Chemistry
1. The de-Broglie wavelength of a particle of mass 1 mg moving with a velocity of $10 \mathrm{~ms}^{-1}$ is $\left(\mathrm{ 2. Correct set of four quantum numbers for the valence electron of strontium $(z=38)$ is 3. Match of following. .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;bord 4. The bond lengths of diatomic molecules of elements $X$, $Y$ and $Z$ respectively are 143, 110 and 121 pm . The atomic nu 5. The correct formula used to determine the formal charge (Q) on an atom in the given Lewis structure of a molecule or ion 6. RMS velocity of one mole of an ideal gas was measen at different temperatures. A graph of $\left(\mu_{\mathrm{ma}}\right 7. Given below are two statements.Statement I : Viscosity of liquid decreases with increase in temperature.Statement II : T 8. A hydrocarbon containing C and H has $92.3 \% \mathrm{C}$ When 39 g of hydrocarbon was completely burnt in 0 $X$ moles o 9. At 300 K for the reaction. $A \rightarrow P$. The $\Delta S_p$ is $5 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$, What is the h 10. Identify the incorrect statements form the following.I. $ \Delta S_{\text {pum }}=\left(\Delta S_{\text {nal }}+\Delta S 11. At $T(\mathrm{~K}), K_c$ for the reaction $A_2(g) \rightleftharpoons B_2(g)$ is 99.0 . Two moles of $A_2(s)$ was heated 12. At $27^{\circ} \mathrm{C}$, the degree of dissociation of weak acid ( $\mathrm{H} A$ ) in its 0.5 M aqueous solution is 13. Aluminium carbide on reaction with $\mathrm{D}_2 \mathrm{O}$ gives $\mathrm{Al}(O D)_3$ and ' $X^{\prime}$. What is ' $X 14. Lithium forms an alloy with ' $X$ '. This alloy is used to make armour plates. What is ' $X$ ' ? 15. In which of the following reaction, dilhydrogen is not evolved? 16. Match the following. .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;bor 17. Arrange the following pestidides in the chronological order of their release into the market.Organophosphates Organochlo 18. From the following identify the groups that exhibit negative resonance $(-R)$ effect when attached to conjugated system$ 19. A dibromide $X\left(\mathrm{C}_4 \mathrm{H}_4 \mathrm{Br}_2\right)$ on dehydrohalogenation gave $Y$ which on reduction w 20. The diffraction pattern of crystalline solid gave a peak at $20=60^{\circ}$. What is the distance ( in cm ) between the 21. The concentration of 1 L of $\mathrm{CaCO}_3$ solution is 1000 ppm . What is its concentration in mol $\mathrm{L}^{-1}$ 22. At 293 K , methane gas was passed into 1 L . of water. The partial pressure of methane is 1 bar. The number of moles of 23. The $E^{-}$of $M\left|M^{2+} \| \mathrm{Cu}^{2+}\right| \mathrm{Cu}$ is 0.3 V .At what concentration of $\mathrm{Cu}^{2+ 24. At 298 K , for a first order resction $(A \rightarrow P)$ the following graph is obtained. The rate constant ( in s ${ } 25. Given below are two statements.Statements I Easily liqueflable gases are readily adsorbed.Statements II Adsorption entha 26. The validity of Freundlich isotherm can be verified by plotting 27. Which one of the following sets in not correctly matched? 28. When chlorine reacts with hot and conc. NaOH . The products formed are 29. Identify the basic oxide from the following. 30. Which of the following does not show optical isomerism? 31. A polymer $X$ is biodegradable and is obtained from the monomers $Y, Z$. What are $Y$ and $Z$ ? 32. Which of the following is an essential amino acid ? 33. Which of the following hormone is responsible for preparing uterus for implantation of fertilised eggs? 34. Identify the correct set form the following. 35. Chlorobenzene ( $X$ ) when reacted with reagent $(A)$ geb converted to phenol $(Y)$. The major product obtained from nit 36. Match the following reactions with the prodact obtained from them. .tg {border-collapse:collapse;border-spacing:0;} .t 37. What are $X$ and $Y$ respectively in the following reaction sequence? 38. Arrange the following in decreasing order of their acidity. 39. What are $X$ and $Y$ in the following set of reactions? 40. An alkyl halide $\mathrm{C}_3 \mathrm{H}_7 \mathrm{CL}$. on reaction with a reagent $X$ gave the major product $Y\left(\
