Chemistry
1. If the longest wavelength of spectral line of Paschen series of $\mathrm{Li}^{2+}$ ion spectrum is $x \mathop {\rm{A}}\l 2. If $v_0$ is the threshold frequency of a metal $X$, the correct relation between de-Broglie wavelength $(\lambda)$ assoc 3. In which of the following sets, elements are not correctly arranged with the property shown in brackets?
4. In which of the following, there is no change in hybridisation of the central atom ?
5. In which of the following sets the sum of bond orders of three species is maximum ?
6. At 240.55 K , for one mole of an ideal gas, a graph of $p$ (on $Y$-axis) and $V^{-1}$ (on $X$-axis) gave a straight line 7. At STP, a closed vessel contains I mole each of He and $\mathrm{CH}_4$. Through a small hole, 2 L of He and LL of $\math 8. 10 g of a metal $(M)$ reacts with oxygen to form 11.6 got oxide. What is the equivalent weight of $M$ ?
9. What is the enthalpy change (in J ) for converting 98 of $\mathrm{H}_2 \mathrm{O}(t)+10^{\circ} \mathrm{C}$ to $\mathrm{ 10. $A, B, C$ and $D$ are some compounds. The entnalpy of formation of $A(g), B(g), C(g)$ and $D(g)$ is $9.7,-110,81$ and $- 11. At equilibrium of the reaction,
$$ A_2(g)+B_2(g) \rightleftharpoons 2 A B(g) $$
The concentrations of $A_2, B_2$ and $A 12. Which of the following when added to 20 mL of a 0.01 M solution of HCl would decrease its pH ? 13. Identify the incorrect statement.
14. Which one of the following alkaline earth metals does not form hydride when it is heated with hydrogen directly? 15. $$ \text { In the given structure of diborane } \theta_1, \theta_2 \text { are respectively } $$ 16. In which of the following sets allotropes of carbon are correctly matched with their uses?
i. Graphite - Crucibles
ii. A 17. Which of the following is/are estimated by tura polluted water with potassium dichromate solution in acidic medium?
$$ \ 18. The number of isomers possible for a dibromo derivate (Molecular weight $=186 \mathrm{u}$ ) of an alkene is $(\mathrm{Br 19. In Kolbe's electrolysis of sodium propanoate, products formed at anode and cathode are respectively 20. Zinc oxide (white) is heated to high temperature for some time.
Observe the following statements regarding above process 21.
Benzoic acid undergoes dimerisation in benzene. $x \mathrm{~g}$ of benzoic acid (molar mass $122 \mathrm{~g} \mathrm{~m 22. At $T(\mathrm{~K})$ two liquids $A$ and $B$ form an ideal solution. The vapour pressures of pure liquid $A$ and $B$ at t 23.
In which of the following Galvanic cells emf is maximum?
(Given, $E_{\mathrm{Mg}^{2+} \mid \mathrm{Mg}}^{\circ}=-2.36 24. Isomerisation of gaseous cyclobutene to butadiene is first order reaction. At $T(\mathrm{~K})$. The rate constant of rea 25. $$ \text { Match List-I with List-II } $$
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black 26. The following data is obtained for coagulating a positively charged sol in 2 hours
.tg {border-collapse:collapse;bord 27. In which of the following metals extraction, impurities are removed as slag?
i. Al
ii. Fe
iii. Cu
iv. Zn
The correct opt 28. Two of the products formed by the reaction of ' $X$ with HCl are gases. What is ' $X$ '?
29. The correct order of oxidising power of the given ions is 30. Match the complexes in List-I with their hybridisation in list-II.
.tg {border-collapse:collapse;border-spacing:0;}
31. $$ \text { Match the following. } $$
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;bord 32. Which of the following is not an essential amino acid ?
33. Which one of the following is NOT a disaccharide?
34. Which of the following molecules contain sulphur atom in their structures?
I. Morphine
II. Heroin
III, Penicillin
IV. Te 35. In Wurtz-Fittig reaction a compound $X$ reacts with alkyl halide. What is $X$ ? 36. $$ \text { The product }(C) \text { in the following reaction sequenceis } $$
37. An organic compound $(X)$ has an empirical formula $\mathrm{C}_4 \mathrm{H}_8 \mathrm{O}$. This gives a pale yellow prec 38. Arrange the following in the correct order of their acidic strength.
