Chemistry
1. The angular momentum of an electron in a stationary state of $\mathrm{Li}^{2+}(Z=3)$ is $3 h / \pi$. The radius and ener 2. Identify the pair of elements in which number of electrons in ( $n-1$ ) shell is same
3. $$
\text { Match the following. }
$$
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border 4. The correct order of bond angles of the molecules $\mathrm{SiCl}_4, \mathrm{SO}_3, \mathrm{NH}_3, \mathrm{HgCl}_2$ is
5. $$ \text { Observe the following structure, } $$
$$ \text { The formal charges on the atoms 1,2,3 respectively are } $$ 6. Two statement are given below.
Statement I : The ratio of the molar volume of a gas to that of an ideal gas at constant 7. At 133.33 K . the rms velocity of an ideal gas is
$$
\left(M=0.083 \mathrm{~kg} \mathrm{~mol}^{-1} ; R=8.3 \mathrm{~J} 8. Given below are two statements.
Statement I : In the decomposition of potassium chlorate Cl is reduced.
Statement II : R 9. Observe the following reaction,
$$ 2 A_2(g)+B_2(g) \xrightarrow{T(\mathrm{~K})} 2 A_2 B(g)+600 \mathrm{~kJ} $$
The stand 10. Identify the molecule for which the enthalpy of atomisation ( $\Delta_a H^{\ominus}$ ) and bond dissociation enthalpy $\ 11. $K_C$ for the reaction, $A_2(g) \stackrel{T(\mathrm{~K})}{\rightleftharpoons} B_2(g)$ is 99.0 . In a 1 L closed flask tw 12. At $27^{\circ} \mathrm{C}, 100 \mathrm{~mL}$ of 0.4 M HCl is mixed with 100 mL of 0.5 M NaOH solution. To the resultant 13. ' $X$ ' on hydrolysis gives two products. One of them is solid. What is ' $X$ '?
14. $\mathrm{Ba}, \mathrm{Ca}$ and Sr form halide hydrates. Their formulae are $\mathrm{BaCl}_2 \cdot x \mathrm{H}_2 \mathrm 15. The bond angles $b_1, b_2$ and $b_3$ in the given structure are respectively (in ${ }^{\circ}$ )
16. Which of the following oxides is acidic in nature?
17. $$ \text { Match the following. } $$
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border 18. The number of nucleophiles in the following list is
$$ \mathrm{CH}_3 \mathrm{NH}_2, \mathrm{CH}_3 \mathrm{CHO}, \mathrm{ 19. An alkene $X\left(\mathrm{C}_4 \mathrm{H}_8\right)$ on reaction with HBr gave $Y\left(\mathrm{C}_4 \mathrm{H}_9 \mathrm{ 20. A solid compound is formed by atoms of $A$ (cations), $B$ (cations) and O (anions). Atoms of O form hcp lattice. Atoms o 21. The density of nitric acid solution is $1.5 \mathrm{~g} \mathrm{~mL}^{-1}$. Its weight percentage is 68 . What is the ap 22. The osmotic pressure of sea water is 1.05 atm . Four experiments were carried as shown in table. In which of the followi 23. Aqueous $\mathrm{CuSO}_4$ solution was electrolysed by passing 2 amp of current for 10 min . What is the weight (in g) o 24. For a first order reaction the concentration of reactant was reduced from $0.03 \mathrm{molL}^{-1}$ to $0.02 \mathrm{mol 25. ' $X$ ' is a protecting colloid. The following data is obtained for preventing the coagulation of 10 mL of gold sol to w 26. Which sol is used as intramuscular injection?
