Chemistry
1. The wavenumber of first spectral line of Lyman series of $\mathrm{He}^{+}$ion is $x \mathrm{~m}^{-1}$. What is the wave 2. The uncertainty in determination of position of a small ball of mass 10 g is $10^{-33} \mathrm{~m}$. With what $\%$ of a 3. In which of the following ionic pairs, second ion is smaller in size than the first ion? 4. The set of elements which obey the general electronic configuration $(n-1) d^{1-10} n s^2$ is? 5. Identify the set of molecules which are not in the correct order of their dipole moments 6. Match the following.
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;bor 7. At 400 K , an ideal gas is enclosed in a $0.5 \mathrm{~m}^3$ vessel at pressure of 203 kPa . What is the change in tempe 8. Match the following.
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid; 9. The standard enthalpy of combustion of C (graphite). $\mathrm{H}_2(g)$ and $\mathrm{CH}_3 \mathrm{OH}(l)$ respectively a 10. Observe the following species.
(i) $\mathrm{NH}_3$
(ii) $\mathrm{AlCl}_3$
(iii) $\mathrm{SnCl}_4$
(iv) $\mathrm{CO}_2$
( 11. The normality of 20 volume solution of hydrogen peroxide is 12. Consider the following reactions.
$$ \begin{array}{r} \mathrm{Cs}+\mathrm{O}_2 \text { (excess) } \rightarrow X \\ \math 13. Choose the correct statement from the following.
I. In vapour phase $\mathrm{BeCl}_2$ exists as chlorobridge dimer.
II. 14. Observe the following reactions (not balanced)
$$ \begin{aligned} & \mathrm{BF}_3+\mathrm{LiAlH}_4 \xrightarrow{\left(\m 15. $\mathbf{Assertion (A)}$ Silicones are used for water proofing of fabrics.
$\mathbf{Reason (R)}$ The repeating unit in s 16. Acrolein $(X)$ is one of the chemicals formed when $\mathrm{O}_3$ and $\mathrm{NO}_2$ react with unburnt hydrocarbons pr 17. An organic compound containing phosphorous on oxidation with $\mathrm{Na}_2 \mathrm{O}_2$ gives a compound ' $X$ '. This 18. The correct IUPAC name of the structure given below is
19. The major product ' $Y^{\prime}$ in the given sequence of reactions is
$$ \mathrm{C}_3 \mathrm{H}_7 \mathrm{OH} \xrighta 20. Compound ' $A$ ' on heating with sodalime gives propane. Identify the compound ' $A$ '. 21. An element with molar mass $2.7 \times 10^{-2} \mathrm{~kg} \mathrm{~mol}^{-1}$ forms a cubic unit cell with edge length 22. At $300 \mathrm{~K}, 0.06 \mathrm{~kg}$ of an organic solute is dissolved in 1 kg water. The vapour pressure of solution 23. The molar conductivity of 0.02 M solution of an electrolyte is $124 \times 10^{-4} \mathrm{~S} \mathrm{~m}^2 \mathrm{~mo 24. The decomposition of benzene diazonium chloride is a first order reaction. The time taken for its decomposition to $\fra 25. 10 mL of 0.5 M NaCl is required to coagulate 1 L of $\mathrm{Sb}_2 \mathrm{~S}_3 \mathrm{sol}$ in 2 hours time. The floc 26. Kaolinite is a silicate mineral of metal ' $X$ ' and calamine is a carbonate mineral of metal ' $Y^{\prime}, X$ and $Y$ 27. $\mathrm{NH}_2 \mathrm{CONH}_2+2 \mathrm{H}_2 \mathrm{O} \rightarrow[\mathrm{X}] \rightleftharpoons 2 \mathrm{NH}_3+\mat 28. Among the hydrides $\mathrm{NH}_3, \mathrm{PH}_3$ and $\mathrm{BiH}_3$, the hydride with highest boiling point is $X$ an 29. Xenon (VI) fluoride on complete hydrolysis gives an oxide of xenon ' $O$ '. The total number of $\sigma$ and $\pi$-bonds 30. In which of the following ions the spin only magnetic moment is lowest? 31. Identify the complex ion with electronic configuration $t_{2 g}^3 e_g^2$. 32. Identify the structure of the polymer 'P' formed in the given reaction
Caprolactam $\xrightarrow[\mathrm{H}_2 \mathrm{O} 33. Which of the following vitamin is also called pyridoxine? 34. The number of -OH groups present in the structures of bithionol, terpineol and chloroxylenol is respectively 35.