39. $$ \text { What is } Y \text { in the given sequence? } $$
40. $$ \text { Identify } B \text { in the given reaction sequence. } $$
Mathematics
1. The domain of the real valued function $f(x)=\sqrt{9-\sqrt{x^2-144}}$ is
2. If set $A$ has 5 elements, set $B$ has 7 elements, then the number of many one functions that can be defined from $A$ to 3. $$ 2+3+5+6+8+9+\ldots .2 n \text { terms }= $$ 4. If the set of equations $x+2 y+3 z=6, x+3 y+5 z=9$, $2 x+5 y+a z=b$ has unique solution, then 5. If $P$ and $Q$ are two $3 \times 3$ matrices such that $|P Q|=1$ and $|P|=9$, then the determinant of adjoint of the mat 6. If $A=\left[\begin{array}{lll}a & 1 & 2 \\ 1 & 2 & b \\ c & 1 & 3\end{array}\right]$ and $\operatorname{adj} A=\left[\be 7. If $Z$ is a complex number such that $|Z| \leq 3$ and $\frac{-\pi}{2} \leq \operatorname{amp} Z \leq \frac{\pi}{2}$, the 8. The locus of the complex number $Z$ such that $\arg \left(\frac{Z-1}{Z+1}\right)=\frac{\pi}{4}$ is
9. All the values of $(8 i)^{\frac{1}{3}}$ are
10. If $\alpha, \beta$ are the roots of the equation $x^2-6 x-2=0$, $\alpha>\beta$ and $a_n=\alpha^n-\beta^n, n \geq 1$, th 11. If both the roots of the equation $x^2-6 a x+2-2 a+9 a^2=0$ exceed 3 , then
12. If $\alpha$ and $\beta$ are two distinct negative roots of $x^5-5 x^3+5 x^2-1=0$, then the equation of least degree with 13. If the number of real roots of $x^9-x^5+x^4-1=0$ is $n$, the number of complex roots having argument on imaginary axis i 14. All the letters of the word 'TABLE' are permuted and the strings of letters (may or may not have meaning) thus formed ar 15. 5 boys and 6 girls are arranged in all possible ways. Let $X$ denote the number of linear arrangements in which no two b 16. The number of ways of distributing 15 apples to three persons $A, B, C$ such that $A$ and $C$ each get at least 2 apples 17. If the $2 \mathrm{nd}, 3 \mathrm{rd}$ and 4 th terms in the expansion of $(x+a)^n$ are $96,216,216$ respectively and $n$ 18. If $|x| 19. $|x| 20. If $M_1$ and $M_2$ are the maximum values of $\frac{1}{11 \cos 2 x+60 \sin 2 x+69}$ and $3 \cos ^2 5 x+4 \sin ^2 5 x$ re 21. $$ 4 \cos \frac{\pi}{7} \cos \frac{\pi}{5} \cos \frac{2 \pi}{7} \cos \frac{2 \pi}{5} \cos \frac{4 \pi}{7}= $$ 22. In a $\triangle A B C$, if $A, B$ and $C$ are in arithmetic progression and $\cos A+\cos B+\cos C=\frac{1+\sqrt{2}+\sqrt 23. The general solution of the equation $\tan x+\tan 2 x-\tan 3 x=0$ is
24. The value of $x$ such that $\sin \left(2 \tan ^{-1} \frac{3}{4}\right)=\cos \left(2 \tan ^{-1} x)\right.$
25. If $\tanh x=\operatorname{sech} y=\frac{3}{5}$ and $e^{x+y}$ is an integer, then $e^{x+ y}$ =
26.
In $\triangle A B C$, if $b+c: c+a: a+b=7: 8: 9$, then the smaller angle (in radians) of that triangle is
27. In $\triangle A B C$, if $(a+c)^2=b^2+3 c a$, then $\frac{a+c}{2 R}=$
28. In $\triangle A B C$, if $A, B$ and $C$ are in arithmetic progression $\Delta=\frac{\sqrt{3}}{2}$ and $r_1 r_2=r_2 r$, t 29. Let $\hat{\mathbf{a}}=3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}, \hat{\mathbf{b}}=2 \hat{\mathbf{i}}+\hat 30. In $\triangle P Q R,(4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}),(2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 31. If $\hat{\mathbf{f}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{g}}=2 \hat{\mathbf{i}}-\hat{\ 32.
