Chemistry
1. In the ground state of hydrogen atom, electron absorbs 1.5 times energy than the minimum energy $\left(2.18 \times 10^{- 2. A golf ball of mass $m \mathrm{~g}$ has a speed of $50 \mathrm{~ms}^{-1}$. If the speed can be measured within accuracy 3. If the first ionisation enthalpy of $\mathrm{Li}, \mathrm{Be}$ and C respectively are $520,899,1086 \mathrm{~kJ} \mathrm 4. In which of the following sets of molecules, the centil atoms of molecules have same hybridisation?
5. The correct increasing order of number of lone pair of electrons on the central atom of $\mathrm{SnCl}_2, \mathrm{XeF}_2 6. Identify the correct statements from the following
I. For an ideal gas, the compressibility factor is 1.0
II. The kineti 7. The following graph is obtained for a gas at different temperatures $\left(T_1, T_2, T_3\right)$. What is the correct or 8. Observe the following stoichiometric equation
$$ \mathrm{P}_4+3 \mathrm{OH}^{-}+3 \mathrm{H}_2 \mathrm{O} \rightarrow \m 9. Given below are two statements :
Statement I For isothermal irreversible change of an ideal gas, $q=-w=p_{\text {ext }}\ 10. A thermodynamic process $(B \rightarrow E)$ was completed as shown below. The work done is equal to area under the limit 11. $K_{\mathrm{c}}$ for the following reaction is 99.0
$$ A_2(g) \stackrel{T(K)}{\rightleftharpoons} B_2(g) $$
In a one lit 12. What is the conjugate base of chloric acid?
13. The correct statements among the following are
(i) saline hydrides produce $\mathrm{H}_2$ gas when reacted with water
(i 14. The correct order of decomposition temperature of $\mathrm{MgCO}_3(X), \mathrm{BaCO}_3(Y), \mathrm{CaCO}_3(Z)$ is
15. Identify the correct statements
i. Oxidation of $\mathrm{NaBH}_4$ with $\mathrm{I}_2$ gives $\mathrm{B}_2 \mathrm{H}_6$
16. Which one of the following is used as piezoelectric material?
17. Two statements are given below :
I. In dry cleaning, the solvent $\mathrm{Cl}_2 \mathrm{C}=\mathrm{CCl}_2$ was earlier u 18. Tropolone is an example for which of the following class of compounds?
19. What are $X$ and $Y$ respectively in the following reaction sequence?
$$ \text { Isopentane } \xrightarrow{\mathrm{KMnO} 20. Some substances are given below
$$ \begin{aligned} & \mathrm{Ag}, \mathrm{CO}_2(s), \mathrm{SiO}_2, \mathrm{ZnS} \\ & \m 21. The $\Delta T_b$ value for 0.01 m KCl solution is 0.01 K . What is the van't Hoff factor?
$$
\left(K_b \text { for wate 22. 200 g of $20 \% \frac{\mathrm{w}}{\mathrm{w}}$ urea solution is mixed with 400 g of $40 \% \frac{w}{w}$ urea solution. W 23. 2.644 g of metal $(M)$ was deposited when 8040 coulombs of electricity was passed through molten $M \mathrm{~F}_2$ salt. 24. The first order reaction, $A(g) \rightarrow B(g)+2 C(g)$ occurs at $25^{\circ} \mathrm{C}$. After 24 minutes the ratio o 25. Which of the following has maximum coagulating power in the coagulation of positively charged sol?