27. The reactions which occur in blast furnace at $500-800 \mathrm{~K}$ during extraction of iron from haematite are
i. $3 \ 28. Which of the following reactions give phosphine?
i. Reaction of calcium phosphide with water
ii. Heating white phosphoro 29. Which transition metal does not form 'MO' type oxide? ( $M=$ transition metal)
30. The paramagnetic complex ion, which has no unpaired electrons in $t_{2 g}$ orbitals is
31. $$ \text { Which of the following is an example for fibre? } $$ 32. When glucose is oxidised with nitric acid the compound formed is
33. The number of essential and non-essential amino acids from the following list respectively is
Val, Gly, Leu, Lys, Pro, S 34. Which of the following pair is not correctly matched?
35. An alkene $X\left(\mathrm{C}_4 \mathrm{H}_8\right)$ does not exhibit cis-trans is memerisn Reaction of $X$ with $\mathrm 36. The two reactions involved in the conversion of benzene diazonium chloride to diphenyl are respectively
37. $$ \text { Consider the reactions, } $$
38. Consider the following reactions,
$Y$ and $Z$ respectively are 39. $$ \text { The incorrect statement about ' } B \text { ' is } $$
$$ \text { The incorrect statement about } B \text { i 40. $$ \text { Benzamide } \xrightarrow{\mathrm{Br}_2 / \mathrm{NaOH}} X \xrightarrow[\text { Alc. } \mathrm{KOH}]{\mathrm{C
Mathematics
1. Let $f(x)=3+2 x$ and $g_n(x)=(f \circ f \circ f o \ldots$ in times $)(x)$, $\forall n \in N$ if all the lines $y=g_n(x)$ 2.
Let $a > 1$ and $0
3. $ \frac{1}{3 \cdot 7}+\frac{1}{7 \cdot 11}+\frac{1}{11 \cdot 15}+\ldots$ to 50 terms $=$
4. $$
\text { If } A=\left[\begin{array}{lll}
1 & 0 & 2 \\
2 & 1 & 3 \\
3 & 2 & 4
\end{array}\right] \text {, then } A^2-5 5. Sum of the positive roots of the equation
$$
\left|\begin{array}{ccc}
x^2+2 x & x+2 & 1 \\
2 x+1 & x-1 & 1 \\
x+2 & -1 6. If the solution of the system of simultaneous linear equations $x+y-z=6,3 x+2 y-z=5$ and $2 x-y-2 z+3=0$ is $x=\alpha, y 7. If the point $P$ represents the complex number $z=x+i y$ in the argand plane and if $\frac{z+i}{z-i}$ is a purely imagin 8. $S=\{z \in C /|z+1-i|=1\}$ represents
9. If $\cos \alpha+\cos \beta+\cos \gamma=\sin \alpha+\sin \beta+\sin \gamma=0$, then $\left(\cos ^3 \alpha+\cos ^3 \beta+\ 10. If $\alpha$ and $\beta$ are two double roots of $x^2+3(a+3) x-9 a=0$ for different values of $a(\alpha>\beta)$, then the 11. If $2 x^2+3 x-2=0$ and $3 x^2+\alpha x-2=0$ have one common root, then the sum of all possible values of $\alpha$ is
12. If the sum of two roots of $x^3+p x^2+q x-5=0$ is equal to its third root, then $p\left(p^2-4 q\right)=$
13. If $P(x)=x^5+a x^4+b x^3+c x^2+d x+e$ is a polynomial such that $P(0)=1, P(1)=2, P(2)=5, P(3)=10$ and $P(4)=17$, then $P 14. If a polygon of $n$ sides has 275 diagonals, then $n$ is
15. The number of positive divisors of 1080 is
16. If $a_n=\sum\limits_{r=0}^n \frac{1}{{ }^n C_r}$, then $\sum\limits_{r=0}^n \frac{r}{{ }^n C_r}=$
17. The coefficient of $x^5$ in the expansion of $\left(2 x^3-\frac{1}{3 x^2}\right)^5$ is
18. $$1+\frac{1}{3}+\frac{1 \cdot 3}{3 \cdot 6}+\frac{1 \cdot 3 \cdot 5}{3 \cdot 6 \cdot 9}+\ldots \text { to } \infty=
$$
