Chemistry
1. The de-Broglie wavelength of an electron with kinetic energy of 2.5 eV is (in m$)\left(1 \mathrm{eV}=1.6 \times 10^{-19} 2. The ratio of ground state energy of $\mathrm{Li}^{2+}, \mathrm{He}^{+}, \mathrm{H}$ is
3. Two statements are given below.
Statement I : Nitrogen has more ionisation enthalpy and electronegativity than beryllium 4. The number of lone pairs of electrons on the central atom of $\mathrm{BrF}_5, \mathrm{XeO}_3, \mathrm{SO}_2$ respectivel 5. The shape of colourless neutral gas formed on thermal decomposition of ammonium nitrate is
6. At $T(\mathrm{~K})$ for one mole of an ideal gas, the graph of $p$ (on $Y$-axis) and $V^{-1}$ (on $X$-axis) gave a strai 7. At 290 K , a vessel (I) contains equal moles of three liquids $(A, B, C)$. The boiling points of $A, B$ and $C$ are $350 8. 100 mL of $0.1 \mathrm{M} \mathrm{Fe}^{2+}$ solution was titrated with $\frac{1}{60} \mathrm{M}$ $\mathrm{Cr}_2 \mathrm{ 9.
Observe the following reaction.
$$ A B \mathrm{O}_3(\mathrm{~s}) \xrightarrow{1000 \mathrm{~K}} A \mathrm{O}(\mathrm{~ 10. A vessel of volume $V \mathrm{~L}$ contains an ideal gas are $T(\mathrm{~K})$. The vessel is partitioned into two equal 11. At $300 \mathrm{~K}, \Delta_r G^{\Theta}$ for the reaction $A_2(g) \rightleftharpoons B_2(g)$ is $-11.5 \mathrm{~kJ} \ma 12. 100 mL of $0.1 \mathrm{M} \mathrm{H} A$ (weak acid) and 100 mL of 0.2 M $\mathrm{Na} A$ are mixed. What is the pH of res 13. Identify the correct statements from the following.
I. Reaction of hydrogen with fluorine occurs even in dark.
II. Manuf 14. Which one of the following alkali metals is the weakes reducing agent as per their $E^{\circ}$ values?
15. In which of the following reactions, hydrogen is oned the products?
I. $\mathrm{NaBH}_4+\mathrm{I}_2 \longrightarrow$
II 16. Two statements are given below.
Statement I : $\mathrm{SnF}_4, \mathrm{PbF}_4$ are ionic in nature.
Statement II : GeCl 17. Match the pollutant is List I with its maximum permissible limit in drinking water given in List II
.tg {border-colla 18. Species $A, B, C, D$ formed in the following bond cleavages respectively are
19. What are $X$ and $Y$ respectively in the following reaction sequence?
20. A compound is formed by atoms of $A, B$ and $C$. Atoms of $C$ form hcp lattice. Atoms of $A$ occupy $50 \%$ of octahedra 21. At $300 \mathrm{~K}, 6 \mathrm{~g}$ of urea was dissolved in 500 mL of water. What is the osmotic pressure (in atm) of r 22. In water, which of the following gases has the highest Henry's law constant at 293 K ?
23. Consider the cell reaction at 300 K .
$$ A(s)+B^{2+}(a q) \rightleftharpoons A^{2+}(a q)+B(s) $$
Its $E^{\ominus}$ is 1. 24. The rate constant of a first order reaction was doubled when the temperature was increased from 300 to 310 K . What is i 25. Which of the following solutions is used in the styptic action which prevents bleeding of blood?
26. ' $A$ ' is a protecting colloid. The following data is obtained for preventing the coagulation of 10 mL of gold sol to w 27. Two statements are given below.
Statement I : The reaction $\mathrm{Cr}_2 \mathrm{O}_3+2 \mathrm{Al} \longrightarrow \ma 28. The basicity of $\mathrm{H}_3 \mathrm{PO}_2, \mathrm{H}_3 \mathrm{PO}_3 \cdot \mathrm{H}_3 \mathrm{PO}_4$ respectively i 29. Which of the following reactions of $\mathrm{KMnO}_4$ occurs in acidic medium ?
30. Which complex among the follwing is most paramagnetic?
31. Polymers that can be softened on heating and hardened on cooling are called
32. The number of -OH groups in open chain and ring structures of D-glucose are respectively
33. Which of the following is correct statement?
34. Which of the following is not correctly matched?
35.
