Chemistry
1. If $n, l$ represent the principal and azimuthal quantum numbers respectively, the formula used to know the number of rad 2. If the radius of first orbit of hydrogen like ion is $1.763 \times 10^{-2} \mathrm{~nm}$, the energy associated with tha 3. If first ionisation enthalpy $\left(\Delta_{i} H\right)$ values of $\mathrm{Na}, \mathrm{Mg}$ and Si are respectively 49 4. Among the oxides $\mathrm{SiO}_{2}, \mathrm{SO}_{2}, \mathrm{Al}_{2} \mathrm{O}_{3}$ and $\mathrm{P}_{2} \mathrm{O}_{3}$ 5. According to molecular orbital theory, which of the following statements is not correct? 6. The melting point of $o$-hydroxybenzaldehyde $(A)$ is lower than that of $p$-hydroxybenzaldehyde $(B)$. This is because 7. At what temperature will the RMS velocity of sulphur dioxide molecules at 400 K be the same as the most probable velocit 8. 0.43 g of a metal of valence 2 was dissolved in 50 mL of $0.5 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}$ solution. The u 9. At $300 \mathrm{~K}, 3.0$ moles of an ideal gas at 3.0 atm pressure is compressed isothermally to one half of its volume 10. At $T(K)$ the equilibrium constants for the following two reactions are given below$ 2 A(g) \rightleftharpoons B(g)+C(g) 11. Identify the pair of hydrides which have polymeric structure 12. Match the following .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;bord 13. The hydroxide of which of the following metal reacts with both acid and alkali? 14. The correct formula of borax is $\mathrm{Na}_{2}\left[\mathrm{~B}_{4} \mathrm{O}_{5}(\mathrm{OH})_{x}\right] \cdot y \ma 15. Formic acid on heating with concentrated $\mathrm{H}_{2} \mathrm{SO}_{4}$ at 373 K gives $X$, a colourless substance and 16. Eutrophication can lead to 17. In which of the following options, the IUPAC name is not correctly matched with the structure of the compound? 18. Consider the following carbocations.
Arrange the above carbocations in the order of decreasing stability 19. Consider the following reaction sequence
$ \text { 2-methylpropane } \xrightarrow{\mathrm{KMnO}_{4}} X \xrightarrow[358 20. Identify the end product $(Z)$ in the sequence of the following reactions.
21. In bcc lattice containing $X$ and $Y$ type of atoms, $X$ type of atoms are present at the corners and $Y$ type of atoms 22. At 300 K , the vapour pressure of toluene and benzene are 3.63 kPa and 9.7 kPa respectively. What is the composition of 23. 0.592 g of copper is deposited in 60 minutes by passing0.5 A current through a solution of copper (II) sulphate. The ele 24. For the gaseous reaction, $\mathrm{N}_{2} \mathrm{O}_{5} \longrightarrow 2 \mathrm{NO}_{2}+\frac{1}{2} \mathrm{O}_{2}$th 25. Match the following .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;bord 26. Copper matte is mixture of 27. $\mathrm{C}+$ Conc. $\mathrm{H}_{2} \mathrm{SO}_{4} \xrightarrow{\Delta} X+Y+\mathrm{H}_{2} \mathrm{O}$$X$ and $Y$ in th 28. Which among the following oxoacids of phosphorous will have $\mathrm{P}-\mathrm{O}-\mathrm{P}$ bonds?I. $\mathrm{H}_{4} 29. The bond angles $\mathrm{H}-\mathrm{O}-\mathrm{N}$ and $\mathrm{O}-\mathrm{N}-\mathrm{O}$ in the planar structure of nit 30. Observe the following $f$-block elements$\mathrm{Eu}(Z=63) ; \mathrm{Pu}(Z=94) ; \mathrm{Cf}(Z=98)$;$\operatorname{Sm}(Z 31. Which one of the following complex ions has geometrical isomers? 32. Which one of the following is not an example of condensation polymer? 33. What is the IUPAC name of the product $Y$ in the given reaction sequence?