19. If $\frac{A}{x-a}+\frac{B x+C}{x^2+b^2}=\frac{1}{(x-a)\left(x^2+b^2\right)}$, then $\mathrm{C}=$
20. If $\cos ^4 \frac{\pi}{8}+\cos ^4 \frac{3 \pi}{8}+\cos ^4 \frac{5 \pi}{8}+\cos ^4 \frac{7 \pi}{8}=k$, then $\sin ^{-1}\l 21. $$
\text { } \frac{\cos 10^{\circ}+\cos 80^{\circ}}{\sin 80^{\circ}-\sin 10^{\circ}}=
$$
22. $\frac{\sin 1^{\circ}+\sin 2^{\circ}+\ldots . . .+\sin 89^{\circ}}{2\left(\cos 1^{\circ}+\cos 2^{\circ}+\ldots+\cos 44^{ 23. The number of ordered pairs $(x, y)$ satisfying the equations $\sin x+\sin y=\sin (x+y)$ and $|x|+|y|=1$ is
24. $$4 \tan ^{-1} \frac{1}{5}-\tan ^{-1} \frac{1}{70}+\tan ^{-1} \frac{1}{99}=$$
25. If $5 \sin h x-\cos h x=5$, then one of the values of $\tan h x$ is
26. In $\triangle A B C$, if $r_1=4, r_2=8$ and $r_3=24$, then $a=$
27. If a circle is inscribed in an equilateral triangle of side $a$, then the area of any square (in sq units) inscribed in 28. Match the items of List I with those of List II (here, $\Delta$ denotes the area of $\triangle A B C$ )
.tg {border-co 29. Let $O(\mathbf{O}), A(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}), B(-2 \hat{\mathbf{i}}+3 \hat{\mathbf{k}}), 30. $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are non-coplanar vectors. If $\alpha \mathbf{d}=\mathbf{a}+\mathbf{b}+\mathbf{c}$ a 31. $\mathbf{u}, \mathbf{v}$ and $\mathbf{w}$ are three unit vectors. Let $\hat{\mathbf{p}}=\hat{\mathbf{u}}+\hat{\mathbf{v} 32. The distance of the point $O(\mathbf{O})$ from the plane $\mathbf{r}$. $(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{ 33. If $\mathbf{a}$ and $\mathbf{b}$ are the two non collinear vectors, then $|\mathbf{b}|\mathbf{a}+|\mathbf{a}| \mathbf{b} 34. $x$ and $y$ are the arithmetic means of the runs of two batsmen $A$ and $B$ in 10 innings respectively and $\sigma_A, \s 35. S is the sample space and $A, B$ are two events of a random experiment. Match the items of List $A$ with the items of Li 36. $P(A \mid A \cap B)+P(B \mid A \cap B)=$
37. Two digits are selected at random from the digits 1 through 9. If their sum is even, then the probability that both are 38. A, B and C are mutually exclusive and exhaustive events of a random experiment and $E$ is an event that occurs in conjun 39. For the probability distribution of a discrete random variable $X$ as given below, then mean of $X$ is
.tg {border-col 40. In a random experiment, two dice are thrown and the sum of the numbers appeared on them is recorded. This experiment is 41. If the line segment joining the points $(1,0)$ and $(0,1)$ subtends an angle of $45^{\circ}$ at a variable point $P$, th 42. If the origin is shifted to a point $P$ by the translationd axes to remove the $y$-term from the equation $x^2-y^2+2 y-1 43. A line $L$ intersects the lines $3 x-2 y-1=0$ and $x+2 y+1=0$ at the points $A$ and $B$. If the point $(1,2)$ bisects th 44. A line $L$ passing through the point $(2,0)$ makes an angle $60^{\circ}$ with the line $2 x-y+3=0$. If $L$ makes an acut 45. If the slope of one line of the pair of lines $2 x^2+h x y+6 y^2=0$ is thrice the slope of the other line, then $h=$