Conversion of $X$ to $Y$ is an example of 36. Which of the following is not an example of allylic halide?
37. What is the major product ' $Z$ ' in the following reaction sequence?
38. Consider the following reactions
$Y$ can not be obtained from which of the following reaction?
39. Assertion (A) : Carboxylic acids are more acidic than phenols
Reason (R) : Resonance structures of carboxylate ion are e 40. In the reaction sequence $Y$ is
$$ \mathrm{CH}_3 \mathrm{CO}_2 \mathrm{H} \xrightarrow[(2) \Delta]{(1) \mathrm{NH}_3} P
Mathematics
1. The range of the real valued function $f(x)=\frac{15}{3 \sin x+4 \cos x+10}$ is
2. Define the function, $f, g$ and $h$ from $R$ to $R$ such that $f(x)=x^2-1, g(x)=\sqrt{x^2+1}$ and $h(x)= \begin{cases}0, 3. If $P$ is the greatest divisor of $49^n+16 n-1$ for all $n \in N$, then the number of factors of $P$ is
4. $A=\left[\begin{array}{lll}0 & 1 & 2 \\ 2 & 3 & 0 \\ 4 & 0 & 3\end{array}\right]$ and $B$ is a matrix such that $A B=B A 5. If $\alpha, \beta$ and $\gamma(\alpha 6. The system of linear equations $x+2 y+z=-3$, $3 x+3 y-2 z=-1$ and $2 x+7 y+7 z=-4$ has
7. $\arg \left[\frac{(1+i \sqrt{3})(-\sqrt{3}-i)}{(1-i)(-i)}\right]$ is equal to
8. If $P(x, y)$ represents the complex number $z=x+iy$ in the argand plane and $\arg \left(\frac{z-3 i}{z+4}\right)=\frac{\ 9. If $\cos \alpha+4 \cos \beta+9 \cos \gamma=0$ and $\sin \alpha+4 \sin \beta+9 \sin \gamma=0$, then 81 $\cos (2 \gamma-2 10. If ' $a$ ' is a rational number, then the roots of the equation $x^2-3 a x+a^2-2 a-4=0$ are
11. The set of all real values ' $a$ ' for which $-1 12. The quotient, when $3 x^5-4 x^4+5 x^3-3 x^2+6 x-8$ is divided by $x^2+x-3$ is 13. If $\alpha_1, \alpha_2, \alpha_3, \alpha_4$ and $\alpha_5$ are the roots of $x^5-5 x^4+9 x^3-9 x^2+5 x-1=0$, then $\frac 14. There were two women participating with some men in a chess tournament. Each participant played two games with the other 15. The number of ways of arranging 9 men and 5 women around circular table, so that no two women come together are
16. If there are 6 alike fruits, 7 alike vegetables and 8 alike biscuits, then the number of ways of selecting any number of 17. If the coefficients of $r$ th, $(r+1)$ th and $(r+2)$ th terms in the expansion of $(1+x)^n$ are in the ratio of $4: 15: 18. If the coefficients of $(2 r+6)$ th and $(r-1)$ th terms in the expansion of $(1+x)^{21}$ are equal, then the value of $ 19. $$ \text { If } \frac{13 x+43}{2 x^2+17 x+30}=\frac{A}{2 x+5}+\frac{B}{x+6} \text {, then } A+B \text { is equal to } $$ 20. $\tan \alpha+2 \tan 2 \alpha+4 \tan 4 \alpha+8 \cot 8 \alpha$ is equal to
21. $\tan 9^{\circ}-\tan 27^{\circ}-\tan 63^{\circ}+\tan 81^{\circ}$ is equal to
22. $\cos 6^{\circ} \sin 24^{\circ} \cos 72^{\circ}$ is equal to
23. The values of $x$ in $(-\pi, \pi)$, which satisfy the equation $8^{1+\cos ^2 x+\cos ^4 x+\ldots \ldots}=4^3$ are 24. $\cot \left(\sum\limits_{n=1}^{50} \tan ^{-1}\left(\frac{1}{1+n+n^2}\right)\right)$ is equal to
25. If $\sinh x=\frac{\sqrt{21}}{2}$, then $\cosh 2 x+\sinh 2 x$ is equal to 26. In a $\triangle A B C$, if $a=13, b=14$ and $c=15$, then $r_1=$
27. In $a \triangle A B C$ if $r: R: r_2=1: 3: 7$, then $\sin (A+C)+\sin B$ is equal to 28. In $\triangle A B C,\left(r_1+r_2\right) \operatorname{cosec}^2 \frac{C}{2}$ is equal to 29. If $A=(1,2,3), B=(3,4,7)$ and $C=(-3,-2,-5)$ are three points, then the ratio in which the point $C$ divides $A B$ exter 30. If the vectors $a \hat{\mathbf{i}}+\mathbf{j}+3 \hat{\mathbf{k}}, 4 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}+\hat{\mathbf{k}} 31. Let $|\hat{\mathbf{a}}|=2=|\hat{\mathbf{b}}|=3$ and the angle between $\hat{\mathbf{a}}$ and $\hat{\mathbf{b}}$ be $\fra 32. The values of $x$ for which the angle between the vectors $x^2 \hat{\mathbf{i}}+2 x \hat{\mathbf{j}}+\hat{\mathbf{k}}$ a 33. If $\hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf 34. Based on the following statements, choose the correct option.