34. What is the value of ' $n$ ' in ' $Z$ ' of the following sequence?Lauryl alcohol $\xrightarrow{\mathrm{H}_{2} \mathrm{SO 35. The organic halide, which does not undergo hydrolysis by $\mathrm{S}_{\mathrm{N}} 1$ mechanism is 36. What is ' $Z$ ' in the given sequence of reactions?
37. What is the % carbon in the product ' $Z$ ' formed in the reaction?
38. Match the following
The correct answer is 39. What are $Y$ and $Z$ respectively in the given reaction sequence?
40. What is $C$ in the given sequence of reactions?
Mathematics
1. If $f(x)$ is a quadratic function such that $f(x) f\left(\frac{1}{x}\right)=f(x)+f\left(\frac{1}{x}\right)$, then $\sqrt 2. $f(x)=a x^{2}+b x+c$ is an even function and$g(x)=p x^{3}+q x^{2}+r x$ is an odd function.If $h(x)=f(x)+g(x)$ and $h(-2) 3. If $1 \cdot 3 \cdot 5+3 \cdot 5 \cdot 7+5 \cdot 7 \cdot 9 \ldots$ to $n$ terms $=n(n+1) f(n)$, then $f(2)=$ 4. $A=\left[\begin{array}{ll}1 & 2 \\\\ 2 & 1\end{array}\right]$ and $B=\left[\begin{array}{ll}x & y \\\\ 1 & 2\end{array}\ 5. If $x=k$ satisfies the equation $\left|\begin{array}{ccc}x-2 & 3 x-3 & 5 x-5 \\\\ x-4 & 3 x-9 & 5 x-25 \\\\ x-8 & 3 x-27 6. If $A$ is a non-singular matrix, then $\operatorname{adj}\left(A^{-1}\right)=$ 7. If the homogeneous system of linear equations $x-2 y+3 z=0,2 x+4 y-5 z=0,3 x+\lambda y+\mu z=0$ has non-trivial solution 8. If $z=\frac{(2-i)(1+i)^{3}}{(1-i)^{2}}$, then $\arg (z)=$ 9. $z=x+i y$ and the point $P$ represents $z$ in the argand plane. If the amplitude of $\left(\frac{2 z-i}{z+2 i}\right)$ i 10. $\alpha, \beta$ are the roots of the equation $x^{2}+2 x+4=0$. If the point representing $\alpha$ in the argand diagram 11. If $\alpha$ is a root of the equation $x^{2}-x+1=0$, then $\left(\alpha+\frac{1}{\alpha}\right)^{3}+\left(\alpha^{2}+\fr 12. $\alpha, \beta$ are the real roots of the equation $x^{2}+a x+b=0$. If $\alpha+\beta=\frac{1}{2}$ and $\alpha^{3}+\beta^ 13. The solution set of the inequation $\sqrt{x^{2}+x-2} > (1-x)$ is 14. If $\alpha, \beta, \gamma$ are the roots of the equation $4 x^{3}-3 x^{2}+2 x-1=0$, then $\alpha^{3}+\beta^{3}+\gamma^{3 15. The equation $16 x^{4}+16 x^{3}-4 x-1=0$ has a multiple root. If $\alpha, \beta, \gamma, \delta$ are the roots of this e 16. The sum of all the 4-digit numbers formed by taking all the digits from $0,3,6,9$ without repetition is 17. The number of ways in which 6 distinct things can be distributed into 2 boxes so that no box is empty is 18. Number of ways in which the number 831600 can be split into two factors which are relatively prime is 19. The coefficient of $x y^{2} z^{3}$ in the expansion of $(x-2 y+3 z)^{3}$ is 20. The set of all real values of $x$ for which the expansion of $\left(125 x^{2}-\frac{27}{x}\right)^{\frac{-2}{3}}$ is val 21. If $\frac{x^{2}}{2 x^{4}+7 x^{2}+6}=\frac{A x+B}{x^{2}+a}+\frac{C x+D}{a x^{2}+3}$, then $A+B+C-2 D=$ 22. If $(\sin \theta-\operatorname{cosec} \theta)^{2}+(\cos \theta+\sec \theta)^{2}=5$ and $\theta$ lies in the third quadra 23. If $0 24. If $\theta$ is an acute angle and $2 \sin ^{2} \theta=\cos ^{4} \frac{\pi}{8}+\sin ^{4} \frac{3 \pi}{8}+\cos ^{4} \frac{ 25. If $2 \tan ^{2} \theta-4 \sec \theta+3=0$, then $2 \sec \theta=$ 