Chemistry
1. The wavelength of an electron is $10^{3} \mathrm{~nm}$. What is its momentum in $\mathrm{kg} \mathrm{ms}^{-1}$ ? ( $\lef 2. Two statements are given below :Statement I : In H atom, the energy of $2 s$ and $2 p$ orbitals is same.Statements II : 3. The set containing the elements with positive electron gain enthalpies is 4. Assertion (A) : The ionic radii of $\mathrm{Na}^{+}$and $\mathrm{F}^{-}$are same.
Reason (R) : Both $\mathrm{Na}^{+}$an 5. The number of lone pairs of electrons on central atom of $\mathrm{ClF}_{3}, \mathrm{NF}_{3}, \mathrm{SF}_{4}, \mathrm{Xe 6. The hybridisation of central atom of $\mathrm{BF}_{3}, \mathrm{SnCl}_{2}, \mathrm{HgCl}_{2}$ respectively is 7. The variation of volume of an ideal gas with its number of moles $(n)$ is obtained as a graph at 300 K and 1 atm pressur 8. Observe the following reaction,$ 2 \mathrm{KClO}_{3}(s) \xrightarrow{\Delta} 2 \mathrm{KCl}(\mathrm{~s})+3 \mathrm{O}_{2 9. The $\Delta_{f} H^{\theta}$ of $\mathrm{AO}(s), \mathrm{BO}_{2}(g)$ and $A B \mathrm{O}_{3}(s)$ is $-635, x$ and $-1210 10. At $27^{\circ} \mathrm{C}, 100 \mathrm{~mL}$ of 0.5 M HCl is mixed with 100 mL of 0.4 M NaOH solution. To this resultant 11. The proper conditions of storing $\mathrm{H}_{2} \mathrm{O}_{2}$ are 12. The standard electrode potentials $E^{\circ}(\mathrm{V})$ for $\mathrm{Li}^{+} / \mathrm{Li}, \mathrm{Na}^{+} / \mathrm{ 13. The alloy formed by beryllium with ' $X$ ' is used in the preparation of high strength springs. ' $X$ ' is 14. What are $X$ and $Y$ respectively in the following reactions ?$ X \stackrel{\mathrm{CO}}{\longleftarrow} \mathrm{~B}_{2} 15. Which of the following statements are correct?(i) $\mathrm{CCl}_{4}$ undergoes hydrolysis easily(ii) Diamond has directi 16. Which of the following industries generate nonbiodegradable wastes? 17. Possible number of isomers including stereoisomers for an organic compound with the molecular formula $\mathrm{C}_{4} \m 18. The alkane which is next to methane in homologous series can be prepared from which of the following reactions?$ \text { 19. At high pressure and regulated supply of air, methane is heated with catalyst ' $X$ to give methanol and with catalyst ' 20. What is ' $ Y $ ' in the following set of reactions? $$ \mathrm{C}_3 \mathrm{H}_4 \xrightarrow[\substack{\mathrm{Hg}^{2+ 21. The molecular formula of a crystal is $A B_{2} \mathrm{O}_{4}$. Oxygen atoms form ccp lattice. Atoms of $A$ occupy $x \% 22. At $T(\mathrm{~K}), 0.1$ mole of a non-volatile solute was dissolved in 0.9 mole of a volatile solvent. The vapour press 23. Two statements are given below.Statement I : Molten NaCl is electrolysed using Pt electrodes. $\mathrm{Cl}_{2}$ is liber 24. For a first order reaction, the graph between $\log \frac{a}{(a-x)}$ (on $y$-axis) and time (in min, on $x$-axis) gave a 25. In Haber's process of manufacture of ammonia, the 'catalyst' the 'promoter' and 'poison for the catalyst' are respective 26. Among the following the calcination process is 27. The correct order of boiling points of hydrogen halides is 28. Observe the following reactions (unbalanced)$ \begin{array}{r} \mathrm{P}_{2} \mathrm{O}_{3}+\mathrm{H}_{2} \mathrm{O} \ 29. Carbon on reaction with hot conc. $\mathrm{H}_{2} \mathrm{SO}_{4}$, gives two oxides along with $\mathrm{H}_{2} \mathrm{ 30. Which of the following orders is correct for the property given? 31. Arrange the following in increasing order of their crystal field splitting energyI. $\left[\mathrm{Co}\left(\mathrm{H}_{ 32. What are ' $X$ ' and ' $Y$ ' respectively in the following reactions ?