Mathematics
1. If a function $ f:R \rightarrow R $ is defined by $ f(x) = x^3 - x $, then $ f $ is 2. If $ f(x) = \sqrt{x - 1} $ and $ g(f(x)) = x + 2x^2 + 1 $, then $ g(x) $ is 3. For all positive integers $ n $ if $ 3^{2n+1} + 2^{n+1} $ is divisible by $ k $, then the number of prime numbers less t 4. If $ \alpha, \beta, \gamma $ are the roots of $ \begin{bmatrix} 1 & -x & -2 \\ -2 & 4 & -x \\ -2 & 1 & -x \end{bmatrix} 5. If the determinant of a 3rd order matrix $ A $ is $ K $, then the sum of the determinants of the matrices $ A^4 $ and $ 6. While solving a system of linear equations $A X=B$ using Cramer's rule with the usual notation if$$ \Delta=\left|\begin{ 7. If real parts of $\sqrt{-5-12 i}, \sqrt{5+12 i}$ are positive values, the real part of $\sqrt{-8-6 i}$ is a negative val 8. The set of all real values of $ c $ for which the equation $ z\overline{z} + (4 - 3i)z + (4 + 3i)\overline{z} + c = 0 $ 9. If $ z = x + iy $ is a complex number, then the number of distinct solutions of the equation $ z^3 + \overline{z} = 0 $ 10. If the roots of the quadratic equation $ x^2 - 35x + c = 0 $ are in the ratio 2 : 3 and $ c = 6K $, then $ K = $ 11. For real values of $ x $ and $ a $, if the expression $ \frac{x^3 - 3x^2 - 3x + 1}{2x^2 - 3x + 1} $ assumes all real val 12. If the sum of two roots $\alpha, \beta$ of the equation $x^4-x^3-8 x^2+2 x+12=0$ is zero and $\gamma, \delta(\gamma>\del 13. $f(x+h)=0$ represents the transformed equation of the equation $f(x)=x^4+2 x^3-19 x^2-8 x+60=0$. If this transformation 14. The number of different ways of preparing a garland using 6 distinct white roses and 6 distinct red roses such that no t 15. The number of ways a committee of 8 members can be formed from a group of 10 men and 8 women such that the committee con 16. If all the letters of the word CRICKET are permuted in all possible ways and the words (with or without meaning), thus f 17. The square root of independent term in the expansion of $ \left( 2x^2 + \frac{5}{x} \right)^5 $ is 18. The coefficient of $x^5$ in $\left(3+x+x^2\right)^6$ is 19. The absolute value of the difference of the coefficients of $x^4$ and $x^6$ in the expansion of $x^2 - 2x^2 + (x + 1)^4( 20. $ \tan 6^\circ + \tan 42^\circ + \tan 66^\circ + \tan 78^\circ = $ 21. The maximum value of $12\sin x - 5\cos x + 3$ is 22. $\sin^2 16^\circ - \sin^2 76^\circ = $ 23. $1+\sin x+\sin ^2 x+\sin ^3 x+\ldots \ldots+\infty=4+2 \sqrt{3}$ and $0 24. $\tan^{-1} 2 + \tan^{-1} 3 = $ 25. $\cosh 1 + 2 = $ 26. In $\triangle ABC$, $\cos A + \cos B + \cos C = $ 27. In a $\triangle A B C$, if $a=26, b=30, \cos c=\frac{63}{65}$, then $c=$ 28. If $H$ is orthocentre of $\triangle A B C$ and $A H=x ; B H=y$; $C H=z$, then $\frac{a b c}{x y z}=$ 29. In a regular hexagon $A B C D E F, \mathbf{A B}=\mathbf{a}$ and $\mathbf{B C}=\mathbf{b}$, then $F A=$ 30. If the points with position vectors $(\alpha \hat{\mathbf{i}}+10 \hat{\mathbf{j}}+13 \hat{\mathbf{k}}),(6 \hat{\mathbf{i 31. If $\mathbf{f}, \mathbf{g}, \mathbf{h}$ be mutually orthogonal vectors of equal magnitudes, then the angle between the v 32. Let $\mathbf{a}, \mathbf{b}$ be two unit vectors. If $\mathbf{c}=\mathbf{a}+2 \mathbf{b}$ and $\mathbf{d}=5 \mathbf{a}-4 33. If the vectors $\mathbf{a}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mat 34. For a set of observations, if the coefficient of variation is 25 and mean is 44 , then the variance is 35. If 5 letters are to be placed in 5 -addressed envelopes, then the probability that atleast one letter is placed in the w 36. A student writes an examination which contains eight true of false questions. If he answers six or more questions correc 37. The probabilities that a person goes to college by car is $\frac{1}{5}$, by bus is $\frac{2}{5}$ and by train is $\frac{ 38. $P, Q$ and $R$ try to hit the same target one after the other. If their probabilities of hitting the target are $\frac{2 39. A box contains $20 \%$ defective bulbs. Five bulbs are chosen randomly from this box. Then, the probability that exactly 40. If a random variable $X$ satisfies poisson distribution with a mean value of 5 , then probability that $X 41. The equation $a x y+b y=c y$ represents the locus of the points which lie on 42. If the axes are rotated through an angle $45^{\circ}$ about the origin in anticlockwise direction, then the transformed 43. If the lines $3 x+y-4=0, x-\alpha y+10=0, \beta x+2 y+4=0$ and $3 x+y+k=0$ represent the sides of a square, then $\alpha 44. $A$ is the point of intersection of the lines $3 x+y-4=0$ and $x-y=0$. If a line having negative slope makes an angle of 45. $2 x^2-3 x y-2 y^2=0$ represents two lines $L_1$ and $L_2$. $2 x^2-3 x y-2 y^2-x+7 y-3=0$ represents another two lines $ 46. The area of the triangle formed by the pair of lines $23 x^2-48 x y+3 y^2=0$ with the line $2 x+3 y+5=0$, is 47. If $\theta$ is the angle between the tangents drawn from the point $(2,3)$ to the circle $x^2+y^2-6 x+4 y+12=0$ then $\t 48. If $2 x-3 y+3=0$ and $x+2 y+k=0$ are conjugate lines with respect to the circle $S=x^2+y^2+8 x-6 y-24=0$, then the lengt 49. If $Q(h, k)$ is the inverse point of the point $P(1,2)$ with respect to the circle $x^2+y^2-4 x+1=0$, then $2 h+k=$ 50. If $(a, b)$ and ( $c, d)$ are the internal and external centres of similitudes of the circles $x^2+y^2+4 x-5=0$ and $x^2 51. A circle $s$ passes through the points of intersection of the circles $x^2+y^2-2 x+2 y-2=0$ and $x^2+y^2+2 x-2 y+1=0$. I 52. The line $x-2 y-3=0$ cuts the parabola $y^2=4 \operatorname{ar}$ at the points $P$ and $Q$. If the focus of this parabol 53. If $4 x-3 y-5=0$ is a normal to the ellipse $3 x^2+8 y^2=k$, then the equation of the tangent drawn to this ellipse at t 54. If the line $5 x-2 y-6=0$ is a tangent to the hyperbola $5 x^2-k y^2=12$, then the equation of the normal to this hyperb 55. If the angle between the asymptotes of the hyperbola $x^2-k y^2=3$ is $\frac{\pi}{3}$ and $e$ is its eccentricity, then 56. Let $P(\alpha, 4,7)$ and $Q(\beta, \beta, 8)$ be two points. If $Y Z$-plane divides the join of the points $P$ and $Q$ i 57. If $(\alpha, \beta, \gamma)$ are the direction cosines of an angular bisector of two lines whose direction ratios are $( 58. If the distance between the planes $2 x+y+z+1=0$ and $2 x+y+z+\alpha=0$ is 3 units, then product of all possible values 59. $\lim \limits_{x \rightarrow 0} \frac{1-\cos x \cdot \cos 2 x}{\sin ^2 x}=$ 60. $\lim \limits_{x \rightarrow-1}\left(\frac{3 x^2-2 x+3}{3 x^2+x-2}\right)^{3 x-2}=$ 61. $f(x)=\left\{\begin{array}{cl}\frac{\left(2 x^2-a x+1\right)-\left(a x^2+3 b x+2\right)}{x+1}, & \text { if } x \neq-1 \ 62. If $f(x)=\left\{\begin{array}{cl}\frac{2 x e^{1 / 2 x}-3 x e^{-1 / 2 x}}{e^{1 / 2 x}+4 e^{-1 / 2 x}} & \text { if } x \n 63. If $y=\tan ^{-1}\left(\frac{2-3 \sin x}{3-2 \sin x}\right)$, then $\frac{d y}{d x}=$ 64. If $x=3\left[\sin t-\log \left(\cot \frac{t}{2}\right)\right]$ and $y=6\left[\cos t+\log \left(\operatorname{tin} \frac{ 