26. If $\sin ^{-1} x-\cos ^{-1} 2 x=\sin ^{-1}\left(\frac{\sqrt{3}}{2}\right)-\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)$, th 27. $\operatorname{sech}^{-1}\left(\frac{3}{5}\right)-\tanh ^{-1}\left(\frac{3}{5}\right)=$ 28. In a $\triangle A B C$, if $a=5, b=3, c=7$, then $\sqrt{\frac{\sin (A-B)}{\sin (A+B)}}=$ 29. In a $\triangle A B C$, if $r_{1}=6, r_{2}=9, r_{3}=18$, then $\cos A=$ 30. $2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ ar 31. A plane $\pi$ passing through the points $2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}, 3 \hat{\mathbf{i}}+4 \hat{\mathbf{k}}$ 32. A unit vector $\hat{\mathbf{e}}=a \hat{\mathbf{i}}+b \hat{\mathbf{j}}+c \hat{\mathbf{k}}$ is coplanar with the vectors $ 33. $\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}, \hat{\mathbf{b}}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\ 34. $\hat{\mathbf{r}} .(\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}})=5$ and $\hat{\mathbf{r}} .(2 \hat{\mathbf{i}}+\h 35. The variance of the data: $1,2,3,5,8,13,17$ is approximately 36. The numbers $2,3,5,7,11,13$ are written on six distinct paper chits. If 3 of them are chosen at random, then the probabi 37. If 4 letters are selected at random from the letters of the word PROBABILITY, then the probability of getting a combinat 38. If two dice are rolled, then the probability of getting a multiple of 3 as the sum of the numbers appeared on the top fa 39. If a random variable $X$ has the following probability distribution, then its variance is .tg {border-collapse:collaps 40. The mean and variance of a binomial variate $X$ are $\frac{16}{5}$ and $\frac{48}{25}$ respectively. IfP $(X > 1)=1-K\le 41. $P$ and $Q$ are the points of trisection of the line segment joining the points $(3,-7)$ and $(-5,3)$. If $P Q$ subtends 42. $(a, b)$ is the point to which the origin has to be shifted by translation of axes so as to remove the first-degree term 43. $A(1,-2), B(-2,3), C(-1,-3)$ are the vertices of a $\triangle A B C . L_{1}$ is the perpendicular drawn from $A$ to $B C 44. The area of the parallelogram formed by the lines $L_{1} \equiv \lambda x+4 y+2=0, L_{2} \equiv 3 x+4 y-3=0$, $L_{3} \eq 45. If $A(1,2), B(2,1)$ are two vertices of an acute angled triangle and $S(0,0)$ is its circumcenter, then the angle subten 46. If the angle between the pair of lines given by the equation $a x^{2}+4 x y+2 y^{2}=0$ is $45^{\circ}$, then the possibl 47. A circle passing through the points $(1,1)$ and $(2,0)$ touches the line $3 x-y-1=0$. If the equation of this circle is 48. A circle passes through the points $(2,0)$ and $(1,2)$. If the power of the point $(0,2)$ with respect to this circle is 49. $x-2 y-6=0$ is a normal to the circle $x^{2}+y^{2}+2 g x+2 f y-8=0$. If the line $y=2$ touches this circle, then the rad 50. The line $x+y+1=0$ intersects the circle $x^{2}+y^{2}-4 x+2 y-4=0$ at the points $A$ and $B$. If $M(a, b)$ is the mid-po 51. A circle $S$ passes through the points of intersection of the circles $x^{2}+y^{2}-2 x-3=0$ and $x^{2}+y^{2}-2 y=0$. If 52. If the common chord of the circles $x^{2}+y^{2}-2 x+2 y+1=0$ and $x^{2}+y^{2}-2 x-2 y-2=0$ is the diameter of a circle $ 53. $(1,1)$ is