26. Identify the autocatalytic reaction from the following
27. The anode and cathode used in electrolytic refining of copper respectively are
28. The disproportionation products of ortho phosphorus acid are
29. In neutral medium potassium permanganate oxidises $I^{-}$to $X$.. Identify the $X$.
30. The spin only magnetic moments of the complexes $\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{3-}$ and $\left[\mathrm{Co}\le 31. PHBV is a biodegradable polymer of two monomers $X$ and $Y . X$ and $Y$ respectively are. 32. The carbohydrate which does not react with ammonical $\mathrm{AgNO}_3$ solution is
33. Identify the amino acid which has
34. The structure given below represents
35. The major product $(X)$ formed in the given reaction is an example of
36. Identify the Swarts reaction from the following 37. An alcohol $X\left(\mathrm{C}_4 \mathrm{H}_{10} \mathrm{O}\right)$ reacts with conc. HCl at room temperature to give $Y\ 38. $$
\text { What is } Y \text { in the following reaction sequence? }
$$
39. A carbonyl compound $X\left(\mathrm{C}_3 \mathrm{H}_6 \mathrm{O}\right)$ on oxidation gave a carboxylic acid $Y\left(\ma 40. The correct sequence of reactions involved in the following conversion is
Mathematics
1. If a real valued function $f:[a, \infty) \rightarrow[b, \infty)$ defined by $f(x)=2 x^2-3 x+5$ is a bijection. Then, $3 2. The domain of the real valued function $f(x)=\frac{1}{\sqrt{\log _{0.5}(2 x-3)}}+\sqrt{4-9 x^2}$ is
3. $$
2 \cdot 5+5 \cdot 9+8 \cdot 13+11 \cdot 17+\ldots \text { to } 10 \text { terms }=
$$
4. $$
\left|\begin{array}{ccc}
1 & 1 & 1 \\
a^2 & b^2 & c^2 \\
a^3 & b^3 & c^3
\end{array}\right|=
$$
5. If $A=\left[\begin{array}{cc}1 & 2 \\ -2 & -5\end{array}\right]$ and $\alpha A^2+\beta A=2 I$ for some $\alpha, \beta \i 6. The system of equations
$$
x+2 y+3 z=6, x+3 y+5 z=9 \text {, }
$$
$2 x+5 y+a z=12$ has no solution when $a=$
7. If $m, n$ are respectively the least positive and greatest negative integer value of $k$ such that $\left(\frac{1-i}{1+i 8. If a complex number $z$ is such that $\frac{z-2 i}{z-2}$ is purely imaginary number and the locus of $z$ is a closed cur 9. Real part of $\frac{(\cos a+i \sin a)^6}{(\sin b+i \cos b)^8}$ is
10. $$
4+\frac{1}{4+\frac{1}{4+\frac{1}{4+\ldots \infty}}}=
$$
11. If $x^2+5 a x+6=0$ and $x^2+3 a x+2=0$ have a common root, then that common root is
12. If $\alpha, \beta, \gamma$ are roots of equations $x^3+a x^2+b x+x=0$, then $\alpha^{-1}+\beta^{-1}+\gamma^{-1}=$
13. If the roots of equation $x^3-13 x^2+K x-27=0$ are in geometric progression, then $K=$
14. If all the letters of the word MASTER are permuted in all possible ways and words (with or without meaning) thus formed 15. If Set $A$ contains 8 elements, then number of subsets of $A$ which contain at least 6 elements is
16. The number of different permutations that can be formed by taking 4 letters at a time from the letters of the word 'REPE 17. Numerically greatest term in the expansion of $(5+3 x)^6$ When, $x=1$, is
18. $$
1-\frac{2}{3}+\frac{2 \cdot 4}{3 \cdot 6}-\frac{2 \cdot 4 \cdot 6}{3 \cdot 6 \cdot 9}+\ldots \infty=
$$
19. If $\frac{1}{x^4+1}=\frac{A x+B}{x^2+\sqrt{2} x+1}+\frac{C x+D}{x^2-\sqrt{2} x+1}$, then $B D-A C=$
20. The smallest positive value (in degrees) of $\theta$ for which $\tan \left(\theta+100^{\circ}\right)=\tan \left(\theta+5 21. The value of $5 \cos \theta+3 \cos \left(\theta+\frac{\pi}{3}\right)+3$ lies between
22. Statement $(\mathrm{S} 1) \sin 55^{\circ}+\sin 53^{\circ}-\sin 19^{\circ}-\sin 17^{\circ}=\cos 2^{\circ}$
Statement (S2 23. The general solution of
$$ \begin{aligned} & 4 \cos 2 x-4 \sqrt{3} \sin 2 x+\cos 3 x-\sqrt{3} \sin 3 x \\ & \qquad+\cos 24. The general solution of $2 \cos ^2 x-2 \tan x+1=0$ is
25. $$
\cosh \left(\sinh ^{-1}(\sqrt{8})+\cosh ^{-1} 5\right)=
$$
26. In a $\triangle A B C$, if $r_1=2 r_2=3 r_3$, then $\sin A: \sin B: \sin C=$
27. In $\triangle A B C$, if $B=90^{\circ}$, then $2(r+R)=$