65. By considering $1^{\prime}=0.0175$, he approximate value of $\cot 45^{\circ} 2^{\prime}$ is 66. A point is moving on the curve $y=x^3-3 x^2+2 x-1$ and the $y$-coordinate of the point is increasing at the rate d 6 uni 67. The length of the tangent drawn at the point $P\left(\frac{\pi}{4}\right)$ on the curve $x^{2 / 3}+y^{2 / 3}=2^{2 / 3}$ 68. The set of all real values of a such that the real valued function $f(x)=x^3+2 a x^2+3(a+1) x+5$ is strictly increasing 69. $\int \frac{1}{x^5 \sqrt[3]{x^3+1}} d x=$ 70. $\int \frac{x+1}{\sqrt{x^2+x+1}} d x=$ 71. $\int\left(\tan ^9 x+\tan x\right) d x=0$ 72. $\int \frac{\operatorname{cosec} x}{3 \cos x+4 \sin x} d x=$ 73. $\int e^{2 x+3} \sin 6 x d x=$ 74. $\lim \limits_{n \rightarrow+\infty}\left[{\frac{1}{n^4}+\frac{1}{\left(n^2+1\right)^{\frac{3}{2}}}+\frac{1}{\left(n^2+4 75. $\int_{\log 4}^{\log 4} \frac{e^{2 x}+e^x}{e^{2 r}-5 e^x+6} d x=$ 76. $\int_1^2 \frac{x^4-1}{x^6-1} d x=$ 77. The area of the region ( in sq units) enclosed by the curve $y=x^3-19 x+30$ and the $X$-axis, is 78. The differential equation representing the family of circles having their centres of Y -axis is $\left(y_1=\frac{d y}{d 79. The general solution of the differential equation $\left(\sin y \cos ^2 y-x \sec ^2 y\right) d y=(\tan y) d r$, is 80. The general solution of the differential equation $(x-y-1) d y=(x+y+1) d x$ is
Physics
1. Match the following． .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;bord 2. Object is projected such that it has to attain maximum range. Another body is projected to reach maximum heigh. If both 3. Ball is projected at an angle of $45^{\circ}$ with the horizontal．It passes through a wall of height $h$ at a horizontal 4. second after projection，a projectile is travelling in a direction inclined at $45^{\circ}$ to horizontal．After two more 5. Three blocks of masses $2 \mathrm{~m}, 4 \mathrm{~m}$ and 6 m are placed as shown in figure. If $\sin 37^{\circ}=\frac{3 6. Two masses $m_1$ and $m_2$ are connected by a light string passing over smooth pulley. When set free $m_1$ moves downwar 7. In an inclastic collision, after collision the kinetic energy 8. A spring of $5 \times 10^3 \mathrm{Nm}^{-1}$ spring constant is stretched initially by 10 cm from unstretched position. 9. The moment of inertia of a solid cylinder and a hollow cylinder of same mass and same radius about the axes of the cylin 10. A wheel of angular speed $600 \mathrm{rev} / \mathrm{min}$ in is made to slow down at a rate of $2 \mathrm{rad} \mathrm{ 11. Time period of a simple pendulum in air is $T$. If the pendulum is in water and executes SHM. Its time period is $t$. Th 12. For a particle executing simple harmonic motion, Match the following statements ( conditions) from Column I to statement 13. Two satellites of masses $m$ and 1.5 m are revolving around the earth with different speeds in two circular orbits of he 14. Two copper wires $A$ and $B$ of lengths in the ratio $1: 2$ and diameters in the ratio $3: 2$ are stretched by foren in 15. 216 small identical liquid drops each of surface area $A$ coalesce to form a bigger drop. If the surface tension of the 16. The length of a metal bar is 20 cm and the ares of cross-section is $4 \times 10^{-4} \mathrm{~m}^2$. If one end of the 17. The work done by an ideal gas of 2 moles in increasins its volume from $V$ to 2 V at constant temperature $T$ is V . The 18. When 403 of heat is absorbed by a monoatomic gas the increase in the internal energy of the gas is 19. In a Carnot engine, the absolute temperature of the source is $25 \%$ more than the absolute temperature of the sink. Th 20. The molar specific heat capacity of a diatomic gas at constant pressure is $C$. The molar specific heat capadtr of a mon 21. Two stretched strings $A$ and $B$ when vibrated together produce 4 beats per second. If the tension applied to the strin 22. The focal length of a thin converging lens in air is 20 cm . When thefens is immersed in a liquid, it behaves like a con 23. In Young's double slit experiment with monochromatic light of wavelength 6000 A . The fringe width is 3 mm . If the dist 24. Two point charges $+6 \mu \mathrm{C}$ and $+10 \mu \mathrm{C}$ kept at certain distance repel each other with a force of 25. In the given circuit, the potential difference across $5 \mu \mathrm{~F}$ capacitor is 26. In a region, the electric field is $30 \hat{\mathbf{i}}+40 \hat{\mathbf{j}} \mathrm{NC}^{-1}$, If the electric potential 27. In a potentiometer, the area of cross-section of the wire is $4 \mathrm{~cm}^2$. The current flowing in the circuit is 1 28. Drift speed $v$ varies with the intensity of electric field $E$ as per the relation. 29. A current carrying coil experiences a torque due to a magnetic field. The value of the torque is $80 \%$ of the maximum 30. An electron in moving with a velocity $\left[\mathbf{i}+3 \hat{\mathbf{j}} \mathrm{~ms}^{-1}\right.$ in an electric fiel 31. A magnet suspended in a uniform magnetic field is heated, so as to reduce its magnetic moment by $19 \%$. By doing this, 32. If the current through an inductor increases from 2A to 3A. The magnetic energy stored in the inductor increases by 33. In the figure. If $A$ and $B$ are identical bulbs, which bulb glows brighter. 34. The solar radiation is 35. Energy required to remove an electron from aluminium surface is 4.2 eV . If light of wavelength $2000 \mathring{A}$ fall 36. If the binding energy of the electron in a hydrogen atom is 13.6 eV . Then, energy required to remove electron from firs 37. A mixture consists of two radioactive materials $A_1$ and $A_2$ with half lives of 20 s and 10 s respectively. Initially 38. If $n_r$ and $n_h$ are concentrations of electron and holes in a semiconductor, then the intrinsic carrier concentration 39. In the given digital circuit, if the inputs are $A=1 B_x$ and $C=1$, then the value of $Y_1$ and $Y_2$ are respectino 40. If the maximum and minimum voltages of an $A M$ wave are $V_{\max }$ and $V_{\min }$ respectively. Then, the modulation
1
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\lim \limits_{x \rightarrow-1}\left(\frac{3 x^2-2 x+3}{3 x^2+x-2}\right)^{3 x-2}=$
A
-3
B
$e^{-1}$
C
$e^{-3}$
D
-1
2
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$f(x)=\left\{\begin{array}{cl}\frac{\left(2 x^2-a x+1\right)-\left(a x^2+3 b x+2\right)}{x+1}, & \text { if } x \neq-1 \\ k_k, & \text { if } x=-1\end{array}\right.$
is a real valued function. If $a, b, k \in R$ and $f$ is continuous on $R$, then $k=$
A
$-\frac{1}{3}$
B
6
C
$a-2$
D
$a=3$
3
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $f(x)=\left\{\begin{array}{cl}\frac{2 x e^{1 / 2 x}-3 x e^{-1 / 2 x}}{e^{1 / 2 x}+4 e^{-1 / 2 x}} & \text { if } x \neq 0 \\ 0 & \text { if } x=0\end{array}\right.$ is a real valued function, then
A
$f^{\prime}\left(0^{\prime}\right)=\frac{-3}{4}$
B
$f^{\prime}\left(0^{-}\right)=2$
C
$f$ is not differentiable at $x=0$
D
$f$ is differentiable at $x=0$
4
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $y=\tan ^{-1}\left(\frac{2-3 \sin x}{3-2 \sin x}\right)$, then $\frac{d y}{d x}=$
A
$\frac{(3-2 \sin x)^2}{13 \sin ^2 x-24 \sin x+13}$
B
$\frac{-5 \cos x}{13 \sin ^2 x-24 \sin x+19}$
C
$\frac{5 \sin x}{13 \sin ^2 x-24 \sin x+13}$
D
$\frac{-5 \sin x}{13 \sin ^2 x-24 \sin x+13}$
Paper analysis
Total Questions
Chemistry
40
Mathematics
80
Physics
40
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