the vertex and $x+y+1=0$ is the directrix of a parabola. If $(a, b)$ is its focus and $(c, d)$ is the point o 54. The axis of a parabola is parallel to $Y$-axis. If this parabola passes through the points $(1,0),(0,2),(-1,-1)$ and its 55. If the focus of an ellipse is $(-1,-1)$, equation of its directrix corresponding to this focus is $x+y+1=0$ and its ecce 56. If the normal drawn at the point $(2,-1)$ to the ellipse $x^{2}+4 y^{i}=8$ meets the ellipse again at $(a, b)$, then $17 57. $P(\theta)$ is a point on the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{9}=1, S$ is its $\mathrm{fOO}_{4 /}$ lying on 58. If $A(-2,4, a), B(1, b, 3), C(c, 0,4)$ and $D(-5,6,1)$ are collinear points, then $a+b+c=$ 59. $A(1,-2,1)$ and $B(2,-1,2)$ are the end points of a line segment. If $D(\alpha, \beta, \gamma)$ is the foot of the perpe 60. The foot of the perpendicular drawn from the point $(-2,-1,3)$ to a plane $\pi$ is $(1,0,-2)$. If $a, b, c$ are the inte 61. $\lim\limits_{x \rightarrow \frac{3}{2}} \frac{\left(4 x^{2}-6 x\right)\left(4 x^{2}+6 x+9\right)}{\sqrt[3]{2 x}-\sqrt[3 62. If the real valued function $f(x)=\int \frac{\left(4^{x}-1\right)^{4} \cot (x \log 4)}{\sin (x \log 4) \log \left(1+x^{2 63. A function $f: R \rightarrow R$ is such that $y f(x+y)+\cos m x y=1+y f(x)$. If $m=2$, then $f^{\prime}(x)=$ 64. If $y=\sqrt{\sin (\log 2 x)+\sqrt{\sin (\log 2 x)+\sqrt{\sin (\log 2 x)+\ldots \infty,}}}$ then $\frac{d y}{d x}=$ 65. If $y=\tan ^{-1}\left[\frac{\sin ^{3}(2 x)-3 x^{2} \sin (2 x)}{3 x \sin ^{2}(2 x)-x^{3}}\right]$, then $\frac{d y}{d x}= 66. Derivative of $(\sin x)^{x}$ with respect to $x^{(\sin x)}$ is 67. For a given function $y=f(x), \delta y$ denote the actual error in $y$ corresponding to actual error $\delta x$ in $x$ a 68. The length of the normal drawn at $t=\frac{\pi}{4}$ on the curve $x=2(\cos 2 t+t \sin 2 t), y=4(\sin 2 t+t \cos 2 t)$ is 69. If Water is poured into a cylindrical tank of radius 3.5 ft at the rate of $1 \mathrm{cu} \mathrm{ft} / \mathrm{min}$, t 70. $y=2 x^{3}-8 x^{2}+10 x-4$ is a function defined on [1,2]. If the tangent drawn at a point $(a, b)$ on the graph of this 71. If $m$ and $M$ are respectively the absolute minimum and absolute maximum values of a function $f(x)=2 x^{3}+9 x^{2}+12 72. $\int \frac{\sec x}{3(\sec x+\tan x)+2} d x=$ 73. $\int \frac{d x}{4+3 \cot x} d x=$ 74. $\int \frac{d x}{(x+1) \sqrt{x^{2}+4}}=$ 75. If $\int e^{x}\left(x^{3}+x^{2}-x+4\right) d x=e^{x} f(x)+c$, then $f(1)=$ 76. $\int_{\frac{\pi}{5}}^{\frac{3 \pi}{10}} \frac{d x}{\sec ^{2} x+\left(\tan ^{2024} x-1\right)\left(\sec ^{2} x-1\right)} 77. $\int_{-\pi / 15}^{\pi / 5} \frac{\cos 5 x}{1+e^{5 x}} d x=$ 78. The area of the region (in sq units) enclosed by the curves $y=8 x^{3}-1, y=0, x=-1$ and $x=1$ is 79. If the equation of the curve which passes through the point $(1,1)$ satisfies the differential equation $\frac{d y}{d x} 80. The general solution of the differential equation $\left(6 x^{2}-2 x y-18 x+3 y\right) d x-\left(x^{2}-3 x\right) d y=0$
Physics