Statement I The variance of the first $n$ even natural num 35. If each of the coefficients $a, b$ and $c$ in the equation $a x^2+b x+c=0$ is determined by throwing a die, then the pro 36. $A$ and $B$ throw a pair of dice alternately and they note the sum of the numbers appearing on the dice. $A$ wins if he 37. $E_1$ and $E_2$ are two independent events of a random experiment such that $P\left(E_1\right)=\frac{1}{2}$ and $P\left( 38. A bag contains 4 red and 5 black balls. Another bag contains 3 red and 6 black balls. If one ball is drawn from first ba 39. If a random variable $X$ has the following probability distribution, then its variance is nearly
$$ \begin{array}{clllll 40. A radar system can detect an enemy plane in one out of 10 consecutive scans. The probability that it cannot detect an en 41. The locus of a variable point which forms a triangle of fixed area with two fixed points is
42. If the axes are rotated through angle ' $\alpha$ ', then the number of values of a such that the transformed equation of 43. $A$ line $L$ passing through the point $P(-5,-4)$ cuts the lines $x-y-5=0$ and $x+3 y+2=0$ respectively at $Q$ and $R$ s 44. If the reflection of a point $A(2,3)$ in $X$-axis is $B$, reflection of $B$ in the line $x+y=0$ is $C$ and the reflectio 45. The equation of a line which makes an angle of $45^{\circ}$ with each of the pair of lines $x y-x-y+1=0$ is
46. If the slope of one of the lines in the pair of lines $8 x^2+a x y+y^2=0$ is thrice the slope of the second line, then $ 47. The triangle $P Q R$ is inscribed in the circle $x^2+y^2=25$. If $Q=(3,4)$ and $R=(-4,3)$, then $\angle Q P R$ is equal 48. The locus of the point of intersection of perpendicular tangents drawn to the circle $x^2+y^2=10$ is
49. The normal drawn at $(1,1)$ to the circle $x^2+y^2-4 x+6 y-4=0$ is
50. Parametric equations of the circle $2 x^2+2 y^2=9$ are
51. Angle between the circles $x^2+y^2-4 x-6 y-3=0$ and $x^2+y^2+8 x-4 y+11=0$ is
52. Equation of the line touching both parabolas $y^2=4 x$ and $x^2=-32 y$ is
53. The length of the latusrectum of $16 x^2+25 y^2=400$ is
54. The line $21 x+5 y=k$ touches the hyperbola $7 x^2-5 y^2=232$, then $k$ is equal to
55. If the equation $\frac{x^2}{7-k}+\frac{y^2}{5-k}=1$ represents a hyperbola, then
56.