33. Two statements are given below :I. Milk sugar is disaccharide of $\alpha$-D-galactose and $\beta$-D-glucoseII. Sucrose i 34. The effects that aspirin can produce in the body are
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border- 35. The reagent ' $X$ ' used in the following reaction to obtain good yield of the product is
36. 37. IUPAC name of the following compound is
38. The bromides formed by the cleavage of ethers $A$ and $B$ with HBr respectively are
39. Identify the set, in which $X$ and $Y$ are correctly matched
40. What are $X$ and $Y$ respectively in the following reactions?
Mathematics
1. The domain of the real valued function $f(x)=\sin ^{-1}\left(\log _{2}\left(\frac{x^{2}}{2}\right)\right)$ is 2. The range of the real valued function $f(x)=\log _{3}\left(5+4 x-x^{2}\right)$ is 3. If $3^{2 n+2}-8 n-9$ is divisible by $2^{p}, \forall n \in \mathrm{~N}$, then the maximum value of $P$ is 4. $A=\left[a_{i j}\right]$ is a $3 \times 3$ matrix with positive integers as its elements. Elements of $A$ are such that 5. If $|\operatorname{adj} A|=x$ and $|\operatorname{adj} B|=y$, then $\left|(\operatorname{adj}(A B))^{-1}\right|=$ 6. The system of equations $x+3 b y+b z=0, x+2 a y+a z=0$ and $x+4 c y+c z=0$ has 7. $\left|\begin{array}{ccc}\frac{-b c}{a^{2}} & \frac{c}{a} & \frac{b}{a} \\ \frac{c}{b} & -\frac{a c}{b^{2}} & \frac{a}{b 8. If $z=x+i y$ satisfies the equation $z^{2}+a z+a^{2}=0, a \in R$, then 9. If $z_{1}, z_{2}, z_{3}$ are three complex numbers with unit modulus such that $\left|z_{1}-z_{2}\right|^{2}+\left|z_{1} 10. If $\omega$ is the complex cube root of unity and$\left(\frac{a+b \omega+c \omega^{2}}{c+a \omega+b \omega^{2}}\right)^{ 11. If $z_{1}=\sqrt{3}+i \sqrt{3}$ and $z_{2}=\sqrt{3}+i$, and $\left(\frac{z_{1}}{z_{2}}\right)^{50}=x+i y$, then the point 12. The solution set of the equation $3^{x}+3^{1-x}-4 13. The common solution set of the inequations $x^{2}-4 x \leq 12$ and $x^{2}-2 x \geq 15$ taken together is 14. The roots of the equation $x^{3}-3 x^{2}+3 x+7=0$ are $\alpha, \beta, \lambda$ and $\omega, \omega^{2}$ are complex cube 15. With respect to the roots of the equation $3 x^{3}+b x^{2}+b x+3=0$, match the items of List I with those fo List II
. 16. The number of ways of arranging all the letters of the word 'COMBINATIONS' around a circle so that no two vowels togethe 17. If all the numbers which are greater than 6000 and less than 10000 are formed with the digits, $3,5,6,7,8$ without repet 18. A man has 7 relatives, 4 of them are ladies and 3 gents; his wife has 7 other relatives, 3 of them are ladies and 4 gent 19. If the coefficient fo $x^{r}$ in the expansion of $\left(1+x+x^{2}+x^{3}\right)^{100}$ is $a_{r}$ and $S=\sum_{r=0}^{300 20. Assertion (A) : $1+\frac{2 \cdot 1}{3 \cdot 2}+\frac{2 \cdot 5}{3 \cdot 6} \frac{1}{4}+\frac{2 \cdot 5 \cdot 8}{3 \cdot 21. If $\frac{1}{x^{4}+x^{2}+1}=\frac{A x+B}{x^{2}+a x+1}+\frac{C x+D}{x^{2}-a x+1}$, then $A+B-C+D=$ 22. If $0 23. $\sin 20^{\circ}\left(4+\sec 20^{\circ}\right)=$ 24. Suppose, $\theta_{1}$ and $\theta_{2}$ are such that $\left(\theta_{1}-\theta_{2}\right)$ lies in 3rd or 4th quadrant. I 25. If $A$ is the solution