1. The range of gravitational forces is 2. In a simple pendulum experiment for the determination of acceleration due to gravity, the error in the measurement of th 3. The position $x$ (in metre) of a particle moving along a straight line is given by $x=t^{3}-12 t+3$, where $t$ is time ( 4. The maximum horizontal range of a ball projected from the ground is 32 m . If the ball is thrown with the same speed hor 5. A block of mass 5 kg is kept on a smooth horizontal surface. A horizontal stream of water coming out of a pipe of area o 6. A constant force of $(8 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}) \mathrm{N}$ acting on a body of mass 2 k 7. A ball $A$ of mass 1.2 kg moving with a velocity of $8.4 \mathrm{~ms}^{-1}$ makes one-dimensional elastic collision with 8. A meter scale is balanced on a knife edge at its centre. When two coins, each of mass 9 g are kept one above the other a 9. A body of mass $m$ and radius $r$ rolling horizontally $m$ an inclined plane to a verticala velocity $v$ rolls up an hei 10. A massless spring of length $l$ and spring constant $k$ oscillates with a time period $T$ when loaded with a mass $m$. T 11. An object of mass $m$ at a distance of $20 R$ from the centre of a planet of mass $M$ and radius $R$ has an initity velo 12. A simple pendulum is made of a metal wire of length $L$, area of cross-section $A$, material of Young's modulus $Y$ and 13. If the excess pressures inside two soap bubbles are in the ratio $2: 3$, then the ratio of the volumes of the somp bubbl 14. The velocities of air above and below the surfaces of a flying aeroplane wing are $50 \mathrm{~ms}^{-1}$ and $40 \mathrm 15. A pendulum clock loses 10.8 s a day when the temperature is $38^{\circ} \mathrm{C}$ and gains 108 s a day when the tempe 16. A liquid cools from a temperature of 368 K to 358 K in 22 min . In the same room, the same liquid takes 12.5 min to cool 17. For a gas in a thermodynamic process, the relation between internal energy $U$, the pressure $p$ and the volume $V$ is $ 18. At a pressure $p$ and temperature $127^{\circ} \mathrm{C}$, a vessel contains 21 g of a gas. A small hole is made into t 19. The tension applied to a metal wire of one metre length produces an elastic strain of $1 \%$. The density of the metal i 20. Two closed pipes when sounded simultaneously in their fundamental modes produce 6 beats per second. If the length of the 21. An object placed at a distance of 24 cm from a concave mirror forms an image at a distance of 12 cm from the mirror. If 22. When the object and the screen are 90 cm apart, it is observed that a clear image is formed on the screen when a convex 23. When a monochromatic light is incident on a surface separating two media, both the reflected and refracted lights have t 24. The electric flux due to an electric field $\mathbf{E}=(8 \hat{\mathbf{i}}+13 \hat{\mathbf{j}}) \mathrm{NC}^{-1}$ throug 25. A capacitor of capacitance $C$ is charged to a potential $V$ and disconnected from the battery. Now, if the space betwee 26. A voltmeter of resistance $400 \Omega$ is used to measure the emf of a cell with an internal resistance of $4 \Omega$. T 27. When two wires are connected in the two gaps of a meter bridge, the balancing length is 50 cm . When the wire in the rig 28. A magnetic field is applied in $y$-direction on an $\alpha$-particle travelling