Chemistry
1. The energy of third orbit of $\mathrm{Li}^{2+}$ ion (in J ) is
2. The number of $d$ electrons in Fe is equal to which of the following?
(i) Total number of ' $s$ ' electrons of Mg .
(ii) 3. The correct order of atomic radii of given element is
4. Which of the following orders are correct regarding their covalent character?
(i) $\mathrm{KF}
(ii) $\mathrm{LiF}
(iii) 5. $$ \text { Observe the following sets. } $$
$$ \begin{array}{lll} \hline \text { Order } & \text { Property } \\ \hline 6. The RMS velocity ( $u_{\mathrm{rms}}$ ) of one mole of an ideal gas was measured at different temperatures and the follo 7. Two statements are given below.
Statement I : Viscosity of liquid decreases with increase in temperature.
Statement II : 8. 0.1 mole of potassium permanganate was heated at $300^{\circ} \mathrm{C}$. What is weight (ing) of the residue?
$$
(\m 9. Identify the correct statements from the following.
I. $\Delta_r G$ is zero for $A \rightleftharpoons B$ reaction.
II. T 10. Observe the following reactions.
$$ \begin{array}{ll} A B(g)+25 \mathrm{H}_2 \mathrm{O}(l) \longrightarrow\left(25 \math 11. $K_C$ for the reaction,
$A_2(g) \stackrel{T(\mathrm{~K})}{\rightleftharpoons} B_2(\mathrm{~g})$
is 39.0. In a closed o 12. At $T(\mathrm{~K})$, the solubility product of $A X$ is $10^{-10}$. What is the molar solubility of $A X$ in 0.1 MHX ?
13. The equation that represents 'coal gasification' is
14. As per standard reduction potential values, which is the strongest reducing agent among the given elements?
15. A Lewis acid ' $X$ ' reacts with $\mathrm{LiAlH}_4$ in ether medium to give a highly toxic gas. ${ }^{\prime} Y^{\prime} 16. The method for preparation of water gas is
17. The BOD values for pure water and highly polluted water are respectively.
18. A mixture of ethyl iodide and $n$-propyl iodide is subjected to Wurtz reaction. The hydrocarbon which will not be forme 19. Which of the following alkenes does not undergo anti Markownikoff addition of HBr ?
20. What are the variables in the graph of powder diffraction pattern of a crystalline solid?
21. 100 mL of $\frac{M}{10} \mathrm{Ca}\left(\mathrm{NO}_3\right)_2$ and 200 mL of $\frac{M}{10} \mathrm{KNO}_3$ solutions a 22. A solution was prepared by dissolving 0.1 mole of a non- volatile solute in 0.9 moles of water. What is the relative low 23. The standard free energy change $\left(\Delta G^{\circ}\right)$ for the following reaction (in kJ ) at $25^{\circ} \mat 24. The rate constant of a first order reaction is $3.46 \times 10^{-2} \mathrm{~s}^{-1}$ at 298 K . What is the rate consta 25. The correct statement regarding chemisorption is
26. Which of the following is incorrectly matched?
27. Improve silver ore $+\mathrm{CN}^{-}+\mathrm{H}_2 \mathrm{O} \xrightarrow{\mathrm{O}_2}[\mathrm{X}]^{-}+\mathrm{OH}^{-}$ 28. In the reaction of sulphur with concentrated sulphuric acid, the oxidised product is $X$ and reduced product is $Y, X$ a 29. Which of the following lanthanoids have [Xe] $4 f^x 5 d^1 6 s^2$ configuration in their ground state.
$$
(X=1-14)
$$
30. How many of the following ligands are stronger than
$$ \begin{aligned} & \mathrm{H}_2 \mathrm{O} \text { ? } \\ & \mathr 31. $$ \text { The common monomer for both terylene and glyptal is } $$ 32. Which of the following structure of proteins represellis its constitution?
33. Carrot and curd are sources for the vitamins repectively.
34. $$ \text { Match the following. } $$
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border 35. The major products $X$ and $Y$ respectively from the following reactions are
36. An isomer of $\mathrm{C}_5 \mathrm{H}_{12}$ on reaction with $\mathrm{Br}_2$ /light gave only one isomer $\mathrm{C}_5 \ 37. What are the major products $X$ and $Y$ respectively in the following reactions?
$$ \begin{aligned} & \left(\mathrm{CH}_ 38. Match the following reagents with the products obtained when they reacted with a ketone.
.tg {border-collapse:collaps 39. What are $X$ and $Y$ respectively in the following reactions?