Conversion of $X$ to $Y$ in the above reaction is 36. $$ \mathrm{CH}_3 \mathrm{CH}_2 \mathrm{OH} \xrightarrow[443 \mathrm{~K}]{\text { Conc. } \mathrm{H}_2 \mathrm{SO}_4} X \ 37. Arrange the following in the increasing order of pKa values
38. What is ' $C$ ' in the following reaction sequence?
39. Identify the products $R$ and $S$ in the reaction sequence given
$\left(\mathrm{CH}_3\right)_3 \mathrm{COH} \xrightarro 40. In the given reaction sequence sequence, $Z$ is
Mathematics
1. If the real valued function $f(x)=\sin ^{-1}\left(x^2-1\right)-3 \log _3\left(3^x-2\right)$ is not defined for all $x \i 2. If $f$ is a real valued function from $A$ onto $B$ defined by $f(x)=\frac{1}{\sqrt{|x-|x||}}$, then $A \cap B=$ 3. Among the following four statements, the statement which is not true, for all $n \in N$ is 4. If $A=\left[\begin{array}{lll}x & y & y \\ y & x & y \\ y & y & x\end{array}\right]$ is a matrix such that $5 A^{-1}=\le 5. If $A=\left[\begin{array}{lll}9 & 3 & 0 \\ 1 & 5 & 8 \\ 7 & 6 & 2\end{array}\right]$ and $A A^T-A^2=\left[\begin{array}{ 6. If $a \neq b \neq c, \Delta_1=\left[\begin{array}{lll}1 & a^2 & b c \\ 1 & b^2 & c a \\ 1 & c^2 & a b\end{array}\right]$ 7. The system of equations $x+3 y+7=0$, $3 x+10 y-3 z+18=0$ and $3 y-9 z+2=0$ has 8. If $x$ and $y$ are two positive real numbers such that $x+i y=\frac{13 \sqrt{-5+12 i}}{(2-3 i)(3+2 i)}$, then $13 y-26 x 9. If $z=x+i y$ and if the point $P$ represents $z$ in the argand plane, then the locus of $z$ satisfying the equation $|z- 10. One of the values of $(-64 i)^{5 / 6}$ is 11. If $\alpha, \beta$ are the roots of the equation $x+\frac{4}{x}=2 \sqrt{3}$, then $\frac{2}{\sqrt{3}}\left|\alpha^{2024} 12. $\alpha, \beta$ are the real roots of the equation $12 x^{\frac{1}{3}}-25 x^{\frac{1}{6}}+12=0$. If $\alpha>\beta$, then 13. If the expression $7+6 x-3 x^2$ attains its extreme value $\beta$ at $x=\alpha$, then the sum of the squares of the root 14. $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3+3 x^2-10 x-24=0$. If $\alpha>\beta>\gamma$ and $\alpha^3 15. $\alpha, \beta$ and $\gamma$ are the roots of the equation $8 x^3-42 x^2+63 x-27=0$. If $\beta 16. All the letters of word 'COLLEGE' are arranged in all possible ways and all the seven letter words (with or without mean 17. If all the possible 3-digit numbers are formed using the digits $1,3,5,7$ and 9 without repeating any digit, then the nu 18. A question paper has 3 parts $A, B$ and $C$. Part $A$ contains 7 questions, part $B$ contains 5 questions and Part Ccont 19. If $p$ and $q$ are the real numbers such that the 7 th term in the expansion of $\left(\frac{5}{p^3}-\frac{3 q}{7}\right 20. If $T_4$ represents the 4 th term in the expansion of $\left(5 x+\frac{7}{x}\right)^{\frac{-3}{2}}$ and $x \notin\left[- 21. If $\frac{2 x^3+1}{2 x^2-x-6}=a x+b+\frac{A}{P x-2}+\frac{B}{2 x+q}$, then 51 apB $=$ 22. $\tan A=\frac{-60}{11}$ and $A$ does not lie in the 4th quadrant. $\sec B=\frac{41}{9}$ and $B$ does not lie in the 1st 23. If $\tan A+\tan B+\cot A+\cot B=\tan A \tan B-\cot A \cot B$ and $0^{\circ} 24. If $\cos ^2 84^{\circ}+\sin ^2 126^{\circ}-\sin 84^{\circ} \cos 126^{\circ}=K$ and $\cot A+\tan A=2 K$, then the possibl 25. The equation that is satisfied by the general solution of the equation $4-3 \cos ^2 \theta=5 \sin \theta \cos \theta$ is 26. If $\sin ^{-1}(4 x)-\cos ^{-1}(3 x)=\frac{\pi}{6}$, then $x=$ 27. If $\sin h^{-1}(-\sqrt{3})+\cos ^{-1}(2)=K$, then $\cosh K=$ 28. In triangle $A B C$, if $a=4, b=3$ and $c=2$, then $2(a-b \cos C)(a-c \sec B)=$ 29. In $\triangle A B C$, if $A=45^{\circ}, C=75^{\circ}$ and $R=\sqrt{2}$, than $r=$ 30. $P$ and $Q$ are the points of trisection of the segment $A B$. If $2 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+3 \hat{\mathbf{ 31. The position vector of the point of intersection of the line joining the