sin x}$, then the value of $\frac{d y}{d x}$ at $x=\frac{\pi}{4}$ is 65. If $x=\cos 2 t+\log (\tan t)$ and $y=2 t+\cot 2 t$, then $\frac{d y}{d x}=$ 66. If $y=44 x^{45}+45 x^{-44}$, then $y^n=$ 67. The approximate value of $\sqrt[3]{730}$ obtained by the application of derivatives is 68. If $\theta$ is the acute angle between the curves $y^2=x$ and $x^2+y^2=2$, then $\tan \theta=$ 69. The vertical angle of a right circular cone is $60^{\circ}$. If water is being poured in to the cone at the rate of $\fr 70. A right circular cone is inscribed in a sphere of radius 3 units. If the volume of the cone is maximum, then semi-vertic 71. If $f(x)=k x^3-3 x^2-12 x+8$ is strictly decreasing for all $x \in R$, then 72. $\int e^{-2 x}\left(\tan 2 x-2 \sec ^2 2 x \tan 2 x\right) d x=$ 73. If $\int x^3 \sin 3 x d x=f(x) \cos 3 x+g(x) \sin 3 x+C$, then 27 $(f(x)+x g(x))=$ 74. $\int \frac{d x}{9 \cos ^2 2 x+16 \sin ^2 2 x}=$ 75. $\int \frac{2 \cos 3 x-3 \sin 3 x}{\cos 3 x+2 \sin 3 x} d x=$ 76. $ \int_{\frac{-3}{4}}^{\frac{\pi-6}{8}} \log (\sin (4 x+3)) d x= $ 77. $\int_0^{16} \frac{\sqrt{x}}{1+\sqrt{x}} d x=$ 78. $\int_0^{32 \pi} \sqrt{1-\cos 4 x} d x=$ 79. The general solution of the differential equation $(9 x-3 y+5) d y=(3 x-y+1) d x$ is 80. The general solution of the differential equation $\frac{d y}{d x}=\frac{2 y^2+1}{2 y^3-4 x y+y}$ is
Physics
1. The related effort to derive the properties of a bigger, more complex system from the properties and interactions of its 2. The error in the measurement of resistance, when $(10 \pm 05)$ A current passing through it produces a potential differe 3. A stone is thrown vertically up from the top end of a window of height 1.8 m with a velocity of $8 \mathrm{~ms}^{-1}$. T 4. A cannon placed on a cliff at a height of 375 m fires a cannon ball with a velocity of $100 \mathrm{~ms}^{-1}$ at an ang 5. A 20 ton truck is travelling along a curved path of radius 240 m . If the centre of gravity of the truck above the groun 6. A block of mass $m$ with an initial kinetic energy $E$ moves up an inclined plane of inclination $\theta$. If $\mu$ is t 7. A man of mass 80 kg goes to the market on a scooter of mass 100 kg with certain speed. On application of brakes, the sto 8. A thin uniform wire of mass $m$ and linear mass density $\rho$ is bent in the form of a circular loop. The moment of ine 9. Three particles $A, B$ and $C$ of masses $m, 2 m$ and $3 m$ are moving towards north, south and east respectively. If th 10. A particle of mass 4 mg is executing simple harmonic motion along $X$-axis with an angular frequency of $40 \mathrm{rad} 11. The ratio of the accelerations due to gravity at heights 1280 km and 3200 km above the surface of the earth is
(Radius o 12. If the length of a string is $P$ when the tension in it is 6 N and its length is $Q$ when the original length of the str 13. The excess pressure inside a soap bubble of radius 0.5 cm is balanced by the pressure due to an oil column of height 4 m 14. Water flows through a horizontal pipe of variable cross-section at the rate of $12 \pi$ litre per minute. The velocity o 15. When 54 g of ice at $-20^{\circ} \mathrm{C}$ is mixed with 25 g of steam at $100^{\circ} \mathrm{C}$, then the final mix 16. A solid sphere at a temperature $T \mathrm{~K}$ is cut in to two hemisphere. The ratio of energies radiated by one hemis 17. If $d Q, d U$ and $d W$ are heat energy absorbed, change in internal energy and external work done respectively by a dia 18. If the temperature of a gas increased from $27^{\circ} \mathrm{C}$ to $159^{\circ} \mathrm{C}$, the increase in the rms 19. A boy standing on a platform observes the frequency of a train horn as it passes by. The change in the frequency noticed 20. If three sources of sound of frequencies $(n-1), n$ and $(n+1)$ are vibrated together, the number of beats produced and 21. A small angled prism is made of a material