Chemistry
1. The difference in radii between fourth and third Bohr orbit of $\mathrm{He}^{+}($in m$)$ is
2. If $\lambda_0$ and $\lambda$ are respectively the threshold wavelength and wavelength of incident light the velocity of 3. The correct order of atomic radii of $\mathrm{N}, \mathrm{F}, \mathrm{Al}, \mathrm{Si}$ is
4. The correct order of covalent bond character of $\mathrm{BCl}_3, \mathrm{CCl}_4, \mathrm{BeCl}_2, \mathrm{LiCl}$ is
5. In which of the following pairs, both molecules possess dipole moment?
6. At $T(\mathrm{~K})$, the $p, V$ and $u_{\mathrm{rms}}$ of 1 mole of an ideal gas were measured. The following graph is o 7. Three layers of liquid are flowing over fixed solid surface as shown below. The correct order of velocity of liquid in t 8. A flask contains 98 mg of $\mathrm{H}_2 \mathrm{SO}_4$. If $3.01 \times 10^{20}$ molecules of $\mathrm{H}_2 \mathrm{SO}_ 9. Identify the correct equation relating $\Delta H, \Delta U$ and $\Delta T$ for 1 mole of an ideal gas from the following 10. The number of extensive properties in the following list is enthalpy, density, volume, internal energy, temperature.
11. 15 moles of $\mathrm{H}_2$ and 5.2 moles of $\mathrm{I}_2$ are mixed and allowed to attain equilibrium at 773 K . At equ 12. The solubility of barium phosphate of molar mass ' $M$ ' $\mathrm{g} \mathrm{mol}^{-1}$ in water is $x \mathrm{~g}$ per 13. Hydrated sodium aluminium silicate is called
14. Which one of the following statements is not correct about the compounds of alkaline earth metals?
15. Consider the following standard electrode potentials ( $E^{\circ}$ in volts) in aqueous solution.
$$ \begin{array}{|c|c| 16. Which of the allotropic forms of carbon is aromatic in nature?
17. The enamel present on teeth becomes much harder due to the conversion of $\left[3 \mathrm{Ca}_3\left(\mathrm{PO}_4\right 18. Number of deactivating group of the following is
$$
-\mathrm{Cl},-\mathrm{SO}_3 \mathrm{H},-\mathrm{OH},-\mathrm{NHC}_2 19. What are $X$ and $Y$ respectively in the following reaction sequence?
20. Identify the incorrect set from the following.
21. The following graph is obtained for vapour pressure (in atm) (on $Y$-axis) and $T$ (in K) (on $X$-axis) for aqueous urea 22. Given below are two statements.
Statement I : Liquids $A$ and $B$ form a non-ideal solution with negative deviation. The 23. The standard reduction potentials of $2 \mathrm{H}^{+} / \mathrm{H}_2, \mathrm{Cu}^{2+} / \mathrm{Cu}, \mathrm{Zn}^{2+} 24. $A \rightarrow P$ is a zero order reaction. At 298 K the rate constant of the reaction is $1 \times 10^{-3} \mathrm{~mol 25. $$ \text { Match List - I, with List-II. } $$
$$ \begin{array}{llll} \hline & \text { List I } & & \text { List II } \\ 26. Identify the method of preparation of a colloidal sol from the following.
27. The flux used in the preparation of wrought iron from cast iron in reverberatory furnace is
28. $\mathrm{P}_2 \mathrm{O}_3+\mathrm{H}_2 \mathrm{O} \rightarrow X$, Red $\mathrm{P}_4+$ alkali $\rightarrow Y$
$X, Y$ are 29. Which of the following occurs with $\mathrm{KMnO}_4$ in neutral medium?
30. Cobalt (III) chloride forms a green coloured complex ' $X$ ' with $\mathrm{NH}_3$. Number of moles of AgCl formed when e 31. The correctly matched set of the following is
32. Identify the correctly matched set from the following.
33. Given below are two statements.
I. Cytosine and guanine are formed in equal quantities in DNA hydrolysis.
II. Adenine an 34. $$ \text { Identify the correctly matched pair from the following. } $$ 35. What are $Y$ and $Z$ respectively in the following reaction sequence?
36. Hydrolysis of an alkyl bromide $\left(\mathrm{C}_5 \mathrm{H}_{11} \mathrm{Br}\right)$ follows first order kinetics. Rea 37. An alcohol $X\left(\mathrm{C}_4 \mathrm{H}_{10} \mathrm{O}\right)$ does not give turbidity with conc. HCl and $\mathrm{Z 38. Which of the following sets of reagents convert toluene to benzaldehyde?
