Chemistry
1. If two particles A and B are moving with the
same velocity, but wavelength of A is found
to be double than that of B. Wh 2. The spectrum of helium is expected to be similar to that of 3. On the basis of Bohr’s model, the radius of
the 3rd orbit is 4. To which group of the periodic table does an element having electronic configuration [Ar] 3d$$^5$$ 4s$$^2$$ belong? 5. Given that ionisation potential and electron
gain enthalpy of chlorine are 13eV and 4 eV
respectively. The electronegati 6. Which of the following represents the correct
order of increasing electron gain enthalpy
with negative sign for the elem 7. Which of the following will have maximum
dipole moment? 8. In which of the following molecules/ions, the central atom is sp$$^2$$ hybridised?
BF$$_3$$, NO$$_2^-$$, NH$$_2^-$$ and 9. For which molecules among the following,
the resultant dipole moment ($$\propto$$) $$\ne$$ 0 ?
10. Which of the following graphs correctly
represents Boyle’s Law?
11. The density of an ideal gas can be given by
........, where p, V, M, T and R respectively
denote pressure, volume, molar 12. When 20 g of CaCO$$_3$$ is treated with 20 g of HCl, the mass of CO$$_2$$ formed would be 13. Which among the following species acts as a
self-indicator? 14. If a chemical reaction is known to be
non-spontaneous at 298 K but spontaneous
at 350 K, then which among the following
15. Standard entropies of $$X_2, Y_2$$ and $$X Y_3$$ are 60, 40 and $$50 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$$ respectively. 16. For the reaction $$\mathrm{SO}_2(g)+\frac{1}{2} \mathrm{O}_2(g) \rightleftharpoons \mathrm{SO}_3(g)$$, the percentage yi 17. Which among the following denotes the correct relationship between $$K_p$$ and $$K_c$$ for the reaction, $$2 A(g) \right 18. Which metal oxide among the following
gives H$$_2$$O$$_2$$ on treatment with dilute acid? 19. Assertion (A) K, Rb and Cs form
superoxides.
Reason (R) The stability of superoxides
increases from K to Cs due to decre 20. When borax is dissolved in water, it gives an alkaline solution. The alkaline solution consists the following products 21. Identify (P) and (Q) in the following reaction.
22. Green chemistry refers to reactions which 23. Assertion (A) Sodium acetate on Kolbe’s
electrolysis gives ethane.
Reason (R) Methyl free radical is formed at
cathode. 24. When difference in boiling points of two
liquids is too small, then the separation is
carried out by 25. In Lassaigne’s test for halogens, it is
necessary to remove X and Y from the
sodium fusion extract, if nitrogen and
sulp 26. The following effect is known as
27. Which of the following will form an ideal solution? 28. The molal elevation constant is the ratio of
elevation in boiling point to 29. When a current of 10 A is passes through
molten AlCl$$_3$$ for 1.608 minutes. The mass of
Al deposited will be
[Atomic m 30. The molar conductivities $$\left(\lambda_{\mathrm{m}}^{\Upsilon}\right)$$ at infinite dilution of $$\mathrm{KBr}, \mathr 31. If the rate constant for a first order reaction is $$2.303 \times 10^{-3} \mathrm{~s}^{-1}$$. Find the time required to 32. A plot of $$\log (x / m)$$ versus $$\log (p)$$ for adsorption of a gas on a solid gives a straight line with a slope of 33. Match the following compounds with their corresponding physical properties.
.tg {border-collapse:collapse;border-spaci 34. What is coordination number of the metal in $$\mathrm{{[Co{(en)_2}C{l_2}]^{2 + }}}$$ ? 35. A compound A is used in paints instead of
salts of lead. Compound A is obtained when a
white compound B is strongly heat 36. Identify the product of the following
reaction.
37. The number of optical isomers possible for
2-bromo-3-chloro butane are 38. During the action of enzyme ‘zymase’
glucose is converted into .............., with the
liberation of carbon dioxide gas 39. The total number of products formed in the
following reaction sequence is
$$\begin{gathered}\mathrm{CH}_3 \mathrm{COCl} 40. In the following reaction sequence, identify
product ‘Q’ and reagent ‘R’.