46. If the equation of the pair of straight lines passing through the point $(1,1)$ and perpendicular to the pair of lines $ 47. Equation of the circle having its centre on the line $2 x+y+3=0$ and having the lines $3 x+4 y-18=0,3 x+4 y+2=0$ as tang 48. If power of a point $(4,2)$ with respect to the circle $x^2+y^2-2 \alpha x+6 y+\alpha^2-16=0$ is 9 , then the sum of the 49. Let $\alpha$ be an integer multiple of 8 . If $S$ is the set of all possible values of $\alpha$ such that the line $6 x+ 50. If the circle $x^2+y^2-8 x-8 y+28=0$ and $x^2+y^2-8 x-6 y+25-\alpha^2=0$ have only one common tangent, then $\alpha=$
51. If the equation of the circle passing through the points of intersection of the circles $x^2-2 x+y^2-4 y-4=0$, $x^2+2 x+ 52. A common tangent to the circle $x^2+y^2=9$ and parabola $y^2=8 x$ is
53. Let F and $F^1$ be the foci of the ellipse $\frac{x^2}{4}+\frac{y^2}{b^2}=1(b 54. If a circle of radius 4 cm passes through the foci of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{4}=1$ and concentric wit 55. If a tangent to the hyperbola $x^2-\frac{y^2}{3}=1$ is also a tangent to the parabola $y^2=8 x$, then equation of such t 56. If $A(1,0,2), B(2,1,0), C(2,-5,3)$ and $D(0,3,2)$ are four points and the point of intersection of the lines $A B$ and $ 57. The direction cosines of two lines are connected by the relations $l+m-n=0$ and $l m-2 m n+n l=0$. If $\theta$ is the ac 58. The distance from a point $(1,1,1)$ to a variable plane $\pi$ is 12 units and the points of intersections of the plane $ 59. $\lim \limits_{x \rightarrow 0} \frac{\sqrt{1+\sqrt{1+x^4}}-\sqrt{2+x^5+x^6}}{x^4}=$
60. $\lim \limits_{x \rightarrow 1} \frac{\sqrt{x}-1}{\left(\cos ^{-1} x\right)^2}=$
61. If a function $f(x)=\left\{\begin{array}{cl}\frac{\tan (\alpha+1) x+\tan 2 x}{x} & \text { if } x>0 \\ \beta & \text { a 62. If $y=\tan (\log x)$, then $\frac{d^2 y}{d x^2}=$
63. For $x 64. If $y=x-x^2$, then the rate of change of $y^2$ with respect to $x^2$ at $x=2$ is
65. If $T=2 \pi \sqrt{\frac{L}{g}}, \mathrm{~g}$ is a constant and the relative error in $T$ is $k$ times to the percentage 66. The angle between the curves $y^2=2 x$ and $x^2+y^2=8$ is
67. If the function $f(x)=\sqrt{x^2-4}$ satisfies the Lagrange's mean value theorem on $[2,4]$, then the value of $C$ is
68. If $x, y$ are two positive integers such that $x+y=20$ and the maximum value of $x^3 y$ is $k$ at $x=\alpha$ and $y=\bet 69. $\int \frac{2 x^2-3}{\left(x^2-4\right)\left(x^2+1\right)} d x=A \tan ^{-1} x+B \log (x-2)+C \log (x+2)$, then $6 A+7 B- 70. $\int \frac{3 x^9+7 x^8}{\left(x^2+2 x+5 x^8\right)^2} d x=$
71. $\int \frac{\cos x+x \sin x}{x(x+\cos x)} d x=$
72. If $\int \sqrt{\frac{2}{1+\sin x}} d x=2 \log |A(x)-B(x)|+C$ and $0 \leq x \leq \frac{\pi}{2}$, then $B\left(\frac{\pi}{ 73. $$ \begin{aligned} &\text { If } \int \frac{3}{2 \cos ^3 x \sqrt{2 \sin 2 x}} d x=\frac{3}{2}(\tan x)^B+\frac{3}{10}(\ta 74. $\int_{-\pi}^\pi \frac{x \sin ^3 x}{4-\cos ^2 x} d x=$
75. $$ \text { } \int\limits_{-3}^3|2-x| d x= $$ 76. $$ \int_{\frac{1}{\sqrt[5]{31}}}^{\frac{1}{\sqrt[5]{242}}} \frac{1}{\sqrt[5]{x^{30}+x^{25}}} d x= $$ 77. Area of the region (in sq units) enclosed by the curves $y^2=8(x+2), y^2=4(1-x)$ and the $Y$-axis is