If $\theta$ is the angle between $\hat{\mathbf{f}}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ and $\hat{\m 33. The distance of a point $(2,3,-5)$ from the plane $\hat{\mathbf{r}} \cdot(4 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+2 \hat{\ 34. If $x_1, x_2, x_3, \ldots . x_n$ are $n$ observations such, that $\Sigma\left(x_i+2\right)^2=28 n$ and $\Sigma\left(x_1 35.
Three numbers are chosen at random from 1 to 20 , then the probability that the sum of three numbers is divisible by 3 36. Two persons $A$ and $B$ throw three unbiased dice one after the another. If $A$ gets the sum 13, then the probability th 37. 8 teachers and 4 students are sitting around a circular table at random, then the probability that no two students sit t 38. A bag contains 6 balls. If three balls are drawn at a time and all of them are found to be green, then the probability t 39. In a binomial distribution the difference between the mean and standard deviation is 3 and the difference between their 40. When an unfair dice is thrown the probability of getting a number $k$ on it is $P(X=k)=k^2 P$, where $k=1,2,3,4,5,6$ and 41. The equation of the locus of points which are equidistant from the point $(2,3)$ and $(4,5)$ is
42. The transformed equation of $x^2-y^2+2 x+4 y=0$ when the origin is shifted to the point $(-1,2)$ is 43. The equation of the side of an equilateral triangle is $x+y=2$ and one vertex is $(2,-1)$. The length of the side is
44. The orthocentre of the triangle formed by lines $x+y+1=0, x-y-1=0$ and $3 x+4 y+5=0$ is
45. If the slope of one of the pair of lines represented by $2 x^2+3 x y+K y^2=0$ is 2 , then the angle between the pair of 46. The length of $x$-intercept made by pair of lines $2 x^2+x y-6 y^2-2 x+17 y-12=0$ is
47. From a point $(1,0)$ on the circle $x^2+y^2-2 x+2 y+1=0$ if chords are drawn to this circle, then locus of the poles of 48. If $A$ and $B$ are the centres of similitude with respect to the circles $x^2+y^2-14 x+6 y+33=0$ and $x^2+y^2+30 x-2 y+1 49. $C_1$ is the circle with centre at $O(0,0)$ and radius $4, C_2$ is a variable circle with centre at $(\alpha, \beta)$ an 50. If the pair of tangents drawn to the circle $x^2+y^2=a^2$ from the point $(10,4)$ are perpendicular. then $a=$ 51. If $x-4=0$ is the radical axis of two orthogonal cirlces out of which one is $x^2+y^2=36$, then the centre of the other 52. If the normal chord drawn at $(2 a, 2 a \sqrt{2})$ on the parabola $y^2=4 a x$ subtends an angle $\theta$ at its vertex, 53. If the ellipse $4 x^2+9 y^2=36$ is confocal with a hyperbola whose length of the transverse axis is 2 , then the points 54. If the eccentricity of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is $\sec \alpha$, then area of the triangle for 55. If $e_1$ and $e_2$ are respectively the eccentricities of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ and its conj 56. The orthocentre of triangle fromed by points $(2,1,5)$ $(3,2,3)$ and $(4,0,4)$ is
57. If $P=(0,1,2), Q=(4,-2,1)$, and $O=(0,0,0)$, then $\angle P O Q=$
58. If the perpendicular distance from $(1,2,4)$ to the plane $2 x+2 y-z+k=0$ is 3 , then $k=$
59. $$\mathop {\lim }\limits_{x \to o} \left[\frac{1}{x}-\frac{1}{e^x-1}\right]= $$ 60. Let $f(x)=\left\{\begin{array}{cl}0, & x=0 \\ 2-x, & \text { for } 0
then which of the following is true
61. If $f(x)=\left(\frac{1+x}{1-x}\right)^{\frac{1}{x}}$ is continuous at $x=0$, then $f(0)=$
62. The function $f(x)=|x-24|$ is
63.