set of the equation $\cos ^{2} x=\cos ^{2} \frac{\pi}{6}$ and $B$ is the solution set of the equa 26. The trigonometric equation $\sin ^{-1} x=2 \sin ^{-1} a$, has a solution 27. If $\sin h x=\frac{12}{5}$, then $\sin h 3 x+\cos h 3 x=$ 28. If $A B C$ is an isosceles triangle with base $B C$, then $r_{1}=$ 29. In $\triangle A B C$, if $r_{1}+r_{2}=3 R, r_{2}+r_{3}=2 R$, then 30. $\mathbf{n}$ is a unit vector normal to the plane $\pi$ containing the vectors $\hat{\mathbf{i}}+3 \hat{\mathbf{k}}$ and 31. If $\mathbf{a}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \mathbf{c}=-\hat{\mathbf{k}}$ are position vectors 32. $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are three vectors each having $\sqrt{2}$ magnitude such that $(\mathbf{a}, \mathbf{ 33. $\mathbf{a}$ is a vector perpendicular to the plane containing non zero vectors $\mathbf{b}$ and $\mathbf{c}$. If $\math 34. If $\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=3(\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat 35. The variance of the first 10 natural numbers which are multiples of 3 is 36. If three numbers are randomly selected from the set $\{1,2,3, \ldots \ldots 50\}$, then the probability that they are in 37. The probability that exactly 3 heads appear in six tosses of an unbiased coin, given that first three tosses resulted in 38. A student has to write the words ABILITY, PROBABILITY, FACILITY, MOBILITY. He wrote one word and erased all the letters 39. Two cards are drawn at random one after the other with replacement from a pack of playing cards. If $X$ is the random va 40. If $X \sim B(6, p)$ is a binomial variate and $\frac{P(X=4)}{P(X=2)}=\frac{1}{9}$, then $p=$ 41. If the locus of the centroid of the triangle with vertices $A(a, 0), B(a \cos t, a \sin t)$ and $C(b \sin ,-b \cos t)$ ( 42. By shifting the origin to the point $(h, 5)$ by the translation of coordinate axes, if the equation $y=x^{3}-9 x^{2}+c x 43. The equation of the straight line whose slope is $\frac{-2}{3}$ and which divides the line segment joining $(1,2),(-3,5) 44. $7 x+y-24=0$ and $x+7 y-24=0$ represent the equal sides of an isosceles triangle. If the third side passes through $(-1, 45. The combined equation of a possible pair of adjacent sides of a square with area 16 square units whose centre is the poi 46. If the line $2 x+b y+5=0$ forms an equilateral to triangle with $a x^{2}-96 b x y+k y^{2}=0$, then $a+3 k=$ 47. A rhombus is inscribed in the region common to the two circles $x^{2}+y^{2}-4 x-12=0$ and $x^{2}+y^{2}+4 x-12=0$. If the 48. If $m$ is the slope and $P(8, \beta)$ is the mid-point of a chord of contact of the circle $x^{2}+y^{2}=125$, then the n 49. A rectangle is formed by the lines $x=4, x=-2, y=5, y=-2$ and a circle is drawn through the vertices of this rectangle. 