points $\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{ 32. If $\mathbf{a}=4 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ and $\mathbf{b}=6 \hat{\mathbf{i}}-2 \hat{\math 33. A plane $\pi_1$ passing through the point $3 \hat{\mathbf{i}}-7 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$ is perpendicular to 34. $\mathbf{a}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}, \mathbf{b}=2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$ and $\mathbf{c}=2 \hat{ 35. If $M_1$ is the mean deviation from the mean of the discrete data $44,5,27,20,8,54,9,14,35$ and $M_2$ is the mean deviat 36. If two dice are thrown, then the probability of getting co-prime numbers on the dice is 37. If two cards are drawn at random simultaneously from a well shuffled pack of 52 playing cards, then the probability of g 38. Bag $P$ contains 3 white, 2 red, 5 blue balls and bag $Q$ contains 2 white, 3 red, 5 blue balls. A ball is chosen at ran 39. If the probability distribution of a random variable $X$ is as follow, then the variance of $X$ is
.tg {border-collaps 40. The mean of a binomial variate $X \sim B(n, p)$ is 1 . If $n>2$ and $P(X=2)=\frac{27}{128}$, then the variance of the di 41. If the distance from a variable point $P$ to the point $(4,3)$ is equal to the perpendicular distance from $P$ to the li 42. $(0, k)$ is the point to which the origin is to be shifted by the translation of the axes so as to remove the first degr 43. $\beta$ is the angle made by the perpendicular drawn from origin to the line $L \equiv x+y-2=0$ with the positive $X$-ax 44. The line $2 x+y-3=0$ divides the line segment joining the points $A(1,2)$ and $B(-2,1)$ in the ratio $a: b$ at the point 45. If $Q$ and $R$ are the images of the point $P(2,3)$ with respect to the lines $x-y+2=0$ and $2 x+y-2=0$ respectively, th 46. If $(2,-1)$ is the point of intersection of the pair of lines $2 x^2+a x y+3 y^2+b x+c y-3=0$, then $3 a+2 b+c=$ 47. $(1, k)$ is a point on the circle passing through the points $(-1,1),(0,-1)$ and $(1,0)$. If $k \neq 0$, then $k=$ 48. If the tangents $x+y+k=0$ and $x+a y+b=0$ drawn to the circle $S=x^2+y^2+2 x-2 y+1=0$ are perpendicular to each other an 49. If $(h, k)$ is the internal centre of similitude of the circles $x^2+y^2+2 x-6 y+1=0$ and $x^2+y^2-4 x+2 y+4=0$, then $4 50. The slope of a common tangent to the circles $x^2+y^2-4 x-8 y+16=0$ and $x^2+y^2-6 x-16 y+64=0$ is 51. $x^2+y^2+2 x-6 y-6=0$ and $x^2+y^2-6 x-2 y+k=0$ are two intersecting circles and $k$ is not an integer. If $\theta$ is t 52. If $(p, q)$ is the centre of the circle which cuts the three circles $x^2+y^2-2 x-4 y+4=0, x^2+y^2+2 x-4 y+1=0$ and $x^2 53. If the focal chord of the parabola $x^2=12 y$, drawn through the point $(3,0)$ intersects the parabola at the points $P$ 54. If the normal drawn at the point $P(9,9)$ on the parabola $y^2=9 x$ meets the parabola again at $Q(a, b)$, then $2 a+b=$ 55. The length of the latus rectum of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b)$ is $\frac{8}{3}$. If the distance 56. $S$ is the focus of the ellips $\frac{x^2}{25}+\frac{y^2}{b^2}=1,(b 57. The slope of the tangent drawn from the point $(1,1)$ to the hyperbola $2 x^2-y^2=4$ is 58. $A(2,3, k), B(-1, k,-1)$ and $C(4,-3,2)$ are the vertices of $\triangle A B C$. If $A B=A C$ and $k>0$, then $\triangle 59. If $A(1,2,-3), B(2,3,-1)$ and $C(3,1,1)$ are the vertices of $\triangle A B C$, then $\left|\frac{-\cos A}{\cos B}\right 60. If $a, b$ and $c$ are the intercepts made on $X, Y, Z$-axes respectively by the plane passing through the points $(1,0,- 61. If $\lim \limits_{x \rightarrow 4} \frac{2 x^2+(3+2 a) x+3 a}{x^3-2 x^2-23 x+60}=\frac{11}{9}$, then $\lim \limits_{x \r 62. If the function
$$
f(x)= \begin{cases}\frac{\tan a(x-1)}{x-1}, & \text { if } 04\end{cases}
$$