40. Arrange the following in decreasing order of their basicity.
Mathematics
1. The domain of the real valued function $f(x)$ $=\log _2 \log _3 \log _5\left(x^2-5 x+11\right)$ is
2. The range of the real valued function $f(x)=\left(\frac{x^2+2 x-15}{2 x^2+13 x+15}\right)$ is
3. $\frac{1}{1 \cdot 5}+\frac{1}{5 \cdot 9}+\frac{1}{9 \cdot 13}+\ldots$. upto $n$ terms $=$
4. If $A=\left|\begin{array}{lll}2 & 3 & 4 \\ 1 & k & 2 \\ 4 & 1 & 5\end{array}\right|$ is singular matrix, then the quadra 5. Let $A$ be a $4 \times 4$ matrix and $P$ be is adjoint matrix, If $|P|=\left|\frac{A}{2}\right|$ then $\left|A^{-1}\righ 6. The system $x+2 y+3 z=4,4 x+5 y+3 z=5,3 x+4 y+3 z=\lambda$ is consistent and $3 \lambda=n+100$, then $n=$
7. The complex conjugate of $(4-3 i)(2+3 i)(1+4 i)$ is.
8. If the amplitude of $(z-2)$ is $\frac{\pi}{2}$, then the locus of $z$ is
9. If $\omega$ is the cube root of unity,
$$
\frac{a+b \omega+c \omega^2}{c+a \omega+b \omega^2}+\frac{a+b \omega+c \omega 10. Roots of the equation $a(b-c) x^2+b(c-a) x+c(a-b)=0$ are
11. If $(3+i)$ is a root of $x^2+a x+b=0$, then $a=$
12. The algebraic equation of degree 4 whose roots are translate of the roots of the equation. $x^4+5 x^3+6 x^2+7 x+9=0$ by 13. If the roots of the equation $4 x^3-12 x^2+11 x+m=0$ are in arithmetic progression, then $m=$
14. The number of 5 -digit odd numbers greater than 40000 that can be formed by using 3,4,5,6,7,0 so that at least one of it 15. The number of ways in which 3 men and 3 women can be arranged in a row of 6 seats, such that the first and last seats mu 16. If a committee of 10 members is to be formed from 8 men and 6 women, then the number of different possible committees in 17. If the eleventh term in the binomial expansion of $(x+a)^{15}$ is the geometric mean of the eighth and twelfth terms, th 18. The sum of the rational terms in the binomial expansion of $\left(\sqrt{2}+3^{1 / 5}\right)^{10}$ is
19. If $\frac{1}{(3 x+1)(x-2)}=\frac{A}{3 x+1}+\frac{B}{x-2}$ and $\frac{x+1}{(3 x+1)(x-2)}=\frac{C}{3 x+1}+\frac{D}{x-2}$, 20. If the period of the function $f(x)=\frac{\tan 5 x \cos 3 x}{\sin 6 x}$ is $\alpha$, then $f\left(\frac{\alpha}{8}\right 21. If $\sin x+\sin y=\alpha, \cos x+\cos y+\beta$, then $\operatorname{cosec}(x+y)=$
22. If $P+Q+P=\frac{\pi}{4}$, then $\cos \left(\frac{\pi}{8}-P\right)+\cos \left(\frac{\pi}{8}-Q\right)+\cos$ $\left(\frac{\ 23. For $a \in R-\{0\}$, if $a \cos x+a \sin x+a=2 k+1$ has a solution, then $k$ lies in the interval
24. If the general solution .set of $\sin x+3 \sin 3 x+\sin 5 x=1$ is $S$, then $\{\sin \alpha / \alpha \in S\}=$
25. If $\theta$ is an acute angle, $\cosh x=K$ and $\sinh x=\tan \theta$, then $\sin \theta=$
26. In a $\Delta$ if the angles are in the ratio $3: 2: 1$, then the ratio of its sides is
27. In a $\triangle A B C$, if $B C=5, C A=6$ and $A B=7$, then the length of the median drawn from $B$ onto $A C$ is
28. In $\triangle A B C$, if $A B: B C: C A=6: 4: 5$, then $R: r$ is equal to
29.
$\mathbf{a}=\alpha \hat{\mathbf{i}}+\beta \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \quad \mathbf{b}=\hat{\mathbf{j}}+2 \hat 30. $\mathbf{c}$ is a vector along the bisector of the internal angle between the vectors $\mathbf{a}=4 \hat{\mathbf{i}}+7 \ 31. $\mathbf{a}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mat 32. $A(1,2,1), B(2,3,2), C(3,1,3)$ and $D(2,1,3)$ are the vertices of a tetrahedron. If $\theta$ is the angle between the fa 33. If $\mathbf{a}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\ 34.
