Chemistry
1. Assuming that the incident radiation is
capable of ejecting photoelectrons from all
the given metals, the lowest kinetic 2. If the energies of two light radiations $$E_1$$ and $$E_2$$ are $$25 \mathrm{~eV}$$ and $$100 \mathrm{~eV}$$ respectivel 3. The electronic configuration of $$\mathrm{Fe}^{3+}$$ is (atomic number of $$\mathrm{Fe}=26$$ ) 4. The element with outer electronic configuration $$(n-1) d^2 n s^2$$, where $$n=4$$, would belong to 5. Choose the correct option regarding the following statements
Statement 1 Nitrogen has lesser electron gain enthalpy than 6. Among the given configurations, identify the element which does not belong to the same family as the others? 7. Which compound among the following has
the highest dipole moment? 8. How many among the given species have a bond order of 0.5 ?
$$\mathrm{H}_2^{+}, \mathrm{He}_2^{+}, \mathrm{He}_2^{-}, \m 9. Match the following.
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.tg td{border-color:black;border-style:solid;bor 10. Among the following the maximum deviation from ideal gas behaviour is expected from 11. Two flasks $$A$$ and $$B$$ have equal volumes. $$A$$ is maintained at $$300 \mathrm{~K}$$ and $$B$$ at $$600 \mathrm{~K} 12. If 0.2 moles of sulphuric acid is poured into
250 mL of water, calculate the concentration
of the solution. 13. For the redox reaction
$$\mathrm{MnO}_4^{-}+\mathrm{C}_2 \mathrm{O}_4^{2-}+\mathrm{H}^{+} \longrightarrow \mathrm{Mn}^{2 14. When the temperature of 2 moles of an ideal
gas is increased by 20$$^\circ$$C at constant pressure.
Find the work involv 15. Using the data provided, find the value of equilibrium constant for the following reaction at $$298 \mathrm{~K}$$ and $$ 16. Calculate the pOH of 0.10 M HCl solution. 17. Which among the following pairs is not an acidic buffer? 18. Assertion (A) The colour of old lead paintings can be restored by washing them with a dilute solution of $$\mathrm{H}_2 19. In the preparation of baking soda, H$$_2$$O and CO$$_2$$ in ratio ......... is used to react with Na$$_2$$CO$$_3$$. 20. The structure of diborane B$$_2$$H$$_6$$ is given
below. Identify the bond angles of x and y. In
diborane, ........... a 21. The incorrect statement(s) among the following is/are 22. Which among the following has the highest
concentration of PAN? 23. What is the IUPAC name of $$\mathrm{CH}_3 \mathrm{CH}\left(\mathrm{CH}_2 \mathrm{CH}_3\right) \mathrm{CHO}$$ ? 24. Among the following, in which type of chromatography, both stationary and mobile phases are in liquid state? 25. The product formed when a hydrocarbon $$X$$ of molecular formula $$\mathrm{C}_6 \mathrm{H}_{10}$$ is reacted with sodami 26. The fcc crystal contains how many atoms in
each unit cell? 27. Which condition is not satisfied by an ideal solution? 28. A solution of urea (molar mass $$60 \mathrm{~g} \mathrm{~mol}^{-1}$$ ) boils at $$100.20^{\circ} \mathrm{C}$$ at the atm 29. At $$291 \mathrm{~K}$$, saturated solution of $$\mathrm{BaSO}_4$$ was found to have a specific conductivity of $$3.648 \ 30. Find the emf of the following cell reaction. Given, $$E_{\mathrm{Cr}^{3+} / \mathrm{Cr}^{2+}}^{\Upsilon}=-0.72 \mathrm{~ 31. For $$\mathrm{C{r_2}O_7^{2 - } + 14{H^ + } + 6{e^ - }\buildrel {Yields} \over
\longrightarrow 2C{r^{3 + }} + 7{H_2}O,{E 32. The protective power of a lyophilic colloidal sol is expressed in terms of 33. Due to $$p \pi-p \pi$$ bonding interactions, nitrogen for $$\mathrm{N}_2$$. But phosphorus forms .................. and 34. Identify the incorrect statements among the following?