78. The sum of the order and degree of the differential equation $\frac{d^4 y}{d x^4}=\left\{c+\left(\frac{d y}{d x}\right)^ 79. $$ \begin{aligned} &\text { The general solution of the differential equation }\\ &(x+y) y d x+(y-x) x d y=0 \text { is 80. The general solution of the differential equation $\left(y^2+x+1\right) d y=(y+1) d x$ is
Physics
1. E, M, L, G represent energy, mass, angular momentum and gravitational constant, respectively. The dimensions of $\frac{E 2. A body starting from rest moving with an acceleration of $\frac{5}{4} \mathrm{~ms}^{-2}$. The distance travelled by the 3. A projectile can have the same range $R$ for two angles of projection. Their initial velocities are same. If $T_1$ and $ 4. If $|\mathbf{P}+\mathbf{Q}|=|\mathbf{P}|=|\mathbf{Q}|$ then the angle between $\mathbf{P}$ and $\mathbf{Q}$ is
5. A $4 \mathrm{~kg}$ mass is suspended as shown in figure. All pulleys are frictionless and spring constant $k$ is $8 \tim 6. A 3 kg block is connected as shown in the figure. Spring constants of two springs $k_1$ and $k_2$ are $50 \mathrm{Nm}^{- 7. Two bodies $A$ and $B$ of masses $2 m$ and $m$ are projected vertically upwards from the ground with velocities $u$ and 8. A body of mass 2 kg collides head on with another body of mass 4 kg . If the relative velocities of the bodies before an 9. The moment of inertia of a solid sphere of mass 20 kg and diameter 20 cm about the tangent to the sphere is
10. A wooden plank of mass 90 kg and length 3.3 m is floating on still water. A girl of mass 20 kg walks from one end to the 11. In a time of 2 s , the amplitude of a damped oscillator becomes $\frac{1}{e}$ times, its initial amplitude $A$. In the n 12. A particle is executing simple harmonic motion with a time period of 3 s . At a position where the displacement of the p 13. The acceleration due to gravity at a height of 6400 km from the surface of the earth is $2.5 \mathrm{~ms}^{-2}$. The acc 14. When the load applied to a wire is increased from 5 kg wt to 8 kg wt . The elongation of the wire increases from 1 mm to 15. The radius of cross-section of the cylindrical tube of a spray pump is 2 cm . One end of the pump has 50 fine holes each 16. The temperature difference across two cylindrical rods $A$ and $B$ of same material and same mass are $40^{\circ} \mathr 17. The efficiency of Carnot cycle is $\frac{1}{6}$. By lowering the temperature of sink by 65 K , it increases to $\frac{1} 18. In a cold storage ice melts at the rate of 2 kg per hour when the external temperature is $20^{\circ} \mathrm{C}$. The m 19. A Carnot engine has the same efficiency between 800 K and 500 K and $x>600 \mathrm{~K}$ and 600 K . The value of $x$ is
20. When the temperature of a gas is raised from $27^{\circ} \mathrm{C}$ to $90^{\circ} \mathrm{C}$. The increase in the rms 21. If the frequency of a wave is increased by $25 \%$, then the change in its wavelength is (medium not changed)