A. $\mathrm{Cl}_2 \mid h v ; \mathrm{H}_2 \math 39. What are $X$ and $Y$ respectively in the following reactions?
40. $$ \text { IUPAC names of the following compounds } A \text { and } B $$ are
Mathematics
1. The range of the real valued function $f(x)=\sin ^{-1}\left(\frac{1+x^2}{2 x}\right)+\cos ^{-1}\left(\frac{2 x}{1+x^2}\r 2. The real valued function $f: R \rightarrow\left[\frac{5}{2}, \infty\right)$ defined by $f(x)=|2 x+1|+|x-2|$ is
3. If $1 \cdot 3 \cdot 5+3 \cdot 5 \cdot 7+5 \cdot 7 \cdot 9+\ldots n$ terms $=n(n+1) f(n)-3 n$, then $f(l)=$
4. If $3 A=\left[\begin{array}{ccc}1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b\end{array}\right]$ and $A A^T=I$, then $\frac{a}{b} 5. $\left|\begin{array}{ccc}a+b+2 c & a & b \\ c & b+c+2 a & b \\ c & a & c+a+2 b\end{array}\right|=$
6. Assertion (A) : If $B$ is a $3 \times 3$ matrix and $|B|=6$, then $|\operatorname{adj}(B)|=36$
Reason (R) : If $B$ is a 7. Imaginary part of $\frac{(1-i)^3}{(2-i)(3-2 i)}$ is
8. The square root of $7+24 i$
9. If $n$ is an integer and $Z=\cos \theta+i \sin \theta, \theta \neq(2 n+1) \frac{\pi}{2}$, then $\frac{1+Z^{2 n}}{1-Z^{2 10. If $x$ is real and $\alpha, \beta$ are maximum and minimum values of $\frac{x^2-x+1}{x^2+x+1}$ respectively, then $\alph 11. If $\alpha$ is a common root of $x^2-5 x+\lambda=0$ and $x^2-8 x-2 \lambda=0(\lambda \neq 0)$ and $\beta, \gamma$ are t 12. The equation $x^4-x^3-6 x^2+4 x+8=0$ has two equal roots. If $\alpha, \beta$ are the other two roots of this equation, 13. The condition that the roots of $x^3-b x^2+c x-d=0$ are in arithmetic progression is
14. There are 6 different novels and 3 different poetry books on a table. If 4 novels and 1 poetry book are to be selected 15. If a five-digit number divisible by 3 is to be formed using the numbers $0,1,2,3,4$ and 5 without repetition, then the 16. Four-digit numbers with all digits distinct are formed using the digits $1,2,3,4,5,6,7$ in all possible ways.If $p$ is t 17. If the ratio of the terms equidistant from the middle term in the expansion of $(l+x)^{12}$ is $\frac{1}{256}(x \in N)$ 18. In the expansion of $\frac{2 x+1}{(1+x)(1-2 x)}$ the sum of the coefficients of the first 5 odd powers of $x$ is
19. If $\frac{x+2}{\left(x^2+3\right)\left(x^4+x^2\right)\left(x^2+2\right)}=\frac{A x+B}{x^2+3}+\frac{C x+D}{x^2+2}$ $+\fr 20. If $A, B, C$ are the angles of triangle, then $\sin 2 A-\sin 2 B+\sin 2 C=$
21. Assertion (A) : If $A=10^{\circ}, B=16^{\circ}$ and $C=19^{\circ}$, then $\tan 2 A \tan 2 B+\tan 2 B \tan 2 C+\tan 2 C \ 22. If $\alpha$ is in the 3rd quadrant, $\beta$ is in the 2nd quadrant such that $\tan \alpha=\frac{1}{7}, \sin \beta=\frac 23. Number of solutions of the trigonometric equation $2 \tan 2 \theta-\cot 2 \theta+1=0$ lying in the interval $[0, \pi]$ i 24. The real values of $x$ that satisfy the equation $\tan ^{-1} x+\tan ^{-1} 2 x=\frac{\pi}{4}$ is
25. $2 \operatorname{coth}^{-1}(4)+\sec h^{-1}\left(\frac{3}{5}\right)=$
26. If 7 and 8 are the length of two sides of a triangle and $a^{\prime}$ is the length of its smallest side. The angles of 27. In $\triangle A B C$, if $a=13, b=14$ and $\cos \frac{C}{2}=\frac{3}{\sqrt{13}}$, then $2 r_1=$
28. In $\triangle A B C$, if $\left(r_2-r_1\right)\left(r_3-r_1\right)=2 r_2 r_3$, then $2(r+R)=$