(i) $$\mathrm{SF}_6$$ does not react with water.
(ii) $$\mathrm{S 35. Which statements among the following are correct about helium?
(i) Liquid helium is used to sustain powerful superconduc 36. The magnetic moment of Fe$$^{2+}$$ is ........ BM. 37. Which of the following statement is not correct? 38. Assertion (A) An optically active amino
acid can exist in three forms depending on
the pH of the solution.
Reason (R) Am 39. The IUPAC name of diacetone alcohol is. 40. Identify the product of the following reaction.
Mathematics
1. The real valued function $$f(x)=\frac{x}{e^x-1}+\frac{x}{2}+1$$ defined on $$R /\{0\}$$ is 2. The domain of the function $$f(x)=\frac{1}{[x]-1}$$, where $$[x]$$ is greatest integer function of $$x$$ is 3. Let $$f: R \rightarrow R$$ be a function defined by $$f(x)=\frac{4^x}{4^x+2}$$, what is the value of $$f\left(\frac{1}{4 4. For what natural number $$n \in N$$, the inequality $$2^n > n+1$$ is valid? 5. The value of $$\left|\begin{array}{ccc}b+c & a & a \\ b & c+a & b \\ c & c & a+b\end{array}\right|$$ is 6. Let $$A, B, C, D$$ be square real matrices such that $$C^T=D A B, D^{\mathrm{T}}=A B C$$ and $$S=A B C D$$, then $$S^2$$ 7. $$A=\left[\begin{array}{ccc}a^2 & 15 & 31 \\ 12 & b^2 & 41 \\ 35 & 61 & c^2\end{array}\right]$$ and $$B=\left[\begin{arr 8. Let $$a, b$$ and $$c$$ be such that $$b+c \neq 0$$ and
$$\begin{aligned}
& \left|\begin{array}{ccc}
a & a+1 & a-1 \\
-b 9. If $$|z-2|=|z-1|$$, where $$z$$ is a complex number, then locus $$z$$ is a straight line 10. If $${\left( {{{1 + i} \over {1 - i}}} \right)^m} = 1$$, then m cannot be equal to 11. If $$1+x^2=\sqrt{3} x$$, then $$\sum_{n=1}^{24}\left(x^n-\frac{1}{x^n}\right)^2$$ is equal to 12. If $$\alpha$$ and $$\beta$$ are the roots of $$11 x^2+12 x-13=0$$, then $$\frac{1}{\alpha^2}+\frac{1}{\beta^2}$$ is equa 13. The value of $$a$$ for which the equations $$x^3+a x+1=0$$ and $$x^4+a x^2+1=0$$ have a common root is 14. If $$a$$ is a positive integer such that roots of the equation $$7 x^2-13 x+a=0$$ are rational numbers, then the smalles 15. Let $$p$$ and $$q$$ be the roots of the equation $$x^2-2 x+A=0$$ and let $$r$$ and $$s$$ be the roots of the equation $$ 16. For $$1 \leq r \leq n, \frac{1}{r+1}\left\{{ }^n P_{r+1}-{ }^{(n-1)} P_{r+1}\right\}$$ is equal to 17. In how many ways 4 balls can be picked from
6 black and 4 green coloured balls such that
at least one black ball is sele 18. In how many ways can 9 examination papers
be arranged so, that the best and the worst