Mathematics
1. Let $$f: R \rightarrow R$$ and $$g: R \rightarrow R$$ be defined by $$f(x)=2 x+1$$ and $$g(x)=x^2-2$$ determine $$(g \ci 2. Given, the function $$f(x)=\frac{a^x+a^{-x}}{2},(a>2)$$, then $$f(x+y)+f(x-y)$$ is equal to 3. If $$f$$ is a function defined on $$(0,1)$$ by $$f(x)=\min \{x-[x],-x-[x]\}$$, then $$(f \circ f o f o f)(x)$$ is equal 4. $$n \in N$$ then, the statement $$8 n+16 \leq 2^n$$ is true for 5. The equation whose roots are the values of the equation $$\left| {\matrix{
1 & { - 3} & 1 \cr
1 & 6 & 4 \cr
6. Let a and b be non-zero real numbers such that $$ab=5/2$$ and given $$A = \left[ {\matrix{
a & { - b} \cr
b & a 7. If $$A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right], 10 B=\left[\begin{array}{ccc}4 & 8. The rank of the matrix $$\left[\begin{array}{ccc}4 & 2 & (1-x) \\ 5 & k & 1 \\ 6 & 3 & (1+x)\end{array}\right]$$ is 1 , 9. If $$a_1, a_2, \ldots . a_9$$ are in GP, then $$\left|\begin{array}{lll}\log a_1 & \log a_2 & \log a_3 \\ \log a_4 & \lo 10. $$(\sin \theta-i \cos \theta)^3$$ is equal to 11. Real part of $$(\cos 4+i \sin 4+1)^{2020}$$ is 12. If $${({x^2} + 5x + 5)^{x + 5}} = 1$$, then the number of integers satisfying this equation is 13. Let $$f(x)=x^3+a x^2+b x+c$$ be polynomial with integer coefficients. If the roots of $$f(x)$$ are integer and are in Ar 14. The sum of the roots of the equation $$e^{4 t}-10 e^{3 t}+29 e^{2 t}-22 e^t+4=0$$ is
15. If a person has 3 coins of different denominations, the number of different sums can be formed is 16. There are 7 identical white balls and 3 identical black balls. The number of distinguishable arrangements in a row of al 17. The number of ways of distributing eight identical rings to three different girls so that every girl gets at least one r 18. If $$\frac{x^4}{(x-1)(x-2)}=f(x)+\frac{A}{x-1}+\frac{B}{x-2}$$, then 19. $$\tan 2 \alpha \cdot \tan (30 Y-\alpha)+\tan 2 \alpha \cdot \tan (60 Y-\alpha)+\tan (60 \Upsilon-\alpha) \cdot \tan (30 20. If $$\sin \alpha - \cos \alpha = m$$ and $$\sin 2\alpha = n - {m^2}$$, where $$ - \sqrt 2 \le m \le \sqrt 2 $$, then 21. The value of $$x$$ satisfying the equation $$3 \operatorname{cosec} x=4 \sin x$$ are 22. If $$\tan ^{-1}\left[\frac{1}{1+1 \cdot 2}\right]+\tan ^{-1}\left[\frac{1}{1+2 \cdot 3}\right]+\ldots+\tan ^{-1} \left[\ 23. If $$\sinh u=\tan \theta$$, then $$\cosh u$$ is equal to
24. In a $$\Delta ABC$$, if a = 3, b = 4 and $$\sin A=\frac{3}{4}$$, then $$\angle CBA$$ is equal to 25. In $$\Delta ABC,A=75\Upsilon$$ and $$B=45\Upsilon$$, then the value of $$b+c\sqrt2$$ is equal to 26. In $$\triangle A B C$$, suppose the radius of the circle opposite to an $$\angle A$$ is denoted by $$r_1$$, similarly $$ 27. A vector makes equal angles $$\alpha$$ with $$X$$ and $$Y$$-axis, and $$90 \Upsilon$$ with $$Z$$-axis. Then, $$\alpha$$ 28. Angle made by the position vector of the point (5, $$-$$4, $$-$$3) with the positive direction of X-axis is 29. If D, E and F are respectively mid-points of AB, AC and BC in $$\Delta ABC$$, then BE + AF is equal to 30. If the volume of the parallelopiped formed by the vectors $$\hat{\mathbf{i}}+a \hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\ 31. If $$\mathbf{a}=\frac{3}{2} \hat{\mathbf{k}}$$ and $$\mathbf{b}=\frac{2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf 32. Let $$\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+3 \hat{\mathbf{j}}+5 \h 33. If $$\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+3 \hat{\mathbf{j}}-\ 34. If $$\mathbf{a}$$ and $$\mathbf{b}$$ are two vectors such that $$|\mathbf{a}|=2, |\mathbf{b}|=3$$ and $$\mathbf{a}+t \ma 35. The variance of the variates 112, 116, 120, 125 and 132 about their AM is 36. Which of the following set of data has least standard deviation? 37. 12 balls are distributed among 3 boxes, then the probability that the first box will contain 3 balls is 38. If the letters of the word REGULATIONS be