If $y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\ldots \infty}}}$, then the value of $\frac{d^2 y}{d x^2}$ at the point $( 64. 64. If $f(0)=0, f^{\prime}(0)=3$, then the derivative of $y=f(f(f(f(f(x)))))$ at $x=0$ is
65. The value of Lagrange's mean value theorem for $f(x)=e^x+24$ in $[0,1]$ is
66. Equation of the normal to the curve $y=x^2+x$ at the point $(1,2)$ is
67. Displacement $s$ of a particle at time $t$ is expressed as $s=2 t^3-9 t$. Find the acceleration at the time when $b^{t 5 68. If a running track of 500 ft is to be laid out enclosing a playground the shape of which is a rectangle with a semi-circ 69. $$
\int \frac{x^2-1}{x^3 \sqrt{2 x^4-2 x^2+1}} d x
$$
70. $$ \int \frac{x^3 \tan ^{-1} x^4}{1+x^8} d x= $$ 71. $$
\int \frac{2}{1+x+x^2} d x=
$$
72. $$ \int \frac{1}{x^2\left(\sqrt{1+x^2}\right)} d x= $$ 73. $$ \int \frac{\sin 7 x}{\sin 2 x \sin 5 x} d x= $$ 74. $$ \int_0^{\pi / 4} \log (1+\tan x) d x= $$ 75. $$\mathop {\lim }\limits_{n \to \infty }\left(\frac{1}{\sqrt{n^2}}+\frac{1}{\sqrt{n^2-1}}+\ldots+\frac{1}{\sqrt{n^2-(n-1 76. The area (in sq units) bounded by the curves $x=y^2$ and $x=3-2 y^2$ is
77. $$\int\limits_\pi ^\pi {}\frac{x \sin x}{1+\cos ^2 x} d x= $$
78. The general solution of the differential equation $(1+\tan y)(d x-d y)+2 x d y=0$ is
79. The general solution of the differential equation $x d y-y d x=\sqrt{x^2+y^2} d x$ is
80. The sum of the order and degree of differential equation $x\left(\frac{d^2 y}{d x^2}\right)^{1 / 2}=\left(1+\frac{d y}{d
Physics
1. The potential difference across the ends of conductor is $\beta 0 \pm 03) \mathrm{V}$ and the current through the conduc 2. A body thrown vertically upwards from the ground reaches a maximum height $H$. The ratio of the velocities of the body a 3. The angle made by the resultant vector of two vectors $2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$ and $2 4. The relation between the horizontal displacement $x$ (in metre) and the vertical displacement $y$ (in metre) of a projec 5. A 100 kg cannon fires a ball of 1 kg horizontally from a cliff of height 500 m . It falls on the ground at a distance of 6. A block of mass 5 kg is placed on a rough horizontal surface having coefficient of friction 0.5 . If a horizontal force 7. The average power generated by a 90 kg mountain climber who climbs a summit of height 600 m in 90 min is (Acceleration d 8. A boy weighing 50 kg finished long jump at a distance of 8 m . Considering that he moved along a parabolic path and his 9. The moment of inetia of a rod about an axis passing through its centre and perpendicular to its length is $\frac{1}{12} 10. A uniform rod of length $2 L$ is placed with one end in contact with the earth and is then inclined at an angle $\alpha$ 11. Two simple harmonic motions are represented by $y_1=5[\sin 2 \pi t+\sqrt{3} \cos 2 \pi t]$ and $y_2=5 \sin \left[2 \pi t 12. When a mass $m$ is connected individually to the springs $k_1$ and $k_2$, the oscillation frequencies are $v_1$ and $v_2 13. A satellite moving round the earth in a circular orbit has kinetic energy $E$. Then, the minimum amount of energy to be 14. The elongation of copper wire of cross-sectional area $3.5 \mathrm{~mm}^2$, in the figure shown, is
$$ \left(Y_{\text {C 15. Water is flowing in streamline manner in a horizontal pipe. If the pressure at a point where cross-sectional area is $10 16. A metal ball of mass 100 g at $20^{\circ} \mathrm{C}$ is dropped in 200 g of water at $80^{\circ} \mathrm{C}$. If the re 17. The efficiency of a heat engine that works between the temperatures where Celsius-Fahrenheit scales coincides and Kelvin 18. Initially the pressure of 1 mole of an ideal gas is $10^5 \mathrm{Nm}^{-2}$ and its volume is 16 L . When it is adiabati 19. An ideal gas is taken around $A B C A$ as shown in the $P^{\prime \prime}$ diagram. The work done during the cycle is