If a line $L$ makes angles $\frac{\pi}{3}$ and $\frac{\pi}{4}$ with $Y$-axis and $Z$-axis respectively, then the angle 57. If $l, m$ and $n$ are the direction cosines of a line that is perpendicular to the lines having the direction ratios $(1 58. The foot of the perpendicular drawn from a point $A(1,1,1)$ on to a plane $\pi$ is $P(-3,3,5)$.If the equation of the pl 59. $$\mathop {\lim }\limits_{x \to \infty } \frac{[2 x-3]}{x} \text { is equal to } $$
60. $\mathop {\lim }\limits_{x \to 0}\frac{\cos 2 x-\cos 3 x}{4 x-\cos 5 x}$ is equal to $\cos 4 x-\cos 5 x$
61. If a real valued function $f(x)=\left\{\begin{array}{cl}\frac{2 x^2+(k+2) x+9}{3 x^2-7 x-6}, & \text { for } x \neq 3 \\ 62. If $y=\tan ^{-1} \frac{x}{1+2 x^2}+\tan ^{-1} \frac{x}{1+6 x^2}+\tan ^{-1} \frac{x}{1+12 x^2}$, then $\left(\frac{d y}{d 63. If $f(x)=5 \cos ^3 x-3 \sin ^2 x$ and $g(x)=4 \sin ^3 x+\cos ^2 x$, then the derivative of $f(x)$ with respect to $g(x)$ 64. If $y=1+x+x^2+x^3+\ldots \ldots \infty$ and $|x| 65. The semi-vertical angle of a right circular cone is $45^{\circ} \%$ If the radius of the base of the cone is measured as 66. If a man of height 1.8 mt , is walking away from the foot of a light pole of height 6 mt , with a speed of 7 km per hour 67. If the curves $2 x^2+k y^2=30$ and $3 y^2=28 x$ cut each other orthogonally, then $k$ is equal to 68. The interval containing all the real values of $x$ such that the real valued function $f(x)=\sqrt{x}+\frac{1}{\sqrt{x}}$ 69. $\int e^{4 x^2+8 x-4}(x+1) \cos \left(3 x^2+6 x-4\right) d x$ is equal to
70. $\int\left[(\log 2 x)^2+2 \log 2 x\right] d x$ is equal to
71. If $\int \log \left(6 \sin ^2 x+17 \sin x+12\right) \cos x d x=f(x)+c$, then $f\left(\frac{\pi}{2}\right)$ is equal to 72. $\int \frac{1}{\left(1+x^2\right) \sqrt{x^2+2}} d x$ is equal to
73. $\int \sin ^4 x \cos ^4 x d x$ is equal to
74. $\int_0^1 \sqrt{\frac{2+x}{2-x}} d x$ is equal to
75. If $M=\int\limits_0^{\infty} \frac{\log t}{1+t^3} d t$ and $N=\int\limits_{-\infty}^{\infty} \frac{t e^{2 t}}{1+e^{3 t}} 76. $\int\limits_{-2}^2\left(4-x^2\right)^{\frac{5}{2}} d x$ is equal to
77. $$ \mathop {\lim }\limits_{x \to \infty }\left[\left(1+\frac{1}{n^3}\right)^{\frac{1}{n^3}}\left(1+\frac{8}{n^3}\right)^ 78. $\int\limits_{-5 \pi}^{5 \pi}(1-\cos 2 x)^{\frac{5}{2}} d x$ is equal to
79. The differential equation of the family of hyperbols having their centres at origin and their axes along coordinates axe 80. The general solution of the differential equation $\left(x y+y^2\right) d x-\left(x^2-2 x y\right) d y=0$ is
Physics
1. In the equation $\left(p+\frac{a}{V^2}\right)(V-b)=R T$, where $p$ is pressure, $V$ is volume, $T$ is temperature, $R$ i 2. A particle starts from rest and moves in a straight line. It travels a distance $2 L$ with uniform acceleration and then 3. A boy throws a ball with a velocity $v_0$ at an angle $\alpha$ to the ground. At the same time he starts running with un 4. A ball at point $O$ is at a horizontal distance of 7 m from a wall. On the wall a target is set at point $C$. If the bal 5. The acceleration of a body sliding down the inclined plane, having coefficient of friction $\mu$ is
6. A body of 2 kg mass slides down with an acceleration of $4 \mathrm{~ms}^{-2}$ on an inclined plane having slope of $30^{ 7. A body of mass 30 kg moving with a velocity $20 \mathrm{~ms}^{-1}$ undergoes one-dimensional elastic collision with anot 8. A force of $(4 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}) \mathrm{N}$ is action on a particle of mass 2 kg di 9. Two blocks of equal masses are tied with a light string passing over a massless pulley (assuming frictionless surfaces ) 10. A ring and a disc of same mass and same diameter are rolling without slipping. Their linear velocities are same, then th 11. The displacement of a particle of mass 2 g executing simple harmonic motion is $x=8 \cos \left(50 t+\frac{\pi}{12}\right 12. The relation between the force ( $F$ in Newton) acting on a particle executing simple harmonic motion and the displaceme 13. The gravitational potential energy of a body on the surface of the earth is $E$. If the body is taken from the surface o 14. A wire of length 100 cm and area of cross-section $2 \mathrm{~mm}^2$ is stretched by two forces of each 440 N applied at 15. Two cylindrical