papers are never together? 19. Which of the following is partial fraction of $$\frac{-x^2+6 x+13}{(3 x+5)\left(x^2+4 x+4\right)}$$ is equal to 20. In a $$\triangle A B C$$, if $$3 \sin A+4 \cos B=6$$ and $$4 \sin B+3 \cos A=1$$, then $$\sin (A+B)$$ is equal to 21. $$\tan \alpha+2 \tan 2 \alpha+4 \tan 4 \alpha+8 \cot 8 \alpha$$ is equal to 22. If $$f(x)=\frac{\cot x}{1+\cot x}$$ and $$\alpha+\beta=\frac{5 \pi}{4}$$, then the value of $$f(\alpha) f(\beta)$$ is eq 23. If $$\theta \in[0,2 \pi]$$ and $$\cos 2 \theta=\cos \theta+\sin \theta$$, then the sum of all values of $$\theta$$ satis 24. For how many distinct values of $$x$$, the following $$\sin \left[2 \cos ^{-1} \cot \left(2 \tan ^{-1} x\right)\right]=0 25. In $$\triangle A B C$$, suppose the radius of the circle opposite to an angle $$A$$ is denoted by $$r_1$$, similarly $$r 26. In $$\triangle A B C \cdot \frac{a+b+c}{B C+A B}+\frac{a+b+c}{A C+A B}=3$$, then $$\tan \frac{C}{8}$$ is equal to 27. Which of the following vector is equally inclined with the coordinate axes? 28. If $$\hat{\mathbf{i}}+4 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$$, a 29. $$X$$ intercept of the plane containing the line of intersection of the planes $$x-2 y+z+2=0$$ and $$3 x-y-z+1=0$$ and a 30. If $$\mathbf{a}$$ and $$\mathbf{b}$$ are two vectors such that $$\frac{\mathbf{a} \cdot \mathbf{b}}{|\mathbf{a}||\mathbf 31. Let $$L_1$$ (resp, $$L_2$$ ) be the line passing through $$2 \hat{\mathbf{i}}-\hat{\mathbf{k}}$$ (resp. $$2 \hat{\mathbf 32. Let $$\mathbf{a}, \mathbf{b}$$ and $$\mathbf{c}$$ be three-unit vectors and $$\mathbf{a} \cdot \mathbf{b}=\mathbf{a} \cd 33. Let $$x$$ and $$y$$ are real numbers. If $$\mathbf{a}=(\sin x) \hat{\mathbf{i}}+(\sin y) \hat{\mathbf{j}}$$ and $$\mathb 34. The mean and variance of $$n$$ observations $$x_1, x_2, x_3, \ldots . . x_n$$ are 5 and 0 respectively. If $$\sum_{i=1}^ 35. Mean of the values $$\sin ^2 10 Y, \sin ^2 20 Y, \sin ^2 30 Y, \ldots \ldots \ldots ., \sin ^2 90 Y$$ is 36. P speaks truth in 70% of the cases and Q in
80% of the cases. In what percent of cases are
they likely to agree in stati 37. If $$A$$ and $$B$$ are two events with $$P(A \cap B)=\frac{1}{3}, P(A \cup B)=\frac{5}{6}$$ and $$P\left(A^C\right)=\fra 38. A coin is tossed 2020 times. The probability of getting head on 1947th toss is 39. A discrete random variable X takes values 10,
20, 30 and 40. with probability 0.3, 0.3, 0.2
and 0.2 respectively. Then t 40. Let $$X$$ be a random variable which takes values $$1,2,3,4$$ such that $$P(X=r)=K r^3$$ where $$r=1,2,3,4$$ then 41. Given, two fixed points $$A(-2,1)$$ and $$B(3,0)$$.