20. The ratio of kinetic energy of a diatomic gas molecule at a high temperature to that of NTP is 21. The vibrations of four air columns are shown below. The ratio of frequencies is
22. A person can see objects clearly when they lie between 40 cm and 400 cm from his eye. In order to increase the maximum d 23. If a slit of width $x$ was illuminated by red light having wavelength $6500\mathop {\rm{A}}\limits^{\rm{^\circ }}$, the 24. A neutral ammonia $\mathrm{NH}_3$ in its vapour state has electric dipole moment of magnitude $5 \times 10^{-30} \mathrm 25. If four charges $q_1=+1 \times 10^{-8} \mathrm{C}, q_2=-2 \times 10^{-8} \mathrm{C}$, $q_3=+3 \times 10^{-8} \mathrm{C}$ 26. Eight capacitors each of capacity $2 \mu \mathrm{~F}$ are arranged as shown in figure. The effective capacitance between 27. If $E_1=4 \mathrm{~V}$ and $E_2=12 \mathrm{~V}$, the current in the circuit and potential difference between the points 28. Two identical cells gave the same current through an external resistance of $2 \Omega$ regardless whether the cells are 29. Two toroids with number of turns 400 and 200 have average radii respectively 30 cm and 60 cm . If they carry the same cu 30. Three rings, each with equal radius $r$ are placed mutually perpendicular to each other and each having centre at the or 31. One bar magnet is in simple harmonic motion with time period $T$ in an earth's magnetic field. If its mass is increased 32. A coil of inductance $L$ is divided into 6 equal parts. All these are connected in parallel. The resultant inductance of 33. A 50 Hz AC circuit has a 10 mH inductor and a $2 \Omega$ resistor in series. The value of capacitance to be placed in se 34. The structure of solids is investigated by using
35. The surface of a metal is first illuminated with a light of wavelength 300 nm and later illuminated by another light of 36. The ratio of minimum wavelength of Balmer series to maximum wavelength in Brackett series in hydrogen spectrum is 37. The half-life period of a radioactive element $A$ is 62 years. It decays into another stable element $B$. An archaeologi 38. The current gain of a transistor in common emitter configuration is 80 . The resistances in collector andbase sides of t 39. Four logic gates are connected as shown in the figure. If the inputs are $A=0, B=1$ and $C=1$, then the values of $Y_1$ 40. The maximum distance between the transmitting and receiving antennas for satisfactory communication in line of sight mod
1
AP EAPCET 2024 - 22th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If both the roots of the equation $x^2-6 a x+2-2 a+9 a^2=0$ exceed 3 , then
A
$a<\frac{3}{2}$
B
$a>\frac{3}{2}$
C
$a<\frac{5}{2}$
D
$a>\frac{11}{9}$
2
AP EAPCET 2024 - 22th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\alpha$ and $\beta$ are two distinct negative roots of $x^5-5 x^3+5 x^2-1=0$, then the equation of least degree with integer coefficients having $\sqrt{-\alpha}$ and $\sqrt{-\beta}$ as its roots, is
A
$x^2-3 x+1=0$
B
$-x^4-5 x^2+5 x+1=0$
C
$-x^4+5 x^2-5 x+1=0$
D
$x^4-3 x^2+1=0$
3
AP EAPCET 2024 - 22th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the number of real roots of $x^9-x^5+x^4-1=0$ is $n$, the number of complex roots having argument on imaginary axis is $m$ and the number of complex roots having argument in 2nd quadrant is $K, m \cdot n \cdot k=$
A
6
B
9
C
12
D
24
4
AP EAPCET 2024 - 22th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
All the letters of the word 'TABLE' are permuted and the strings of letters (may or may not have meaning) thus formed are arranged in dictionary order. Then, the rank of the word 'TABLE' counted from the rank of the word 'BLATE' is
A
50
B
97
C
61
D
37
Paper analysis
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Chemistry
40
Mathematics
80
Physics
40
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