of refractive index $\frac{3}{2}$. The ratio of the angles of minimum deviati 22. If you are using eye glasses of power 2 D, your near point is 23. The diameter of the objective of a telescope is 3.6 m . The limit of resolution of the telescope for a light of waveleng 24. Two point charges of magnitudes $-8 \mu \mathrm{C}$ and $+32 \mu \mathrm{C}$ are separated by a distance of 15 cm in air 25. If half of the space between the plates of a parallel plate capacitor is filled with a medium of dielectric constant 4 , 26. The potential difference between the ends of a straight conductor of length 20 cm is 16 V . If the drift speed of the el 27. The potential difference $V$ across the filament of the bulb shown in the given Wheatstone bridge varies as $V=i(2 i+1)$ 28. Two points $A$ and $B$ on the axis of a circular current loop are at distances of 4 cm and $3 \sqrt{3} \mathrm{~cm}$ fro 29. Two charged particles $A$ and $B$ of masses $m$ and $2 m$, charges $2 q$ and $3 q$ respectively moving with same velocit 30. If a bar magnet of moment $10^{-4} \mathrm{Am}^2$ is kept in a uniform magnetic field of $12 \times 10^{-3} \mathrm{~T}$ 31. A train with an axle of length 1.66 m is moving towards north with a speed of $90 \mathrm{kmh}^{-1}$. If the vertical co 32. The natural frequency of an $L-C$ circuit is 120 kHz . When the capacitor in the circuit is totally filled dielectric ma 33. A plane electromagnetic wave of electric and magnetic fields $E_0$ and $B_0$ respectively incidents on a surface. If the 34. If the de-Broglie wavelength of a neutron at a temperature of $77^{\circ} \mathrm{C}$ is $\lambda$, then the de-Broglie 35. The ratio of the wavelengths of radiation emitted when an electron in the hydrogen atom jumps from 4th orbit to 2 nd orb 36. The half lives of two radioactive material $A$ and $B$ are respectively $T$ and $2 T$. If the ratio of the initial masse 37. The energy released by the fission of one uranium nucleus is 200 MeV . The number of fissions per second required to pro 38. A zener diode of zener voltage 30 V is connected in circuit as shown in the figure. The maximum current through the zene 39. Two logic gates are connected as shown in the figure. If the inputs are $A=1$ and $B=0$, then the values of $Y_1$ and $Y 40. A message signal of peak voltage 12 V is used to amplitude modulate a carrier signal of frequency 1.2 MHz . The amplitud
1
TG EAPCET 2024 (Online) 9th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $\cos x+\cos y=\frac{2}{3}$ and $\sin x-\sin y=\frac{3}{4}$, then $\sin (x-y)+\cos (x-y)=$
A
$\frac{161}{145}$
B
$\frac{127}{145}$
C
$\frac{1}{2}$
D
$\frac{8}{9}$
2
TG EAPCET 2024 (Online) 9th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
The solution set of the equation $\cos ^2 2 x+\sin ^2 3 x=1$ i
A
$\left\{x \left\lvert\, x=n \pi+\frac{\pi}{2}\right., n \in Z\right\}$
B
$\left\{x \left\lvert\, x=2 n \pi \pm \frac{\pi}{4}\right., n \in Z\right\}$
C
$\left\{x \left\lvert\, x=\frac{n \pi}{5}\right., n \in Z\right\}$
D
$\left\{x \left\lvert\, x=n \pi+(-1)^n \frac{n \pi}{6}\right., n \in Z\right\}$
3
TG EAPCET 2024 (Online) 9th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $2 \tan ^{-1} x=3 \sin ^{-1} x$ and $x \neq 0$, then $8 x^2+1=$
A
13
B
5
C
$\sqrt{7}$
D
$\sqrt{17}$
4
TG EAPCET 2024 (Online) 9th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
Match the functions given in List I with their relevant characteristics from List II.
The correct answer is
| List I | List II |
| (A) sinh x | (I) Domains is (-1,1), even function |
| (B) sec hx | (II) Domain is [1,∞), neither even nor odd function |
| (C) tan hx | (III) Even function |
| (D) cosec h⁻¹x | (IV) Range is R, odd function |
| (V) Range is (-1,1), odd function |
A
A-II, B-III, C-IV, D-V
B
A-V, B-I, C-II, D-III
C
A-IV, B-II, C-I, D-V
D
A-IV, B-III, C-V, D-II
Paper analysis
Total Questions
Chemistry
40
Mathematics
80
Physics
40