domain, then $6 a+9 b^4=$ 63. If $y=\log \left[\tan \sqrt{\frac{2^x-1}{2^x+1}}\right], x>0$, then $\left(\frac{d y}{d x}\right)_{x=1}=$ 64. If $y=\cos ^{-1}\left(\frac{6 x-2 x^2-4}{2 x^2-6 x+5}\right)$, then $\frac{d y}{d x}=$ 65. If $\log y=y^{\log x}$, then $\frac{d y}{d x}=$ 66. If $y=a \cos 3 x+b e^{-x}$, then $y^{\prime \prime}(3 \sin 3 x-\cos 3 x)=$ 67. The approximate value of $\sec 59^{\circ}$ obtained by taking $1^{\circ}$ $=0.0174$ and $\sqrt{3}=1.732$ is 68. The equation of the normal drawn to the curve $y^3=4 x^5$ at the point $(4,16)$ is 69. A point $P$ is moving on the curve $x^3 y^4=2^7$. The $x$-coordinate of $P$ is decreasing at the rate of 8 units per sec 70. If the function $f(x)=x^3+a x^2+b x+40$ satisfies the conditions of Rolle's theorem on the interval $[-5,4]$ and $-5,4$ 71. If $x$ and $y$ are two positive integers such that $x+y=24$ and $x^3 y^5$ is maximum, then $x^2+y^2=$ 72. $\int \sqrt{4 \cos ^2 x-5 \sin ^2 x} \cos x d x=$ 73. $\int\left(\frac{4 \tan ^4 x+3 \tan ^2 x-1}{\tan ^2 x+4}\right) d x=$ 74. $\int\left(\frac{\left(\sin ^4 x+2 \cos ^2 x-1\right) \cos x}{(1+\sin x)^6}\right) d x=$ 75. $\int(\log x)^3 d x=$ 76. $\int_0^\pi\left(\sin ^3 x+\cos ^2 x\right)^2 d x=$ 77. $\int_{\frac{-\pi}{8}}^{\frac{\pi}{8}} \frac{\sin ^4(4 x)}{1+e^{4 x}} d x=$ 78. The area of the region enclosed by the curves $y^2=4(x+1)$ and $y^2=5(x-4)$ is 79. If $A$ and $B$ are arbitrary constants, then the differential equation having $y=A e^{-x}+B \cos x$ as its general solut 80. The general solution of the differential equation $\frac{d y}{d x}+\frac{\sin (2 x+y)}{\cos x}+2=0$ is
Physics
1. Which of the following statement regarding nature of physical laws is not correct? 2. The internal and external diameters of hollow cylinder measured with vernier callipers are $(5.73 \pm 0.01) \mathrm{cm}$ 3. A body moving with uniform acceleration, travels a distance of 25 m in the fourth second and 37 m in the sixth second. T 4. A body is projected from the ground at an angle of $\tan ^{-1}(\sqrt{7})$ with the horizontal. At half of the maximum he 5. An aircraft executes a horizontal loop of radius 9 km at a constant speed of $540 \mathrm{kmh}^{-1}$. The wings of the a 6. A body thrown vertically upwards from the ground reaches a maximum height $h$. The ratio of the kinetic and potential en 7. A ball of mass 1.2 kg moving with a velocity of $12 \mathrm{~ms}^{-1}$ makes one-dimensional collision with anothe stati 8. An alphabet $T$ made of two similar thin uniform metal plates of each length $L$ and width $a$ is placed on a horizontal 9. A solid sphere and a disc of same mass $M$ and radius $R$ - are kept such that their curved surfaces are in contact and 10. If a body dropped freely from a height of 20 m reaches the surface of a planet with a velocity of $31.4 \mathrm{~ms}^{-1 11. Two stars of masses $M$ and $2 M$ that are at a distance $d$ apart, are revolving one around another. The angular veloci 12. A block of mass 2 kg is tied to one end of a 2 m long metal wire of $1.0 \mathrm{~mm}^2$ area of cross-section and rotat 13. A big liquid drop splits into $n$ similar small drops under isothermal conditions, then in the process 14. A wooden cube of side 10 cm floats at the interface between water and oil with its lower surface 3 cm below the interfac 15. 37 g of ice at $0^{\circ} \mathrm{C}$ temperature is mixed with 74 g of water at $70^{\circ} \mathrm{C}$ temperature. Th 16. The thickness of a uniform rectangular metal plate is 5 mm and the area of each surface is $5 \mathrm{~cm}^5$. In steady 17. The ratio of the specific heat capacities of a gas is 1.5 . When the gas undergoes adiabatic process, its volume is doub 18. A vessel contains hydrogen and nitrogen gases in the ratio $2: 3$ by mass. If the temperature of the mixture of the gase 19. The difference between the fundamental frequencies of an open pipe and a closed