arranged in such a way that relative positions
of the letters of the word GULA 39. A random variable X has the probability distribution
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-c 40. A die is tossed thrice. If event of getting an even number is a success, then the probability of getting at least 2 succ 41. If the axes are rotated through an angle $$45 \Upsilon$$, the coordinates of the point $$(2 \sqrt{2},-3 \sqrt{2})$$ in t 42. the sum of the squares of the intercepts made the line $$5x-2y=10$$ on the coordinate axes equals 43. For three consecutive odd integers $$a \cdot b$$ and $$c$$, if the variable line $$a x+b y+c=0$$ always passes through t 44. The line which is parallel to X-axis and crosses the curve $$y=\sqrt x$$ at an angle of 45$$\Upsilon$$ is 45. If $$2x+3y+4=0$$ is the perpendicular bisector of the line segment joining the points A(1, 2) and B($$\alpha,\beta$$), t 46. The equation of the pair of straight lines perpendicular to the pair $$2 x^2+3 x y+2 y^2+10 x+5 y=0$$ and passing though 47. If the centroid of the triangle formed by the lines $$2 y^2+5 x y-3 x^2=0$$ and $$x+y=k$$ is $$\left(\frac{1}{18}, \frac 48. If $$m_1$$ and $$m_2,\left(m_1>m_2\right)$$ are the slopes of the lines represented by $$5 x^2-8 x y+3 y^2=0$$, then $$m 49. If the slope of one of the lines represented by $$a x^2+2 h x y+b y^2=0$$ is the square of the other then, $$\left|\frac 50. Find the equations of the tangents drawn to the circle $$x^2+y^2=50$$ at the points where the line $$x+7=0$$ meets it. 51. If the chord of contact of tangents from a point on the circle $$x^2+y^2=r_1^2$$ to the circle $$x^2+y^2=r_2^2$$ touches 52. Find the equation of the circle passing through $$(1,-2)$$ and touching the $$X$$-axis at $$(3,0)$$. 53. Let $$L_1$$ be a straight line passing through the origin and $$L_2$$ be the straight line $$x+y=1$$. If the intercepts 54. The radius of the circle whose center lies at $$(1,2)$$ while cutting the circle $$x^2+y^2+4 x+16 y-30=0$$ orthogonally, 55. The point which has the same power with respect to each of the circles $$x^2+y^2-8 x+40=0, x^2+y^2-5 x+16=0$$ and $$x^2+ 56. If one end of focal chord of the parabola $$y^2=8x$$ is $$\left(\frac{1}{2},2\right)$$, then the length of the focal cho 57. If a point $$P(x, y)$$ moves along the ellipse $$\frac{x^2}{25}+\frac{y^2}{16}=1$$ and if $$C$$ is the center of the ell 58. The asymptotes of the hyperbola $$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$$, with any tangent to the hyperbola form a triangle 59. The ratio in which the YZ-plane divides the line joining (2, 4, 5) and (3, 5, $$-$$4) is 60. The direction cosines of a line which makes
equal angles with the coordinate axes are 61. Let $$O$$ be the origin and $$P$$ be a point which is at a distance of 3 units from the origin. If the direction ratios 62. $$\lim _\limits{z \rightarrow 1} \frac{z^{(1 / 3)}-1}{z^{(1 / 6)}-1}$$ is equal to 63. $$f(x)=\left\{\begin{array}{cc}
\frac{72^x-9^x-8^x+1}{\sqrt{2}-\sqrt{1+\cos x}}, & x \neq 0 \\
K \log 2 \log 3, & x=0
\e 64. If the function $$f(x)$$, defined below is continuous in the interval $$[0, \pi]$$, then $$f(x)=\left\{\begin{array}{cc} 65. If $$y=x+\frac{1}{x}$$, then which among the following holds? 66. If $$y=\tan ^{-1}\left(\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}\right)$$, where $$x^2 \leq 1$$. Then, 67. If $$3 \sin x y+4 \cos x y=5$$, then $$\frac{d y}{d x}$$ is equal to 68. $$f(x)=\sqrt{x^2+1}: g(x)=\frac{x+1}{x^2+1}: h(x)=2 x-3$$, then the value of $$f^{\prime}\left[h^{\prime}\left(g^{\prime 69. If the error committed in measuring the
radius of a circle is 0.05%, then the
corresponding error in calculating its are 70. The stationary points of the curve $$y=8 x^2-x^4-4$$ are 71. Which statement among the following is true?