Mean deviation about the mean for the following data is
$$ \begin{array}{llllll} \hline \text { Class Interval } & 0-6 35. If 12 dice are thrown at a time, then the probability that a multiple of 3 does not appear on any dice is
36. If a number is drawn at random from the set $\{1,3,5,7, \ldots . .59\}$, then the probability that it lies in the interv 37. In a class consisting of 40 boys and 30 girls. $30 \%$ of the boy and $40 \%$ of the girls are good at Mathematics. If a 38. A basket contains 12 apples in which 3 are rotten. If 3 apples are drawn at random simultaneously from it, then the prob 39. 7 coins are tossed simultaneously and the number of heads turned up is denoted by random variable $X$. If $\mu$ is the m 40. A manufacturing company noticed that $1 \%$ of its products are defective. If a dealer order for 300 items from this com 41. $P$ is a variable point such that the distance of $P$ from $A$ $(4,0)$ is twice the distance of $P$ from $B(-4,0)$. If t 42. When the origin is shifted to $(h, k)$ by translation of axes, the transformed equation of $x^2+2 x+2 y-7=0$ does not co 43. Let $\alpha \in R$. If the line $(\alpha+1) x+\alpha y+\alpha=1$ passes through a fixed point $(h, k)$ for all $\alpha$, 44. If $(\alpha, \beta)$ is the orthocentre of the triangle with the vertices $(2,2),(5,1),(4,4)$, then $\alpha+\beta=$
45. The area of the triangle formed by the lines represented by $3 x+y+15=0$ and $3 x^2+12 x y-13 y^2=0$ is
46. If all chords of the curve $2 x^2-y^2+3 x+2 y=0$, which subtend a right angle at the origin always passing through the p 47. $2 x-3 y+1=0$ and $4 x-5 y-1=0$ are the equations of two diameters of the circle $S \equiv x^2+y^2+2 g x+2 f y-11=0 . Q$ 48. If the inverse point of the point $(-1,1)$ with respect to the circle $x^2+y^2-2 x+2 y-1=0$ is $(p, q)$, then $p^2+q^2=$ 49. If $(a, b)$ is the mid-point of the chord $2 x-y+3=0$ of the circle $x^2+y^2+6 x-4 y+4=0$, then $2 a+3 b=$
50. If a direct common tangent drawn to the circle $x^2+y^2-6 x+4 y+9=0$ and $x^2+y^2+2 x-2 y+1=0$ touches the circles at $A 51. The radius of the circle which cuts the circles $x^2+y^2-4 x-4 y+7=0, x^2+y^2+4 x-4 y+6=0$ and $x^2+y^2+4 x+4 y+5=0$ ort 52. The equation of the normal drawn to the parabola $y^2=6 x$ at the point $(24,12)$ is
53. If $A_1, A_2, A_3$ are the areas of ellipse $x^2+4 y^2-4=0$ its director circle and auxiliary circle respectively, then 54. The equation of the pair of asymptotes of the hyperbola $4 x^2-9 y^2-24 x-36 y-36=0$ is
55. The equation of one of the tangents drawn from the point $(0,1)$ to the hyperbola $45 x^2-4 y^2=5$ is
56. Consider the tetrahedron with the vertices $A(3,2,4)$, $B\left(x_1, y_1, 0\right), C\left(x_2, y_2, 0\right)$ and $D\lef 57. If $P(2, \beta, \alpha)$ lies on the plane $x+2 y-z-2=0$ and $Q(\alpha,-1, \beta)$ lies on the plane $2 x-y+3 z+6=0$, th 58. Let $\pi$ be the plane that passes through the point $(-2,1,-1)$ and parallel to the plane $2 x-y+2 z=0$. Then the foot 59. If $f(x)=\frac{5 x \cdot \operatorname{cosec}(\sqrt{x})-1}{(x-2) \operatorname{cosec}(\sqrt{x})}$, then $\lim \limits_{ 60. $\lim \limits_{x \rightarrow 2} \frac{\sqrt{1+4 x}-\sqrt{3+3 x}}{x^3-8}=$
61. If
$$
\lim _{x \rightarrow \infty} \frac{(\sqrt{2 x+1}+\sqrt{2 x-1})^8+(\sqrt{2 x+1}-\sqrt{2 x-1})^8\left(P x^4-16\rig 62. The rate of change of $x^{\sin x}$ with respect to $(\sin x)^x$ is