Find the locus of a point $$P$$ which moves such that the angle $$\a 42. When the coordinate axes are rotated through an angle 135$$\Upsilon$$, the coordinates of a point $$P$$ in the new syste 43. If $$A(4,7), B(-7,8)$$ and $$C(1,2)$$ are the vertices of $$\triangle A B C$$, then the equation of perpendicular bisect 44. The ratio in which the straight line $$3 x+4 y=6$$ divides the join of the points $$(2,-1)$$ and $$(1,1)$$ is 45. Find the equation of a line passing through the point $$(4,3)$$, which cuts a triangle of minimum area from the first qu 46. If the orthocenter of the triangle formed by the lines $$2 x+3 y-1=0, x+2 y+1=0$$ and $$a x+b y-1=0$$ lies at origin, th 47. The equation $$8 x^2-24 x y+18 y^2-6 x+9 y-5=0$$ represents a 48. Find the angle between the pair of lines represented by the equation $$x^2+4 x y+y^2=0$$. 49. If the acute angle between lines $$a x^2+2 h x y+b y^2=0$$ is $$\frac{\pi}{4}$$, then $$4 h^2$$ is equal to 50. The angle between the lines represented by $$\cos \theta(\cos \theta+1) x^2-\left(2 \cos \theta+\sin ^2 \theta\right) x 51. The equations of the tangents to the circle $$x^2+y^2=4$$ drawn from the point $$(4,0)$$ are 52. If $$P(-9,-1)$$ is a point on the circle $$x^2+y^2+4 x+8 y-38=0$$, then find equation of the tangent drawn at the other 53. Find the equation of a circle whose radius is 5 units and passes through two points on the $$X$$-axis, which are at a di 54. If a foot of the normal from the point $$(4,3)$$ to a circle is $$(2,1)$$ and $$2 x-y-2=0$$, is a diameter of the circle 55. The length of the tangent from any point on the circle $$(x-3)^2+(y+2)^2=5 r^2$$ to the circle $$(x-3)^2+(y+2)^2=r^2$$ i 56. The equation of the circle, which cuts orthogonally each of the three circles
$$\begin{aligned}
& x^2+y^2-2 x+3 y-7=0, \ 57. Find the equation of the parabola which
passes through (6, $$-$$2), has its vertex at the
origin and its axis along the 58. In an ellipse, if the distance between the foci
is 6 units and the length of its minor axis is
8 units, then its eccentr 59. If the points (2, 4, $$-$$1), (3, 6, $$-$$1) and (4, 5, $$-$$1) are three consecutive vertices of a parallelogram,
then 60. $$A(-1,2-3), B(5,0,-6)$$ and $$C(0,4,-1)$$ are the vertices of a $$\triangle A B C$$. The direction cosines of internal 61. If the projections of the line segment AB on xy, yz and zx planes are $$\sqrt{15},\sqrt{46},7$$ respectively, then the p 62. Find the equation of the plane passing through the point $$(2,1,3)$$ and perpendicular to the planes $$x-2 y+2 z+3=0$$ a 63. If $$f(x)=\left\{\begin{array}{cc}\frac{e^{\alpha x}-e^x-x}{x^2}, & x \neq 0 \\ \frac{3}{2}, & x=0\end{array}\right.$$
64. The value of $$k(k > 0)$$, for which the function $$f(x)=\frac{\left(e^x-1\right)^4}{\sin \left(\frac{x^2}{k^2}\right) \ 65. If $$\log \left(\sqrt{1+x^2}-x\right)=y\left(\sqrt{1+x^2}\right)$$, then $$\left(1+x^2\right) \frac{d y}{d x}+x y$$ is e 66. If $$f^{\prime \prime}(x)$$ is continuous at $$x=0$$ and $$f^{\prime \prime}(0)=4$$, then find the following value.