50. The equation of a circle which passes through the points of intersection of the circles $2 x^{2}+2 y^{2}-2 x+6 y-3=0, x^ 51. If the equation of the circle which cuts each of the circles $x^{2}+y^{2}=4, x^{2}+y^{2}-6 x-8 y+10=0$ and $x^{2}+y^{2}+ 52. The equation of the circle passing through the origin and cutting the circles $x^{2}+y^{2}+6 x-15=0$ and $x^{2}+y^{2}-8 53. $S=(-1,1)$ is the focus, $2 x-3 y+1=0$ is the directrix corresponding, to $S$ and $\frac{1}{2}$ is the eccentricity of a 54. $S=y^{2}-4 a x=0, S^{\prime}=y^{2}+a x=0$ are two parabolas and $P(t)$ is a point on the parabola $S^{\prime}=0$. If $A$ 55. $a$ and $b$ are the semi-major and semi-minor axes of an ellipse whose axes are along the coordinate axes, If its latus 56. If the extremities of the latus recta having positive ordinate of the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 57. If the tangent drawn at a point $P(t)$ on the hyperbola $x^{2}-y^{2}=c^{2}$ cuts $X$-axis at $T$ and the normal drawn at 58. If the harmonic conjugate of $P(2,3,4)$ with respect to the line segment joining the points $A(3,-2,2)$ and $B(6,-17,-4) 59. If $L$ is the line of intersection of two planes $x+2 y+2 z=15$ and $x-y+z=4$ and the direction ratio of the line $L$ ar 60. The foot of the perpendicular drawn from $A(1,2,2)$ oril the the plane $x+2 y+2 z-5=0$ is $B(\alpha, \beta, \gamma)$. If 61. If $0 \leq x \leq \frac{\pi}{2}$, then $\lim _{x \rightarrow a} \frac{|2 \cos x-1|}{2 \cos x-1}$ 62. The real valued function $f(x)=\frac{|x-a|}{x-a}$ is 63. If $f(x)=3 x^{15}-5 x^{10}+7 x^{5}+50 \cos (x-1)$, then $\lim\limits_{h \rightarrow 0} \frac{f(1-h)-f(1)}{h^{3}+3 h}$ 64. If the function $f(x)=\left\{\begin{array}{cl}\frac{\left(e^{k x}-1\right) \sin k x}{4 \tan x} & x \neq 0 \\ P & x=0\end 65. If $y=\log \left(x-\sqrt{x^{2}-1}\right)$, then $\left(x^{2}-1\right) y^{\prime \prime}+x y^{\prime}+e^{y}+\sqrt{x^{2}-1 66. The maximum interval in which the slopes of the tangents drawn to the curve $y=x^{4}+5 x^{3}+9 x^{2}+6 x+2$ increase is 67. If $A=\{P(\alpha, \beta) /$ the tangent drawn at $P$ to the curve $y^{3}-3 x y+2=0$ is horizontal line $\}$ and $B=\{Q(a 68. In a $\triangle A B C$, the sides $b, c$ are fixed. In measuring angle $A$, if there is an error of $\delta A$, then the 69. $y=f(x)$ and $x=g(y)$ are two curves and $P(x, y)$ is a common point of the two curves. If at $P$ on the curve $y=f(x), 70. If Rolle's Theorem is applicable for the function $f(x)=\left\{\begin{array}{cl}x^{p} \log x, & x \neq 0 \\ 0, & x=0\end 71. The sum of the maximum and minimum values of the function $f(x)=\frac{x^{2}-x+1}{x^{2}+x+1}$ is 72. If $\int \frac{1}{x^{4}+8 x^{2}+9} d x=\frac{1}{k}$$\left[\frac{1}{\sqrt{14}} \tan ^{-1}(f(x))-\frac{1}{\sqrt{2}} \tan ^ 73. If $\int\left(1+x-x^{-1}\right) e^{\left(x+x^{-1}\right)} d x=f(x)+C$, then $f(1)-f(-1)=$ 74. $ \int \frac{1}{x^{m} \sqrt[m]{x^{m}+1}} d x =$ 75. If $\int(\sqrt{\operatorname{cosec} x+1}) d x=k \tan ^{-1}(f(x))+C$, then $\frac{1}{k} f\left(\frac{\pi}{6}\right)=$ 76. $\frac{3}{25} \int_{0}^{25 \pi} \sqrt{\left|\cos x-\cos ^{3} x\right|} d x=$ 77. If the area of the region enclosed by the curve $a y=x^{2}$ and the line $x+y=2 a$ is $k a^{2}$, then $k=$ 78. If $m, l, r, s, n$ are integers such that $9 > m > l > s > n > r > 2$ and $\int_{-2 \pi}^{2 \pi} \sin ^{m} x \cos ^{n} x 79. The order and degree of the differential equation$ \frac{d y}{d x}=\left(\frac{d^{2} y}{d x^{2}}+2\right)^{\frac{1}{2}}+ 80. If $y=\sin x+A \cos x$ is general solution of $\frac{d x}{d y}+f(x) y=\sec x$, then an integrating factor of the differe