63. If $y=\frac{\alpha x+\beta}{\gamma \alpha+\delta}$, then $2 y_1 y_3=$
64. Which one of the following is false ?
65. The point which lies on the tangent drawn to the curve $x^4 e^y+2 \sqrt{y+1}=3$ at the point $(1,0)$ is
66. If $f(x)=x^x$, then the interval in which $f(x)$ decrease is
67. If the Rolle's theorem is applicable for the function $f(x)$ defined by $f(x)=x^3+P x-12$ on $[0,1]$ then the value of $ 68. The number of all the value of $x$ for which the function $f(x)=\sin x+\frac{1-\tan ^2 x}{1+\tan ^2 x}$ attains it maxi 69. If $x \in\left[2 n \pi-\frac{\pi}{4}, 2 n \pi+\frac{3 \pi}{4}\right]$ and $n \in Z$, then $\int \sqrt{1-\sin 2 x} d x=$
70. $\int e^x\left(\frac{x+2}{x+4}\right)^2 d x=$
71. If $\int \frac{1}{1-\cos x} d x=\tan \left(\frac{x}{\alpha}+\beta\right)+c$, then one of the values of $\frac{\pi \alpha 72. If $729 \int_1^3 \frac{1}{x^3\left(x^2+9\right)^2} d x=a+\log b$, then $(a-b)=$
73. If $n \geq 2$ is a natural number and $0 74. $\lim \limits_{n \rightarrow \infty} \frac{1^{17}+2^{77}+\ldots+n^{77}}{n^{78}}=$
75. $$ \text { If } f(x)=\left\{\begin{array}{cc} \frac{6 x^2+1}{4 x^3+2 x+3} & , 0 76. If $\int_1^n[x] d x=120$, then $n=$
77. The area of the region under the curve $y=|\sin -\cos x|$, $0 \leq x \leq \frac{n}{2}$ and above $X$-axis, is (in sq uni 78. The differential equation formed by eliminating $a$ and $b$ from the equation $y=a e^{2 x}+b x e^{2 x}$ is
79. If $y=a^3 e^{y^2 x+c}$ is the general solution of a differential equation, where $a$ and $c$ are arbitrary constants and 80. The solution of differential equation $\left(x+2 y^3\right) \frac{d y}{d x}=y$ ls
Physics
1. Five equal resistances each $2 R$ connected as shown in figure. A battery of $V$ volts connected between $A$ and $B$. Th 2. A lamp is rated at $240 \mathrm{~V}, 60 \mathrm{~W}$. When in use the resistance of the filament of the lamp is 20 times 3. When an electron placed in a uniform magnetic field is accelerated from rest through a potential difference $V_1$. It e 4. A rectangular loop of sides 25 cm and 10 cm carrying a current of 10 A is placed with its longer side parallel to a lon 5. If the vertical component of the earth's magnetic field is 0.45 G at a location and angle of dip is $60^{\circ}$, then 6. $X$ and $Y$ are two circuits having coefficient of mutual inductance 3 mH and resistance $10 \Omega$ and $4 \Omega$ res 7. Two figures are shown as Fig. $A$ and Fig. $B$. The time constant of Fig. $A$ is $\tau_A$ and time constant of Fig. $B$ 8. Which of the following produces electromagnetic waves?
9. A blue lamp emits light of mean wavelength $4500$ Å. The lamp is rated at 150 W and $8 \%$ efficiency. Then, the number 10. The ground state energy of hydrogen atom is -13.6 eV . The potential energy of the electron in this state is
11. If the energy released per fission of a ${ }_{92}^{235} \mathrm{U}$ nucleus is 200 MeV . The energy released in the fiss 12. The semiconductor used for fabrication of visible LEDS must at least have a band gap of
13. In a common emitter amplifier, AC current gains 40 and input resistance is $2 \mathrm{k} \Omega$. The load resistance is 14. An information signal of frequency 10 kHz is modulated with a carried wave of frequency $3.62 \mathrm{MHz}^{}$ The uppe 15. The time period of revolution of a satellite $T$ around the carth depends on the radius of the circular orbit $R$. mass 16. An object projected upwards from the foot of a tower. The object crosses the top of the tower twice with an interval of 17. The centripetal acceleration of a particle in uniform circular motion is $18 \mathrm{~ms}^{-2}$. If the radius of the ci 18. The horizontal range of a projectile projected at an angle of $45^{\circ}$ with the horizontal is 50 m . The height of 19. A body of mass 1.5 kg is moving towards south with a uniform velocity of $8 \mathrm{~ms}^{-1}$. A force of 6 N is applie 20. The upper $\left(\frac{1}{n}\right)$ th of