$$\l 67. If $$y=e^{x^2+e^{x^2+e^{x^2+\cdots \infty}}}$$, then $$\frac{d y}{d x}$$ is equal to 68. $$\frac{d}{d x}\left[\tan ^{-1}\left(\frac{\cos x}{1+\sin x}\right)\right]$$ is equal to 69. The maximum value of $$f(x)=\sin (x)$$ in the interval $$\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$$ is 70. Given, $$f(x)=x^3-4x$$, if x changes from 2 to 1.99, then the approximate change in the value of $$f(x)$$ is 71. If the curves $$\frac{x^2}{a^2}+\frac{y^2}{4}=1$$ and $$y^3=16 x$$ intersect at right angles, then $$a^2$$ is equal to 72. Let $$x$$ and $$y$$ be the sides of two squares such that, $$y=x-x^2$$. The rate of change of area of the second square 73. If $$f^{\prime \prime}(x)$$ is a positive function for all $$x \in R, f^{\prime}(3)=0$$ and $$g(x)=f\left(\tan ^2(x)-2 \ 74. $$\int \frac{1+x+\sqrt{x+x^2}}{\sqrt{x}+\sqrt{1+x}} d x$$ is equal to 75. $$\int(\cos x) \log \cot \left(\frac{x}{2}\right) d x$$ is equal to 76. $$\int \sqrt{e^{4 x}+e^{2 x}} d x$$ is equal to 77. If $$\int \frac{1}{1+\sin x} d x=\tan (f(x))+c$$, then $$f^{\prime}(0)$$ is equal to 78. If $$\int_0^{\pi / 2} \tan ^n(x) d x=k \int_0^{\pi / 2} \cot ^n(x) d x$$, then 79. $$\int_0^2 x e^x d x$$ is equal to 80. If $$x^2+y^2=1$$, then
Physics
1. The speed of ripples $$(v)$$ on water surface depends on surface tension $$(\sigma)$$, density $$(\rho)$$ and wavelength 2. An object travelling at a speed of 36 km/h
comes to rest in a distance of 200 m after the
brakes were applied. The retar 3. A ball is projected upwards. Its acceleration
at the highest point is 4. A 500 kg car takes a round turn of radius
50 m with a velocity of 36 km/h. The
centripetal force acting on the car is 5. A motor cyclist wants to drive in horizontal circles on the vertical inner surface of a large cylindrical wooden well of 6. Two blocks $$A$$ and $$B$$ of masses $$4 \mathrm{~kg}$$ and $$6 \mathrm{~kg}$$ are as shown in the figure. A horizontal 7. What is the shape of the graph between
speed and kinetic energy of a body? 8. A quarter horse power motor runs at a speed
of 600 rpm. Assuming 60% efficiency, the
work done by the motor in one rotat 9. A particle of mass m is projected with a
velocity u making an angle $$\theta$$ with the
horizontal. The magnitude of ang 10. A sphere of mass m is attached to a spring of
spring constant k and is held in unstretched
position over an inclined pla 11. A girl of mass M stands on the rim of a
frictionless merry-go-round of radius R and
rotational inertia I, that is not mo 12. A block of mass $$\mathrm{l} \mathrm{kg}$$ is fastened to a spring of spring constant of $$100 ~\mathrm{Nm}^{-1}$$. The 13. The scale of a spring balance which can measure from 0 to $$15 \mathrm{~kg}$$ is $$0.25 \mathrm{~m}$$ long. If a body su 14. The distance through which one has to dig
the Earth from its surface, so as to reach the
point where the acceleration du 15. Infinite number of masses each of 3kg are
placed along a straight line at the distances
of 1 m, 2m, 4m, 8m, ...... from 16. Young's modulus of a wire is $$2 \times 10^{11} \mathrm{Nm}^{-2}$$. If an external stretching force of $$2 \times 10^{11 17. Identify the incorrect statement regarding Reynold's number $$\left(R_e\right)$$. 18. Expansion during heating 19. Match the following.
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;bor 20. Which of the following is not a reversible
process? 21. Which one of the graphs below best
illustrates the relationship between internal
energy U of an ideal gas and temperatur 22. A refrigerator with coefficient of
performance 0.25 releases 250 J of heat to a
hot reservoir. The work done on the work 23. A vessel has 6 g of oxygen at pressure p and
temperature 400 K. A small hole is made in
it, so that oxygen leaks out. Ho 24. Match the following.