along $x$-direction. The motion of the $ 29. A straight wire carrying a current of $2 \sqrt{2} \mathrm{~A}$ is making an angle of $45^{\circ}$ with the direction of 30. The magnetising field which produces a magnetic flux of $22 \times 10^{-6} \mathrm{~Wb}$ in a metal bar of area of cross 31. The energy stored in a coil of inductance 80 mH carrying a current of 2.5 A is 32. A capacitor and a resistor are connected in series to an AC source. If the ratio of the capacitive reactance of the capa 33. For the displacement current through the plates of a parallel plate capacitor of capacitance $30 \mu \mathrm{~F}$ to be 34. The work functions of two photosensitive metal surfaces $A$ and $B$ are in the ratio $2: 3$. If $x$ and $y$ are the slop 35. In hydrogen atom, the frequency of the photon emitted when an electron jumps from second orbit to first orbit is $f$. Th 36. If the ratio of the radii of nuclei ${ }_{52} X^{A}$ and ${ }_{13} \mathrm{AI}^{27}$ is $5: 3$, then the number of neutr 37. Half-life periods of two nuclei $A$ and $B$ are $T$ and $2 T$ respectively. Initially $A$ and $B$ have same number of nu 38. Match the devices given in List-I with their uses given in List-II. .tg {border-collapse:collapse;border-spacing:0;} . 39. To get output 1 for the following logic circuit, the correct choice of the inputs is 40. The maximum distance between the transmitting and receiving antennas is $D$. If the heights of both transmitting and rec
1
TG EAPCET 2024 (Online) 11th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $y=\tan ^{-1}\left[\frac{\sin ^{3}(2 x)-3 x^{2} \sin (2 x)}{3 x \sin ^{2}(2 x)-x^{3}}\right]$, then $\frac{d y}{d x}=$
A
$\frac{6 x \cos (2 x)-3 \sin (2 x)}{x^{2}-\sin ^{2}(2 x)}$
B
$\frac{6 x \sin (2 x)-3 \cos (2 x)}{x^{2}+\sin ^{2}(2 x)}$
C
$\frac{2 x \cos (2 x)-\sin (2 x)}{x^{2}+\sin ^{2}(2 x)}$
D
$\frac{6 x \cos (2 x)-3 \sin (2 x)}{x^{2}+\sin ^{2}(2 x)}$
2
TG EAPCET 2024 (Online) 11th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
Derivative of $(\sin x)^{x}$ with respect to $x^{(\sin x)}$ is
A
$\frac{(\sin x)^{x-1}[(\sin x) \log (\sin x)+x \cos x]}{x^{(\sin x-1)}[x \cos x(\log x)+\sin x]}$
B
$\frac{(\sin x)^{x}[(\sin x)(\log (\sin x)+x \cos x)]}{x^{(\sin x)}[x \cos x(\log x)+\sin x]}$
C
$\frac{x^{\sin x-1}[x \cos x(\log x)+\sin x]}{(\sin x)^{x-1}[(\sin x) \log (\sin x)+x \cos x]}$
D
$\frac{x^{\sin x}[x \cos x(\log x)+\sin x]}{(\sin x)^{x}[(\sin x) \log (\sin x)+x \cos x]}$
3
TG EAPCET 2024 (Online) 11th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
For a given function $y=f(x), \delta y$ denote the actual error in $y$ corresponding to actual error $\delta x$ in $x$ and $d y$ denotes the approximately value of $\delta y$. If $y=f(x)=2 x^{2}-3 x+4$ and $\delta x=0.02$, then the value of $\delta y-d y$ when $x=5$ is
A
0.0008
B
0.008
C
0.0004
D
0.004
4
TG EAPCET 2024 (Online) 11th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The length of the normal drawn at $t=\frac{\pi}{4}$ on the curve $x=2(\cos 2 t+t \sin 2 t), y=4(\sin 2 t+t \cos 2 t)$ is
A
$\frac{4}{\pi} \sqrt{1+\pi^{2}}$
B
$4 \sqrt{1+\pi^{2}}$
C
$4 \pi$
D
$\frac{4}{\pi}$
Paper analysis
Total Questions
Chemistry
40
Mathematics
80
Physics
40