an inclined plane is smooth and the remaining lower part is rough with coeff 21. A spring of spring constant $200 \mathrm{~N}-\mathrm{m}^{-1}$ is initially stretched by 10 cm from the unstretched posi 22. A ball falls freely from rest from a height of 6.25 m on a hard horizontal surface. If the ball reaches a heightd 81 cm 23. The masses of a solid cylinder and hollow cylinder ate 3.2 kg and 1.6 kg respectively. Both the solid and hollow cylinde 24. A solid sphere of mass 50 kg and radius 20 cm is rotating about its diameter with an angular velocity d 420 rpm . The an 25. The mass of a particle is 1 kg and it is moving along $X$-axis. The period of its oscillation is $\frac{\pi}{2}$. Its p 26. The potential energy of a particle of mass 10 g as a function of displacement $x$ is $\left(50 x^2+100\right) \mathrm{J 27. If the time period of revolution of a satellite is $T$, the its kinetic energy is proportional to
28. The elastic energy stored per unit volume in terms of longitudinal strain $\varepsilon$ and Young's modulus $Y$ is
29. A large tank filled water to a height $h$ is to be emptied through a small hole at the bottom. The ratio of the time tak 30. A slab consists of two identical plates of copper and brass. The free face of the brass is at $0^{\circ} \mathrm{C}$ an 31. A monoatomic gas of $n$ moles is heated from temperature $T_1$ to $T_2$ under two different conditions, (i) at constant 32. In a Carnot engine, when the temperatures are $T_2=0^{\circ} \mathrm{C}$ and $T_1=200^{\circ} \mathrm{C}$, its efficien 33. Heat energy absorbed by a system going through the cyclic process shown in the figure is
34. A polyatomic gas with $n$ degrees of freedom has a mean kinetic energy per molecule given by (if $N$ is Avogadro's numb 35. A car sounding a horn of frequency 1000 Hz passes a stationary observer. The ratio of frequen'ies of the horn noted by 36. A ray of light travels from an optically denser to rare medium. The critical angle for the media is $C$. The maximum pos 37. The angle of polarisation for a medium with respect to air is $60^{\circ}$. The critical angle of this medium with respe 38. A point charge $q \mathrm{C}$ is placed at the centre of a cube of a side length $L$. Then, the electric flux linked wit 39. Three equal electric charges of each charge $q$ are placed at the vertices of an equilateral triangle of side of length 40. Eight drops of mercury of equal radii and possessing equal charge combine to form a big drop. If the capacity of each d
1
AP EAPCET 2024 - 21th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $729 \int_1^3 \frac{1}{x^3\left(x^2+9\right)^2} d x=a+\log b$, then $(a-b)=$
A
4
B
$-\frac{4}{5}$
C
$\frac{4}{5}$
D
-4
2
AP EAPCET 2024 - 21th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $n \geq 2$ is a natural number and $0<\theta<\frac{\pi}{2}$, then $\int \frac{\left(\cos ^n \theta-\cos \theta\right)^{1 / n}}{\cos ^{n+1} \theta} \sin \theta d \theta=$
A
$\frac{n}{n-1}\left(\cos ^{(1-n)} \theta-1\right)^2+c$
B
$\frac{n}{(n+1)(1-n)}\left(\cos ^{(1-n)} \theta-1\right)^{1+\frac{1}{n}}+c$
C
$\frac{1}{n-1}\left(\cos ^{(n-1)} \theta-1\right)^2+c$
D
$\frac{n}{1-n^2}\left(1-\cos ^{(1-n)} \theta\right)^{(n+1) / n}+c$
3
AP EAPCET 2024 - 21th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\lim \limits_{n \rightarrow \infty} \frac{1^{17}+2^{77}+\ldots+n^{77}}{n^{78}}=$
A
$\frac{1}{77}$
B
1
C
76
D
$\frac{1}{78}$
4
AP EAPCET 2024 - 21th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$$ \text { If } f(x)=\left\{\begin{array}{cc} \frac{6 x^2+1}{4 x^3+2 x+3} & , 0 < x < 1 \\ x^2+1 & , 1 \leq x < 2 \end{array} \text {, then } \int_0^2 f(x) d x=\right. $$
A
$\frac{1}{2} \log 3+\frac{10}{3}$
B
$\frac{1}{2} \log 3-\frac{10}{3}$
C
$\frac{1}{2} \log 3+\frac{13}{3}$
D
$\frac{1}{2} \log 3+\frac{20}{3}$
Paper analysis
Total Questions
Chemistry
40
Mathematics
80
Physics
40
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