pipe of same length is 100 Hz . The diff 20. The displacement equations of sound waves produced by two sources are given by $y_1=5 \sin 400 \pi t$ and $y_2=8 \sin 40 21. When an object of height 12 cm is placed at a distance from a convex lens, an image of height 18 cm is formed on a scree 22. A thin plano-convex lens of focal length 73.5 cm has a circular aperture of diameter 8.4 cm . If the refractive index of 23. In Young's double slit experiment, intensity of light at a point on the screen, where the path difference becomes $\lamb 24. Two point charges $-10 \mu \mathrm{C}$ and $-5 \mu \mathrm{C}$ are situated on $X$-axis at $x=0$ and $x=\sqrt{2} \mathrm 25. A $10 \mu \mathrm{~F}$ capacitor is charged by a 100 V battery. It is disconnected from the battery and is connected to 26. A conductor of length 1.5 m and area of cross-section $3 \times 10^{-5} \mathrm{~m}^2$ has electrical resistance of $15 27. The relation between the current $i$ (in ampere) in a conductor and the time $t$ (in second) is $i=12 t+9 t^2$. The char 28. A long straight rod of diameter 4 mm carries a steady current $i$. The current is uniformly distributed across its cross 29. A straight wire of length 20 cm carrying a current of $\frac{3 .}{\pi^2} \mathrm{~A}$ is bent in the form of a circle. T 30. A circular coil carrying a current of 2.5 A is free to rotate about an axis in its plane perpendicular to an external fi 31. A circular coil of area $200 \mathrm{~cm}^2$ and 50 turns is rotating about its vertical diameter with an angular speed 32. An inductor and a resistor are connected in series to an AC source of 10 V . If the potential difference across the indu 33. If the peak value of the magnetic field of an electromagnetic wave is $30 \times 10^{-9} \mathrm{~T}$, then the peak val 34. The de-Broglie wavelength of a proton is twice the de-Broglie wavelength of an alpha particle. The ratio of the kinetic 35. The ratio of the centripetal accelerations of the electron in two successive orbits of hydrogen is $81: 16$. Due to ${ } 36. The operation of a nuclear reactor is said to be critical when the value of neutron multiplication factor $K i s$ 37. An $\alpha$-particle of energy $E$ is liberated during the decay of a nucleus of mass number 236. The total energy relea 38. The voltage gain of a transistor in common emitter configuration is 160 . The resistances in base and collector sides of 39. Normally a capacitor is connected across the output terminals of a rectifier to 40. The process of the loss of strength of a signal while propagating through a medium is
1
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3+3 x^2-10 x-24=0$. If $\alpha>\beta>\gamma$ and $\alpha^3+3 \beta^2-10 \gamma-24=11 k$, then $k=$
A
1
B
11
C
5
D
55
2
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\alpha, \beta$ and $\gamma$ are the roots of the equation $8 x^3-42 x^2+63 x-27=0$. If $\beta<\gamma<\alpha$ and $\beta, \gamma$ and $\alpha$ are in geometric progression, then the extreme value of the expression $\gamma x^2+4 \beta x+\alpha$ is
A
$\frac{3}{4}$
B
3
C
$\frac{3}{2}$
D
$\frac{21}{4}$
3
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
All the letters of word 'COLLEGE' are arranged in all possible ways and all the seven letter words (with or without meaning) thus formed are arranged in the dictionary order. Then, the rank of the word 'COLLEGE' is
A
119
B
149
C
176
D
179
4
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If all the possible 3-digit numbers are formed using the digits $1,3,5,7$ and 9 without repeating any digit, then the number of such 3 -digit numbers which are divisible by 3 is
A
6
B
12
C
18
D
24
Paper analysis
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Mathematics
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Physics
40
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