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;bor 25. Light of wavelength $$300 \mathrm{~nm}$$ in medium $$A$$ enters into medium $$B$$ through a plane surface. If the freque 26. In Young’s double slit experiment, the
separation between the slits is halved and the
distance between the screen is dou 27. Gauss's law helps in 28. Charge on the outer sphere is $$q$$ and the inner sphere is grounded. The charge on the inner sphere is $$q^{\prime}$$, 29. Four capacitors with capacitances $$C_1=l \propto \mathrm{F}, C_2=1.5 \propto \mathrm{F}, C_3=2.5 \propto \mathrm{F}$$ a 30. In a potentiometer of 10 wires, the balance
point is obtained on the 6th wire. To shift the
balance point to 8th wire, w 31. In a co-axial, straight cable, the central conductor and the outer conductor carry equal currents in opposite directions 32. The magnetic field, of a given length of wire
for single turn coil, at its centre is B, then its
value for two turns coi 33. A solenoid of length $$60 \mathrm{~cm}$$ with 15 turns per $$\mathrm{cm}$$ and area of cross-section $$4 \times 10^{-3} 34. A bulb of resistance $$280 \Omega$$ is supplied with a 200 V AC supply. What is the peak current? 35. The magnetic field of a plane electromagnetic wave is given by $$B=(400 \propto \mathrm{T})\sin \left[\left(4.0 \times 1 36. The de-Broglie wavelength associated with a
proton under the influence of an electric
potential of 100 V is 37. The ionisation potential of hydrogen atom is
13.6 V. How much energy need to be
supplied to ionise the hydrogen atom in 38. Which of the following statement is correct? 39. The length of germanium rod is $$0.925 \mathrm{~cm}$$ and its area of cross-section is $$1 \mathrm{~mm}^2$$. If for germ 40. In an amplitude modulated signal, the maximum amplitude is $$15 \mathrm{~V}$$ and minimum amplitude is $$5 \mathrm{~V}$$
1
AP EAPCET 2021 - 19th August Evening Shift
MCQ (Single Correct Answer)
+1
-0
A sphere of mass m is attached to a spring of spring constant k and is held in unstretched position over an inclined plane as shown in the figure. After letting the sphere go, find the maximum length by which the spring extends, given the sphere only rolls.
A
$$\frac{2 m g \sin \theta}{k}$$
B
$$\frac{k}{2 m g \sin \theta}$$
C
$$\frac{2 \sin \theta}{k m g}$$
D
$$\frac{2 m g \cos \theta}{k}$$
2
AP EAPCET 2021 - 19th August Evening Shift
MCQ (Single Correct Answer)
+1
-0
A girl of mass M stands on the rim of a frictionless merry-go-round of radius R and rotational inertia I, that is not moving. She throws a rock of mass m horizontally in a direction that is tangent to the outer edge of the merry-go-round. The speed of the rock, relative to the ground is v. Afterwards, the linear speed of the girl is
A
$$\frac{m v R^2}{I+M R^2}$$
B
$$\frac{(m+M) v R^2}{I+M R^2}$$
C
$$\frac{m v R^2}{I+(M+m) R^2}$$
D
$$\frac{m v R^2}{I+(M-m) R^2}$$
3
AP EAPCET 2021 - 19th August Evening Shift
MCQ (Single Correct Answer)
+1
-0
A block of mass $$\mathrm{l} \mathrm{kg}$$ is fastened to a spring of spring constant of $$100 ~\mathrm{Nm}^{-1}$$. The block is pulled to a distance $$x=10 \mathrm{~cm}$$ from its equilibrium position $$(x=0 \mathrm{~cm})$$ on a frictionless surface, from rest at $$t=0$$. The kinetic energy and the potential energy of the block when it is $$5 \mathrm{~cm}$$ away from the mean position is
A
$$0.375 \mathrm{~J}, 0.125 \mathrm{~J}$$
B
$$0.125 \mathrm{~J}, 0.375 \mathrm{~J}$$
C
$$0.125 \mathrm{~J}, 0.125 \mathrm{~J}$$
D
$$0.375 \mathrm{~J}, 0.375 \mathrm{~J}$$
4
AP EAPCET 2021 - 19th August Evening Shift
MCQ (Single Correct Answer)
+1
-0
The scale of a spring balance which can measure from 0 to $$15 \mathrm{~kg}$$ is $$0.25 \mathrm{~m}$$ long. If a body suspended from this balance oscillates with a time period $$\frac{2 \pi}{5} \mathrm{~s}$$, neglecting the mass of the spring, find the mass of the body suspended.
A
24 kg
B
1 kg
C
20 kg
D
7 kg
Paper analysis
Total Questions
Chemistry
40
Mathematics
80
Physics
40
AP EAPCET
Papers
2022