28. In a $\triangle A B C$, if $(a-b)(s-c)=(b-c)(s-a)$, then $r_1+r_3=$
29. If $L M N$ are the mid-points of the sides $P Q, Q R$ and $R P d$ $\triangle P Q R$ respectively, then
$$
\begin{aligne 30. Let $\mathbf{a} \times \mathbf{b}=7 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}$ and $\mathbf{a}=\hat{\mathbf 31. Let $A B C$ be an equilateral triangle of side a. $M$ and $N$ are two points on the sides $A B$ and $A C$, respectively 32. Let $\mathbf{a}$ and $\mathbf{b}$ be two non-collinear vector of unit modulus. If $\mathbf{u}=\mathbf{a}-(\mathbf{a} \cd 33. The shortest distance between the skew lines $\mathbf{r}=(-\hat{\mathbf{i}}-2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}})+t(3 \ 34. If $m$ and $M$ denote the mean deviations about mean and about median respectively of the data $20,5,15,2$, $7,3,11$, th 35. If 7 different balls are distributed among 4 different boxes, then the probability that the first box contains 3 balls i 36. Out of first 5 consecutive natural numbers, if two different numbers $x$ and $y$ are chosen at random, then the probabil 37. A bag contains 2 white, 3 green and 5 red balls. If three balls are drawn one after the other without replacement, then 38. There are 2 bags each containing 3 white and 5 black balls and 4 bags each containing 6 white and 4 black balls. If a ba 39. If two cards are drawn randomly from a pack of 52 playing cards, then the mean of the probability distribution of number 40. In a consignment of 15 articles, it is found that 3 are defective. If a sample of 5 articles is chosen at random from it 41. If a variable straight line passing through the point of intersection of the lines $x-2 y+3=0$ and $2 x-y-1=0$ intersect 42. Point $(-1,2)$ is changed to $(a, b)$, when the origin is shifted to the point $(2,-1)$ by translation of axes, Point $( 43. The point $(a, b)$ is the foot of the perpendicular drawn from the point $(3,1)$ to the line $x+3 y+4=0$. If $(p, q)$ is 44. A ray of light passing through the point $(2,3)$ reflects on $Y$-axis at a point $P$. If the reflected ray passes throug 45. The area (in sq units) of the triangle formed by the lines $6 x^2+13 x y+6 y^2=0$ and $x+2 y+3=0$ is
46. The angle subtended by the chord $x+y-1=0$ of the circle $x^2+y^2-2 x+4 y+4=0$ at the origin is
47. Let $P$ be any point on the circle $x^2+y^2=25$. Let $L$ be the chord of contact of $P$ with respect to the circle $x^2+ 48. If the circles $S \equiv x^2+y^2-14 x+6 y+33=0$ and $S^1 \equiv x^2+y^2-a^2=0(a \in N)$ have 4 common tangents, then pos 49. If the area of the circum-circle of triangle formed by the line $2 x+5 y+\alpha=0$ and the positive coordinate axes is $ 50. The circle $S \equiv x^2+y^2-2 x-4 y+1=0$ cuts the $Y$-axis at $A, B(O A>O B)$. If the radical axis of $S \equiv 0$ and 51. If the circle $S=0$ cuts the circles $x^2+y^2-2 x+6 y=0$, $x^2+y^2-4 x-2 y+6=0$ and $x^2+y^2-12 x+2 y+3=0$ orthogonally, 52. The normal drawn at a point $(2,-4)$ on the parabola $y^2 \pm 8 x$ cuts again the same parabola at $(\alpha, \beta)$, th 53. If a tangent of slope 2 to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ touches the circle $x^2+y^2=4$, then maximum 54. The locus of the mid-points of the chords of the hyperbola $x^2-y^2=a^2$ which touch the parabola $y^2=4 a x$ is
55. If the product of eccentricities of the ellipse $\frac{x^2}{16}+\frac{y^2}{b^2}=1$ and the hyperbola $\frac{x^2}{9}-\fra 56. If $A(1,2,0), B(2,0,1), C(-3,0,2)$ are the vertices of $\triangle A B C$, then the length of the internal bisector of $\ 57. The perpendicular distance from the point $(-1,1,0)$ to the line joining the points $(0,2,4)$ and $(3,0,1)$ is
58. A line $L$ passes through the points $(1,2,-3)$ and $(\beta, 3,1)$ and a plane $\pi$ passes through the points $(2,1,-2) 59. $$
\lim \limits_{x \rightarrow 3} \frac{x^3-27}{x^2-9}=
$$
60. If $f(x)=\left\{\begin{array}{ll}3 a x-2 b, & x>1 \\ a x+b+1, & x