22. An object lying 100 cm inside water is viewed normally from air. If the refractive index of water is $\frac{4}{3}$, then 23. In Young's double slit experiment two slits are placed 2 mm from each other. Interference pattern is observed on a scree 24. Two spheres $A$ and $B$ of radii 4 cm and 6 cm are given charges of $80 \mu \mathrm{C}$ and $40 \mu \mathrm{C}$ respecti 25. The angle between the electric dipole moment of a dipole and the electric field strength due to it on the equatorial lin 26. Two condensers $C_1$ and $C_2$ in a circuit are joined as shown in the figure. The potential of point $A$ is $V_1$ and t 27. A block has dimensions $1 \mathrm{~cm}, 2 \mathrm{~cm}$ and 3 cm . Ratio of the maximum resistance to minimum resistance 28. A current of 6 A enters one corner $P$ of an equilateral triangle $P Q R$ having three wires of resistance $2 \Omega$ ea 29. The value of shunt resistance that allows only $10 \%$ of main current through the galvanometer of resistance $99 \Omega 30. In hydrogen atom an electron is making $6.6 \times 10^{15} \mathrm{rev} / \mathrm{s}$ around the nucleus of radius $0.47 31. Any magnetic material loses its magnetic property when it is
32. When two coaxial coils having same current in same direction are brought to each other, then the value of current in bot 33. A resistance of $20 \Omega$ is connected to a source of an alternating potential $V=200 \sin (10 \pi t)$. If $t$ is the 34. The average value of electric energy density in an electromagnetic wave is where $E_0$ is peak value
35. An electron of mass $m$ with initial velocity $\mathbf{v}=v_0 \hat{\mathbf{i}}\left(v_0>0\right)$ enters in an electric 36. $\mu$-meson of charge $e$, mass $208 m_e$ moves in a circular orbit around a heavy nucleus having charge $+3 e$. The qua 37. A nucleus with atomic mass number $A$ produces another nucleus by loosing 2 alpha particles. The volume of the new nucle 38. A full wave rectifier circuit is operating from 50 Hz mains. The fundamental frequency in the ripple output will be
39. A p-n junction diode is used as
40. A carrier is simultaneously modulated by two sine waves with modulation indices of 0.3 and 0.4 , then the total modulati
1
AP EAPCET 2024 - 20th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$S=\{z \in C /|z+1-i|=1\}$ represents
A
the circle with centre at $(-1,1)$ and radius 1 unit
B
the circle with cente at $(1,-1)$ and radius 1 unit
C
the closed circular disc with centre at $(1,-1)$ and radius 1 unt
D
the closed circular disc with centre at( $-1,1$ ) and radius 1 unt
2
AP EAPCET 2024 - 20th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\cos \alpha+\cos \beta+\cos \gamma=\sin \alpha+\sin \beta+\sin \gamma=0$, then $\left(\cos ^3 \alpha+\cos ^3 \beta+\cos ^3 \gamma\right)^2+\left(\sin ^3 \alpha+\sin ^3 \beta+\sin ^3 \gamma\right)^2=$
A
1
B
$\frac{3}{4}$
C
$\frac{9}{16}$
D
$\frac{9}{8}$
3
AP EAPCET 2024 - 20th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\alpha$ and $\beta$ are two double roots of $x^2+3(a+3) x-9 a=0$ for different values of $a(\alpha>\beta)$, then the minimum value of $x^2+\alpha x-\beta=0$ is
A
$\frac{69}{4}$
B
$-\frac{69}{4}$
C
$-\frac{35}{4}$
D
$\frac{35}{4}$
4
AP EAPCET 2024 - 20th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $2 x^2+3 x-2=0$ and $3 x^2+\alpha x-2=0$ have one common root, then the sum of all possible values of $\alpha$ is
A
-35
B
7.5
C
-7.5
D
-1.5
Paper analysis
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80
Physics
40
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