29. If $\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-\hat{\mathbf{k}},-3 \ 30. If $\mathbf{a}, \mathbf{b}, \mathbf{c}, \mathbf{d}$ are position vectors of 4 points such that $2 a+3 b+5 c-10 d=0$, the 31. If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are 3 vectors such that $|\mathbf{a}|=5,|\mathbf{b}|=8,|\mathbf{c}|=11$ and $\ma 32. Angle between the planes, $\mathbf{r} \cdot(12 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-3 \hat{\mathbf{k}})=5$ and, $\mathbf{ 33. The shortest distance between the skew lines $\mathbf{r}=(2 \hat{\mathbf{i}}-\hat{\mathbf{j}})+t(\hat{\mathbf{i}}+2 \hat 34. The coefficient of variation for the frequency distribution is
$$ \begin{array}{|c|l|l|l|} \hline \boldsymbol{x}_{\bolds 35. If all the letters of the word 'SENSELESSNESS' are arranged in all possible ways and an arrangement among them is chosen 36. If two numbers $x$ and $y$ are chosen one after the other at random with replacement from the set of number $\{1,2,3, \l 37. Bag $A$ contains 3 white and 4 red balls, bag $B$ contains 4 white and 5 red balls and bag $C$ is contains 5 white and 6 38. Two persons $A$ and $B$ throw a pair of dice alternately until one of them gets the sum of the numbers appeared on the d 39. An urn contains 3 black and 5 red balls. If 3 balls are drawn at random from the urn, the mean of the probability distri 40. If $X \sim B(5, p)$ is a binomial variate such that $P(X=3)=P(X=4)$, then $P(|X-3| 41. The perimeter of the locus of the point $P$ which divides the line segment QA internally in the ratio $1: 2$, where $A= 42. Suppose the axes are to be rotated through an angle $\theta$ so as to remove the $x y$ form from the equation $3 x^2+2 43. $P$ is a point on $x+y+5=0$, whose perpendicular distance from $2 x+3 y+3=0$ is $\sqrt{13}$, then the coordinates of $P 44. For $\lambda, \mu \in R,(x-2 y-1)+\lambda(3 x+2 y-11)=0$ and $(3 x+4 y-11)+\mu(-x+2 y-3)=0$ represent two families of li 45. If the pair of lines represented by $3 x^2-5 x y+P y^2=0$ and $6 x^2-x y-5 y^2=0$ have one line in common, then the sum 46. Area of the region enclosed by the curves $3 x^2-y^2-2 x y+4 x+1=0$ and $3 x^2-y^2-2 x y+6 x+2 y=0$ is
47. If the equation of the circle whose radius is 3 units and which touches internally the circle $x^2+y^2-4 x-6 y-12=0$ at 48. The equation of the circle touching the circle $x^2+y^2-6 x+6 y+17=0$ externally and to which the lines $x^2-3 x y-3 x+ 49. The pole of the straight line $9 x+y-28=0$ with respect to the circle $2 x^2+2 y^2-3 x+5 y-7=0$ is
50. The equation of a circle which touches the straight lines $x+y=2, x-y=2$ and also touches the circle $x^2+y^2=1$ is
51. The radical axis of the circle $x^2+y^2+2 g x+2 f y+c=0$ and $2 x^2+2 y^2+3 x+8 y+2 c=0$ touches the circle $x^2+y^2+2 52. If the ordinates of points $P$ and $Q$ on the parabola $y^2=12 x$ are in the ratio $1: 2$. Then, the locus of the point 53. The product of perpendiculars from the two foci of the ellipse $\frac{x^2}{9}+\frac{y^2}{25}=1$ on the tangent at any p 54. The value of $c$ such that the straight line joining the points $(0,3)$ and $(5,-2)$ is tangent to the curve $y=\frac{c} 55. The descending order of magnitude of the eccentricities of the following hyperbolas is
A. A hyperbola whose distance bet 56. If the plane $x-y+z+4=0$ divides the line joining the points $P(2,3,-1)$ and $Q(1,4,-2)$ in the ratio $l: m$, then $l+m$ 57. If the line with direction ratios $(1, \alpha, \beta)$ is perpendicular to the line with direction ratios $(-1,2,1)$ and 58. Let $P\left(x_1, y_1, z_1\right)$ be the foot of perpendicular drawn from the point $Q(2,-2,1)$ to the plane $x-2 y+z=1$ 59. $$\mathop {\lim }\limits_{x \to 0} \left( {{{\sin (\pi {{\cos }^2}x} \over {{x^2}}}} \right) = $$ 60. $$\mathop {\lim }\limits_{x \to 1} \left( {{{x + {x^2} + {x^3} + ... + {x^n} - n} \over {x - 1}}} \right) = $$ 61. If the function $f(x)=\frac{\sqrt{1+x}-1}{x}$ is continuous at $x=0$, then $f(0)=$