$\lim \limits_{x \rightarrow 1} f(x)$ exists, then the 61. The function $f(x)=\left\{\begin{array}{ll}\frac{2}{5-x}, & x 62. If $y=f(x)$ is a thrice differentiable function and a bijection, then $\frac{d^2 x}{d y^2}\left(\frac{d y}{d x}\right)^3 63. If $f(x)=\left\{\begin{array}{cl}x^\alpha \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x=0\end{array}\right.$
whic 64. Let $f(x)=\min \left\{x, x^2\right\}$ for every real number of $x$, then
65. If $y=\left(1+\alpha+\alpha^2+\ldots\right) e^{\eta x}$, where $\alpha$ and $n$ are constants, then the relative error i 66. If the equation of tangent at $(2,3)$ on $y^2=a x^3+b$ is $y=4 x-5$, then the value of $a^2+b^2=$
67. If Rolle's theorem is applicable for the function $f(x)=x(x+3) e^{-x / 2}$ on $[3,0]$, then the value of $c$ is
68. For all $x \in[0,2024]$ assume that $f(x)$ is differentiable, $f(0)=-2$ and $f^{\prime}(x) \geq 5$. Then, the least poss 69. $$
\int \frac{2 x^2 \cos x^2-\sin x^2}{x^2} d x=
$$
70. If $\int \frac{\log \left(1+x^4\right)}{x^3} d x=f(x) \log \left(\frac{1}{g(x)}\right)+\tan ^{-1}$
$(h(x))+c$, then $h(x 71. Let $f(x)=\int \frac{x}{\left(x^2+1\right)\left(x^2+3\right)} d x$. If $f(3)=\frac{1}{4} \log \left(\frac{5}{6}\right)$, 72. $$
\int \frac{2 \cos 2 x}{(1+\sin 2 x)(1+\cos 2 x)} d x=
$$
73. $$
\int\left(\frac{x}{x \cos x-\sin x}\right)^2 d x=
$$
74. If $\lim \limits_{n \rightarrow \infty}\left[\left(1+\frac{1}{n^2}\right)\left(1+\frac{4}{n^2}\right)\left(1+\frac{9}{n^ 75. $$
\int_0^\pi x \sin ^4 x \cos ^6 x d x=
$$
76. If $I_n=\int_0^{\frac{\pi}{4}} \tan ^n x d x$, then $I_{13}+I_{11}=$
77. The area (in sq units) of the smaller region lying above the $X$-axis and bounded between the circle $x^2+y^2=2 a x$ and 78. The difference of the order and degree of the differential equation $\left(\frac{d^2 y}{d x^2}\right)^{-\frac{7}{2}}\lef 79. If $x d y+\left(y+y^2 x\right) d x=0$ and $y=1$ at $x=1$, then
80. The solution of $x d y-y d x=\sqrt{x^2+y^2} d x$ when $y(\sqrt{3})=1$ is
Physics
1. The percentage error in the measurement of mass and velocity are $3 \%$ and $4 \%$, respectively. The percentage error i 2. A car travelling at 80 kmph can be stopped at a distance of 60 m by applying brakes. If the same car travels at 160 kmph 3. A 2 kg ball thrown vertically upward and another 3 kg ball projected with certain angle $\left(\theta \neq 90^{\circ}\ri 4. In a sport event, a disc is thrown such that it reaches its maximum range of 80 m , the distance travelled in first 3 s 5. A block of mass 18.5 kg kept on a smooth horizontal surface is pulled by a rope of 3 m length by a horizontal force of 4 6. A block of mass 1.5 kg kept on a rough horizontal surface is given a horizontal velocity of $10 \mathrm{~ms}^{-1}$. If t 7. A force of $\left(6 x^2-4 x+3\right) \mathrm{N}$ acts on a body of mass 0.75 kg and displaces it from $x=2 \mathrm{~m}$ 8. A ball falls freely from rest on to a hard horizontal floor and repeatedly bounces. If the velocity of the ball just bef 9. A solid cylinder rolls down an inclined plane without slipping. If the translation kinetic energy of the cylinder is 140 10. Two blocks of masses $m$ and $2 m$ are connected by a massless string which passes over a fixed frictionless pulley. If 11. The displacement of a particle executing simple harmonic motion is $y=A \sin (2 t+\phi) \mathrm{m}$, where $t$ is time i 12. The displacement of a damped oscillator is $x(t)=\exp (-0.2 t) \cos (3.2 t+\phi)$, where $t$ is time in second The time 13. Maximum height reached by a rocket fired with a speed equal to $50 \%$ of the escape speed from the surface of the earth 14. If the work done in stretching a wire by 1 min is 2 J . The work necessary for stretching another wire of satrs material 15. If $S_1, S_2$ and $S_3$ are the tensions at liquid-air, solid-air and solid-liquid interfaces respectively and $\theta$ 16. If ambient temperature is 300 K , the rate of cooling at 600 K is $H$. In the same surroundings, the rate of cooling at 17. An ideal heat engine operates in Carnot cycle between $127^{\circ} \mathrm{C}$ and $27^{\circ} \mathrm{C}$. It absorbs $ 18. One mole of a gas having $\gamma=\frac{7}{5}$ is mixed with one mole of a gas having $\gamma=\frac{4}{3}$. The value of 19. A Carnot heat engine has an efficiency of $10 \%$. If the same engine is worked backward to obtain a refrigerator, then 20. The rms velocity of a gas molecules oí mass $m$ at a given temperature is proportional to