Physics
1. Wave picture of light has failed to explain 2. A capacitor of capacitance $(4.0 \pm 0.2) \mu \mathrm{F}$ is charged to a potential of $(10.0 \pm 0 \mathrm{l}) \mathrm{ 3. A body is thrown vertically upwards with a velocity of $35 \mathrm{~ms}^{-1}$ from the ground. The ratio of the speeds o 4. From a height of $h$ above the ground, a ball is projected up at an angle $30^{\circ}$ with the horizontal. If the ball 5. A block is kept on a rough horizontal surface. The acceleration of the block increases from $6 \mathrm{~ms}^{-2}$ to $11 6. The kinetic energy of a body of mass 4 kg moving with a velocity of $(2 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}-\hat{\mathbf 7. A ball $P$ of mass 0.5 kg moving with a velocity of $10 \mathrm{~ms}^{-1}$ collides with another ball $Q$ of mass 1 kg a 8. A circular plate of radius $r$ is removed from a uniform circular plate $P$ of radius $4 r$ to form a hole. If the dista 9. A hollow cylinder and a solid cylinder initially at restat the top of an inclined plane are rolling down without slippin 10. A block kept on a frictionless horizontal surface is connected to one end of a horizontal spring of constant $100 \mathr 11. The ratio of the radii of a planet and the earth is $1: 2$, the ratio of their mean densities is $4: 1$. If the accelera 12. A wire of cross-sectional area $10^{-6} \mathrm{~m}^{2}$ is elongated by $0.1 \%$ when the tension in it is 1000 N . The 13. The work done in blowing a soap bubble of volume $V$ is $W$. The work done in blowing the bubble of volume 2 V from the 14. Three identical vessels are filled up to the same height with three different liquids $A, B$ and $C$ of densities $\rho_ 15. Steam of mass 60 g at a temperature $100^{\circ} \mathrm{C}$ is mixed with water of mass 360 g at a temperature $40^{\ci 16. The temperature difference between the ends of two cylindrical rods $A$ and $B$ of the same material is $2: 3$. In stead 17. When $Q_{1}$ amount of heat supplied to a monoatomic gas, the work done by the gas is $W$. When $Q_{2}$ amount of heat i 18. The temperature at which the rms speed of oxygen molecules is $75 \%$ or rms speed of nitrogen molecules at a temperatur 19. The path difference between two particles of a sound wave is 50 cm and the phase difference between them is $1.8 \pi$. I 20. A source at rest emits sound waves of frequency 102 Hz . Two observers are moving away from the source of sound in oppos 21. The power of a thin convex lens placed in air is +4 D . The refractive index of the material of the convex lens is $\fra 22. The refractive index of the material of a small angled prism is 1.6. If the angle of minimum deviation is $4.2^{\circ}$, 23. The Brewster angle for air to glass transition of light is (Refractive index of glass $=15$ ) 24. A proton and an $\alpha$-particle are both accelerated from rest in a uniform electric field. The ratio of work done by 25. Two capacitors of capacitances $1 \mu \mathrm{~F}$ and $2 \mu \mathrm{~F}$ can separately withstand potentials of 6 kV a 26. The resistance of a wire is $2.5 \Omega$ at a temperature 373 K . If the