vessels $A$ and $B$ of different areas of cross-section kept on same horizontal plane are filled with wa 16. Water of mass $m$ at $30^{\circ} \mathrm{C}$ is mixed with with 5 g of ice at $-20^{\circ} \mathrm{C}$. If the resultant 17. Two ideal gases $A$ and $B$ of same number of moles expand at constant temperatures $T_1$ and $T_2$ respectively such th 18. When 80 J of heat is absorbed by a monoatomic gas, its volume increases by $16 \times 10^{-5} \mathrm{~m}^3$. The pressu 19. The efficiency of a Carnot heat engine is $25 \%$ and the temperature of its source is $127^{\circ} \mathrm{C}$. Without 20. The total internal energy of 2 moles of a monoatomic gas at a temperature $27^{\circ} \mathrm{C}$ is $U$. The total inte 21. The fundamental frequency of an open pipe is 100 hz If the bottom end of the pipe is closed and $1 / 3$ rd of the pipe i 22. When a convex lens is immersed in a liquid of refractive index equal to $80 \%$ of the refractive index of the material 23. The angle between the axes of a polariser and an analyser is $45^{\circ}$. If the intensity of the unpolarised light inc 24. The magnitude of an electric field which can just suspend a deuteron of mass $3.2 \times 10^{-27} \mathrm{~kg}$ freely i 25. Two charges 5 nC and -2 nC are placed at points $( 5 cm\mathrm{~}$ $0,0)$ and $(23 \mathrm{~cm}, 0,0)$ in a region of sp 26. The space between the plates of a parallel plate capacitor is halved and a dielectric medium of relative permittivity 10 27. A battery of emf 8 V and internal resistance $0.5 \Omega$ is being charged by a 120 V DC supply using a series resister 28. Resistance of a wire is $8 \Omega$. It is drawn in such a way that it experiences a longitudinal strain of $400 \%$. The 29. Current flows in a conductor from east to west. The direction of the magnetic field at a point below the conductor is to 30. Two infinite length wires carry currents 8 A and $6^{\mathrm{A}}$ respectively and are placed along $X$ and $Y$-axes res 31. A short magnet oscillates with a time period 0.1 s at a place where horizontal magnetic field is $24 \mu \mathrm{~T}$. A 32. A metallic wire loop of side $(l) 0.1 \mathrm{~m}$ and resistance of $1 \Omega$ is moved with a constant velocity in a u 33. In the circuit shown in the figure, neglecting the source resistance, the voltmeter and ammeter readings respectively ar 34. The radiation of energy $E$ falls normally on a perfectly reflecting surface. The momentum transferred to the surface is 35. Light of wavelength $4000\mathop {\rm{A}}\limits^{\rm{o}}$ is incident on a sodium surface for which the threshold wavel 36. The principle quantum number $n$ corresponding to the exited state of $\mathrm{He}^{+}$ion. If on transition to the grou 37. Which physical quantity is measured in barn?
38. $$ \text { Truth table for the given circuit is } $$
39. If $R_C$ and $R_B$ are respectively the resistances of in collector and base sides of the circuit and $\beta$ is the cur 40. Which one of the following is not classified as pulse modulation?
1
AP EAPCET 2024 - 22th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $y=1+x+x^2+x^3+\ldots \ldots \infty$ and $|x|<1$, then $y^{\prime \prime}$ is equal to
A
$2 y^{\prime}$
B
$\frac{2 y}{y^{\prime}}$
C
$\frac{y^{\prime}}{2 y}$
D
$2 y^2 y^{\prime}$
2
AP EAPCET 2024 - 22th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
The semi-vertical angle of a right circular cone is $45^{\circ} \%$ If the radius of the base of the cone is measured as 14 cm with an error of $\left(\frac{\sqrt{2}-1}{11}\right) \mathrm{cm}$, then the approximate error in measuring its total surface area is (in sq cm)
A
14
B
8
C
5
D
3
3
AP EAPCET 2024 - 22th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If a man of height 1.8 mt , is walking away from the foot of a light pole of height 6 mt , with a speed of 7 km per hour on a straight horizontal road opposite to the pole, then the rate of change of the length of his shadow is (in kmph )
A
7
B
5
C
3
D
2
4
AP EAPCET 2024 - 22th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If the curves $2 x^2+k y^2=30$ and $3 y^2=28 x$ cut each other orthogonally, then $k$ is equal to
A
5
B
3
C
2
D
1
Paper analysis
Total Questions
Chemistry
40
Mathematics
80
Physics
40
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