(i) the function $$f(x)=x|x|$$ is strictly increasing on $$R-\{0\}$$.
(ii) 72. For which value(s) of $$a$$ $$f(x)=-x^3+4 a x^2+2 x-5$$ is decreasing for every $$x$$ ? 73. The distance between the origin and the normal to the curve $$y=e^{2 x}+x^2$$ drawn at $$x=0$$ is units 74. If $$\int \frac{d x}{x\left(\sqrt{\left.x^4-1\right)}\right.}=\frac{1}{k} \sec ^{-1}\left(x^k\right)$$, then the value o 75. $$\int \frac{e^x(x+3)}{(x+5)^3} d x$$ is equal to 76. If $$\int \frac{(x-1)^2}{\left(x^2+1\right)^2} d x=\tan ^{-1}(x)+g(x)+k$$, then $$g(x)$$ is equal to 77. If $$\int \frac{1-(\cot x)^{2021}}{\tan x+(\cot x)^{2022}} d x=\frac{1}{A} \log\left|(\sin x)^{2023}+(\cos x)^{2023}\rig 78. $$\int_2^4\{|x-2|+|x-3|\} d x$$ is equal to 79. $$\int\limits_{-1 / 2}^{1 / 2}\left\{[x]+\log \left(\frac{1+x}{1-x}\right)\right\} d x$$ is equal to 80. The solution of the differential equation $$\frac{d^2 y}{d x^2}+y=0$$ is
Physics
1. An electric generator is based on 2. Which of the following decreases, in motion
on a straight line, with constant retardation? 3. When a ball is thrown with a velocity of 50 ms$$^{-1}$$ at an angle 30$$\Upsilon$$ with the horizontal, it remains in th 4. One of the rectangular components of a force
of 40 N is 20$$\sqrt3$$ N. What is the other
rectangular component? 5. An object dropped in a stationary lift takes time $$t_1$$ to reach the floor. It takes time $$t_2$$ when lift is moving 6. When a body is placed on a rough plane (coefficient of friction $$=~\propto$$ ) inclined at an angle $$\theta$$ to the h 7. A metal ball of mass 2 kg moving with a
velocity of 36 km/h has a head on collision
with a stationary ball of mass 3 kg. 8. A body of mass 8 kg, under the action of a
force, is displaced according to the equation, $$s=\frac{t^2}{4}$$ m, where t 9. A particle of mass m, moving with a velocity
v makes an elastic collision in one dimension
with a stationary particle of 10. Which of the following type of wheels of
same mass and radius will have largest
moment of inertia? 11. The sum of moments of all the particles in a
system about its centre of mass is always 12. Assertion (A) Two identical trains move in
opposite senses in equatorial plane with
same speeds relative to the Earth’s 13. A spring is stretched by 0.40 m when a mass
of 0.6 kg is suspended from it. The period of
oscillations of the spring loa 14. A heavy brass sphere is hung from a spring
and it executes vertical vibrations with period
T. The sphere is now immersed 15. A particle is kept on the surface of a uniform
sphere of mass 1000 kg and radius 1 m. The
work done per unit mass agains 16. The acceleration due to gravity at a height (1/20)th of the radius of Earth above the Earth's surface is 9 ms$$^{-2}$$. 17. The Young's modulus of a rubber string of length $$12 \mathrm{~cm}$$ and density $$1.5 ~\mathrm{kgm}^{-3}$$ is $$5 \time 18. The lower end of a capillary tube is dipped
into water and it is observed that the water
in capillary tube rises by 7.5 19. An ideal liquid flows through a horizontal
tube of variable diameter. The pressure is
lowest where the 20. In a steady state, the temperature at the end $$A$$ and end $$B$$ of a $$20 \mathrm{~cm}$$ long rod $$A B$$ are $$100 \U 21. If two rods of length $$L$$ and $$2 L$$, having coefficients of linear expansion $$\alpha$$ and $$2 \alpha$$ respectivel 22. A system is taken from state-A to state-B
along two different paths. The heat absorbed
and work done by the system along 23. A gas ($$\gamma$$ = 1.5 ) is suddenly compressed to
(1/4 )th its initial volume. Then, find the ratio
of its final to in 24. A cylinder has a piston at temperature of $$30 \Upsilon$$C. There is all round clearance of $$0.08 \mathrm{~mm}$$ betwee 25. A balloon contains 1500 m$$^3$$ of He at 27$$\Upsilon$$C and 4 atmospheric pressure, the volume of He at $$-3\Upsilon$$C 26. The sources of sound A and B produce a
wave of 350 Hz in same phase. A particle P is
vibrating under an influence of the 27. In a diffraction pattern due to a single slit of width $$a$$, the first minimum is observed at an angle $$30 \Upsilon$$ 28. Which statement(s) among the following are
incorrect?