21. The speed of a wave on a string is $150 \mathrm{~ms}^{-1}$ when the tension is 120 N . The percentage increase in the te 22. The minimum deviation produced by a hollow prism filled with a certain liquid is found to be $30^{\circ}$. The light ray 23. In Young's double slit experiment, the intensity at a point where the path difference is $\frac{\lambda}{6}$ ( $\lambda$ 24. Two particles of equal mass $m$ and equal charge $q$ are separated by a distance of 16 cm . They do not experience any f 25. In the following diagram, the work done in moving a point charge from point $P$ to points $A, B$ and $C$ are $W_A, W_B$ 26. Four condensers each of capacitance $8 \mu \mathrm{~F}$ are joined as shown in the figure. The equivalent capacitance be 27. A steady current is flowing in a metallic conductor of non-uniform cross-section. The physical quantity which remains co 28. The resistance between points $A$ and $C$ in the given network is
29. A wire shaped in a regular hexagon of side 2 cm carries a current of 4 A . The magnetic field at the centre of hexagon i 30. A tightly wound coil of 200 turns and of radius 20 cm carrying current 5 A . Magnetic field at the centre of the coil is 31. The domain in ferromagnetic material is in the form of a cube of side $2 \mu \mathrm{~m}$. Number of atoms in that domai 32. Magnetic field at a distance of $r$ from $Z$-axis is $B=B_0$ $r t \hat{\mathbf{k}}$ present in the region. $B_0$ is cons 33. A series $L-C-R$ circuit is shown in the figure. Where the inductance of 10 H , capacitance $40 \mu \mathrm{~F}$ and res 34. An electromagnetic wave travel in a medium with a speed of $2 \times 10^8 \mathrm{~ms}^{-1}$. The relative permeability 35. The longest wavelength of light that can initiate photo electric effect in the metal of work function 9 eV is
36. A hydrogen atom falls from $n$th higher energy orbit to first energy orbit $(n=1)$. The energy released is equal to 12.7 37. The decrease in each day in the uranium mass of the material in a uranium reactor operating at a power of 12 MW is (Ener 38. When a signal is applied to the input of a transistor, it was found that output signal is phase-shifted by $180^{\circ}$ 39. The voltage $V_0$ in the network shown is 40. A message signal of 3 kHz is used to modulate a carric signal frequency 1 MHz , using amplitude modulation. The upper si
1
AP EAPCET 2024 - 19th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $A=\left[\begin{array}{cc}1 & 2 \\ -2 & -5\end{array}\right]$ and $\alpha A^2+\beta A=2 I$ for some $\alpha, \beta \in R$, then $\alpha+\beta=$
A
7
B
10
C
12
D
5
2
AP EAPCET 2024 - 19th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
The system of equations
$$
x+2 y+3 z=6, x+3 y+5 z=9 \text {, }
$$
$2 x+5 y+a z=12$ has no solution when $a=$
A
5
B
6
C
7
D
8
3
AP EAPCET 2024 - 19th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $m, n$ are respectively the least positive and greatest negative integer value of $k$ such that $\left(\frac{1-i}{1+i}\right)^k=-i$, then $m-n=$
A
4
B
0
C
6
D
2
4
AP EAPCET 2024 - 19th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If a complex number $z$ is such that $\frac{z-2 i}{z-2}$ is purely imaginary number and the locus of $z$ is a closed curve, then the area of the region bounded by that closed curve and lying in the first quadrant is $\frac{z-2 i}{z-2}$
A
$2 \pi$
B
$\frac{\pi}{2}$
C
$\pi$
D
$\frac{\pi}{4}$
Paper analysis
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Chemistry
40
Mathematics
80
Physics
40
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