62. If $3 f(x)-2 f(1 / x)=x$, then $f(2)=$
63. If $\frac{d}{d x}\left(\frac{1+x^2+x^4}{1+x+x^2}\right)=a x+b$, then $(a, b)=$
64. If $y=\sin ^{-1} x$, then $\left(1-x^2\right) y_2-x y_1=$
65. If the percentage error in the radius of circle is 3 , then the percentage error in its area is
66. The equation of the tangent to the curve $y=x^3-2 x+7$ at the point $(1,6)$ is
67. The distance ( s ) travelled by a particle in time $t$ is given by $S=4 t^2+2 t+3$. The velocity of the particle, when $ 68. If $a^2 x^4+b^2 y^4=c^6$, then maximum value of $x y$ is equal to
69. $\int \frac{\sin ^6 x}{\cos ^8 x} d x=$
70. $\int \frac{x^5}{x^2+1} d x=$
71. $$\int {\left( {\sum\limits_{r = 0}^\infty {{{{x^r}{3^r}} \over {r!}}} } \right)dx = } $$ 72. $\int \frac{x^4+1}{x^6+1} d x=$
73. $\int e^x(x+1)^2 d x=$
74. $$\int\limits_0^{\pi /4} {{{{x^2}} \over {{{(x\,\sin \,x + \cos \,x)}^2}}}dx = } $$ 75. $\int_0^1 \frac{x}{(1-x)^{\frac{3}{4}}} d x=$
76. $$ \int_{-1}^1\left(\sqrt{1+x+x^2}-\sqrt{1-x+x^2}\right) d x= $$ 77. $\int_1^5(|x-3|+|1-x|) d x=$
78. The differential equation formed by eliminating arbitrary constants $A, B$ from the equation $y=A \cos 3 x+B \sin 3 x$ i 79. If $\cos x \frac{d y}{d x}-y \sin x=6 x,\left(0 80.
$\frac{d y}{d x}=\frac{y+x \tan \frac{y}{x}}{x} \Rightarrow \sin \frac{y}{x}=$
Physics
1. The length of the side of a cube is $1.2 \times 10^{-2} \mathrm{~m}$. Its volume up to correct significant figure is
2. The velocity of a particle is given by the equation $v(x)=3 x^2-4 x$, where $x$ is the distance covered by the particle. 3. The acceleration of a particle which moves along the positive $X$-axis varies with its position as shown in the figure. 4. The maximum height attained by projectile is increased by $10 \%$ by keeping the angle of projection constant. What is t 5. A light body of momentum $p_L$ and a heavy body of momentum $p_H$ both have the same kinetic energy, then
6. A block of metal 4 kg is in rest on a frictionless surface. It was targeted by a jet releasing water of $2 \mathrm{~kg} 7. A person climbs up a conveyor belt with a constant acceleration. The speed of the belt is $\sqrt{\frac{g h}{6}}$ and coe 8. A machine with efficiency $\frac{2}{3}$ used 12 J of energy in lifting 2 kg block through certain height and it is allow 9. A solid cylinder rolls down on an inclined plane of height $h$ and inclination $\theta$. The speed of the cylinder at th 10. Three particles of each mass $m$ are kept at the three vertices of an equilateral triangle of side $l$. The moment of in 11. In a spring block system as shown in figure. If the spring constant $k=9 \pi^2 \mathrm{Nm}^{-1}$, then the time period o 12. A body is executing simple harmonic motion. At a displacement $x$ its potential energy is $E_1$ and at a displacement $y 13. A particle is projected from the surface of the earth with a velocity equal to twice the escape velocity. When particle 14. A 4 kg stone attached at the end of a steel wire is being whirled at a constant speed $12 \mathrm{~ms}^{-1}$ in a horizo 15. A spherical ball of radius $1 \times 10^{-4} \mathrm{~m}$ and of density $10^4 \mathrm{kgm}^{-3}$ falls freely under gra 16. A metal block is made from mixture of 2.4 kg of aluminium, 1.6 kg of brass and 0.8 kg of copper. The metal block is init 17. An ideal gas is found to obey $p V^{\frac{3}{2}}=$ constant during an adiabatic process. If such a gas initially at temp 18. The condition $d W=d Q$ holds good in the following process.