(i) A negative test charge experiences a force
opposite to the dir 29. In the given circuit, if the potential
difference between A and B is 80 V, then the
equivalent capacitance between A and 30. A cell of emf 1.8 V gives a current of 17 A when directly connected to an ammeter of resistance 0.06 $$\Omega$$. Interna 31. In which of the following case no force
exerted by a magnetic field on a charge? 32. A long thin hollow metallic cylinder of radius
R has a current i ampere. The magnetic
induction B away from the axis at 33. The plane of a dip circle is set in the geographic meridian and the apparent dip is $$\delta_1$$. It is then set in a ve 34. Assertion (A) It is more difficult to move a
magnet into a coil with more loops.
Reason (R) This is because emf induced 35. Two inductors A and B when connected in
parallel are equivalent to a single inductor of
inductance 1.5 H and when connec 36. A resonant frequency of a current is $$f$$. If the
capacitance is made four times the initial
value, then the resonant f 37. The law which states that a variation in an
electric field causes magnetic field, is 38. Radiation of wavelength $$300 \mathrm{~nm}$$ and intensity $$100 \mathrm{~W}-\mathrm{m}^{-2}$$ falls on the surface of a 39. Potential energy between a proton and an electron is given by $$U=\frac{K e^2}{3 R^3}$$, then radius of Bohr's orbit can 40. A transistor is connected in common emitter configuration. The collector supply is $$8 \mathrm{~V}$$ and the voltage dro
1
AP EAPCET 2021 - 19th August Morning Shift
MCQ (Single Correct Answer)
+1
-0
In $$\Delta ABC,A=75\Upsilon$$ and $$B=45\Upsilon$$, then the value of $$b+c\sqrt2$$ is equal to
A
a
B
3a
C
2a
D
4a
2
AP EAPCET 2021 - 19th August Morning Shift
MCQ (Single Correct Answer)
+1
-0
In $$\triangle A B C$$, suppose the radius of the circle opposite to an $$\angle A$$ is denoted by $$r_1$$, similarly $$r_2 \leftrightarrow \angle B$$ and $$r_3 \leftrightarrow \angle C$$. If $$r$$ is the radius of inscribed circle, then, what is the value of $$\frac{a b-r_1 r_2}{r_3}$$ is equal to
A
$$r_1 r_2 r_3$$
B
$$r$$
C
$$r_1 r_2 \frac{r_3}{2}$$
D
$$\frac{r}{2}$$
3
AP EAPCET 2021 - 19th August Morning Shift
MCQ (Single Correct Answer)
+1
-0
A vector makes equal angles $$\alpha$$ with $$X$$ and $$Y$$-axis, and $$90 \Upsilon$$ with $$Z$$-axis. Then, $$\alpha$$ is equal to (c) 45Yand 135Y (d) $90 \mathrm{Y}$
A
$$60\Upsilon$$ or $$120 \Upsilon$$
B
$$30\Upsilon$$ or $$150 \Upsilon$$
C
$$45\Upsilon$$ or $$135 \Upsilon$$
D
$$90\Upsilon$$
4
AP EAPCET 2021 - 19th August Morning Shift
MCQ (Single Correct Answer)
+1
-0
Angle made by the position vector of the point (5, $$-$$4, $$-$$3) with the positive direction of X-axis is
A
$$\frac{\pi}{2}$$
B
$$\frac{\pi}{6}$$
C
$$\frac{\pi}{4}$$
D
$$\frac{\pi}{3}$$
Paper analysis
Total Questions
Chemistry
40
Mathematics
80
Physics
40
AP EAPCET
Papers
2022