temperature coeffficient of resistance of the m 27. When two identical resistors are connected in series to an ideal cell, the current through each resistor is 2 A . If the 28. An electron falling freely under the influence of gravity enters a uniform magnetic field directed towards south. The el 29. Two long straight parallel wires $A$ and $B$ separated by 5 m carry currents 2 A and 6 A respectively in the same direct 30. A short bar magnet placed in a uniform magnetic field making an angle with the field experiences a torque.If the angle m 31. The mutual inductance of two coils is 8 mH . The current in one coil changes according to the equation $I=12 \sin 100 t$ 32. An inductor of inductive reactance $R$, a capacitor of capacitive reactance $2 R$ and a resistor of resistance $R$ are c 33. The efficiency of a bulb of power 60 W is $16 \%$. The peak value of the electric field produced by the electromagnetic 34. The work function of a photosensitive metal surface is 1.1 eV . Two light beams of energies 1.5 eV and 2 eV incident on 35. The ground state energy of hydrogen atom is -13.6 cv . The potential energy of the electron in the first excited state o 36. After the decay of a single $\beta$-particle, the parent and daughter nuclei are 37. $\mathrm{A}_{92} \mathrm{U}^{238}$ nucleus decays to a ${ }_{82} \mathrm{~Pb}^{214}$ nucleus. The number of $\alpha$ and 38. In an $n$-type semiconductor, electrons are majority charge carriers and holes are minority charge carriers. The charge 39. The region in the output voltage versus input voltage graph where a transistor can be used as an amplifier is 40. For an amplitude modulated wave, the maximum and minimum amplitudes are found to be 10 V and 2 V respectively. Then, the
1
TG EAPCET 2024 (Online) 10th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If the coefficient fo $x^{r}$ in the expansion of $\left(1+x+x^{2}+x^{3}\right)^{100}$ is $a_{r}$ and $S=\sum_{r=0}^{300} a_{r}$ then $\sum_{r=0}^{300} r \cdot a_{r}=$
A
(50) S
B
$(25) \mathrm{S}$
C
$(150) \mathrm{S}$
D
$(100) \mathrm{S}$
2
TG EAPCET 2024 (Online) 10th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
Assertion (A) : $1+\frac{2 \cdot 1}{3 \cdot 2}+\frac{2 \cdot 5}{3 \cdot 6} \frac{1}{4}+\frac{2 \cdot 5 \cdot 8}{3 \cdot 6 \cdot 9} \frac{1}{8}+\ldots \infty=\sqrt[3]{4}$
Reason (R) : |x| < 1,(1-x) $=1+n x+\frac{n(n+1)}{1 \cdot 2} x^2$$+\frac{n(n+1)(n+2)}{1 \cdot 2 \cdot 3} x^{3}+\ldots$
The correct answer is :
A
(A) and (R) are correct, ( $R$ ) is the correct explanation of $(A)$
B
(A) and (R) are correct, but (R) is not correct explanalion of (A)
C
(A) is correct but (R) is not correct
D
(A) is not correct but (R) is correct
3
TG EAPCET 2024 (Online) 10th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $\frac{1}{x^{4}+x^{2}+1}=\frac{A x+B}{x^{2}+a x+1}+\frac{C x+D}{x^{2}-a x+1}$, then $A+B-C+D=$
A
$a$
B
$2 a$
C
$3 a$
D
$4 a$
4
TG EAPCET 2024 (Online) 10th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $0 < \theta < \frac{\pi}{4}$ and $8 \cos \theta+15 \sin \theta=15$, then $15 \cos \theta-8 \sin \theta=$
A
15
B
7
C
8
D
23
Paper analysis
Total Questions
Chemistry
40
Mathematics
80
Physics
40