19. The efficiency of a Carnot engine found to increase from $25 \%$ to $40 \%$ on increasing the temperature ( $T_1$ ) of s 20. Match the following ( $f$ is number of degrees of freedom)
$$
\begin{array}{llll}
\hline& \text { Gases } & & \frac{C_p 21. When a wave enters into a rarer medium from a denser medium, the property of the wave which remains constant is
22. The focal length of the objective lens of a telescope is 30 cm and that of its eye lens is 3 cm . It is focussed on a sc 23. In case of diffraction, if $a$ is a slit width and $\lambda$ is the wavelength of the incident light, then the required 24. The electric field intensity $E$ at a distance of 3 m from a uniform long straight wire of linear charge density $0.2 \m 25. When a parallel plate capacitor is charged up to 95 V , its capacitance is $C$. If a dielectrtic slab of thickness 2 mm 26. The capacitance of an isolated sphere of radius $r_1$ is increased by 5 times, when it is enclosed by an earthed concen 27. The charge $q$ (in coulomb) passing through a $10 \Omega$ resistor as a function of time $t$ (in second) is given by $q= 28. A cell of emf 1.2 V and internal resistance $2 \Omega$ is connected in parallel to another cell of emf 1.5 V and interna 29. A proton and an alpha particle moving with energies in the ratio $1: 4$ enter a uniform magnetic field of 3 T at right 30. A charged particle moving along a straight line path enters a uniform magnetic field of 4 mT at right angles to the dire 31. At a place the horizontal component of earth's magnetic field $3 \times 10^{-5} \mathrm{~T}$ and the magnetic declinatio 32. The current passing through a coil of 120 turns and inductance 40 mH is 30 mA . The magnetic flux linked with the coil i 33. A resistor of resistance $R$, inductor of inductive reactance $2 R$ and a capacitor of capacitive reactance $X_C$ are co 34. The rms value of the electric field of an electromagnetic wave emitted by a source is $660 \mathrm{NC}^{-1}$. The averag 35. The maximum wavelength of light which causes photoelectric emission from photosensitive metal surface is $\lambda_0$. Tw 36. The electrostatic potential energy of the electron in an orbit of hydrogen is -6.8 eV . The speed of the electron in thi 37. The surface areas of two nuclei are in the ratio $9: 25$. The mass number of the nuclei are in the ratio
38. Pure silicon at 300 K has equal electron and hole concentration of $1.5 \times 10^{16} \mathrm{~m}^{-3}$. If the hole c 39. In $n-p-n$ transistor circuit, the collector current is 10 mA . If $95 \%$ of the electrons emitted reach the collector, 40. A transmitter of power 10 kW emits radio waves of wavelength 500 m . The number of photons emitted por second by the tra
1
AP EAPCET 2024 - 21th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
The equation $x^4-x^3-6 x^2+4 x+8=0$ has two equal roots. If $\alpha, \beta$ are the other two roots of this equation, then $\alpha^2+\beta^2=$
A
4
B
5
C
6
D
7
2
AP EAPCET 2024 - 21th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
The condition that the roots of $x^3-b x^2+c x-d=0$ are in arithmetic progression is
A
$9 c b=2 b^3+27 d$
B
$9 c b=2 d^3+27 b$
C
$9 c b=2 d^3+27 b$
D
$9 c d=2 b^3+27 d$
3
AP EAPCET 2024 - 21th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
There are 6 different novels and 3 different poetry books on a table. If 4 novels and 1 poetry book are to be selected and arranged in a row on a shelf such that the poetry book is always in the middle, then the number of such possible arrangements is
A
270
B
180
C
540
D
1080
4
AP EAPCET 2024 - 21th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If a five-digit number divisible by 3 is to be formed using the numbers $0,1,2,3,4$ and 5 without repetition, then the total number of ways this can be done is
A
120
B
144
C
192
D
216
Paper analysis
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Mathematics
80
Physics
40
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