AP EAPCET 2021 - 20th August Morning Shift | AP EAPCET Year Wise Previous Years Questions

Chemistry

Mathematics

1. $$f(x)=\sin x+\cos x \cdot g(x)=x^2-1$$, then $$g(f(x))$$ is invertible if 2. If $$f: z \rightarrow z$$ is defined by $$f(x)=x^9-11 x^8-2 x^7+22 x^6+x^4 -12 x^3+11 x^2+x-3, \forall x \in z$$, then $ 3. Let $$f(x)=x^3$$ and $$g(x)=3^x$$, then the quadratic equation whose roots are solutions of the equation $$(f \circ g)(x 4. The trace of the matrix $$A=\left[\begin{array}{ccc}1 & -5 & 7 \\ 0 & 7 & 9 \\ 11 & 8 & 9\end{array}\right]$$ is 5. If $$A, B$$ and $$C$$ are the angles of a triangle, then the system of equations $$-x+y \cos C+z \cos B=0, x \cos C-y+z 6. If $$\left[\begin{array}{cc}1 & -\tan \theta \\ \tan \theta & 1\end{array}\right]\left[\begin{array}{cc}1 & \tan \theta 7. If $$z_1=2+3 i$$ and $$z_2=3+2 i$$, where $$i=\sqrt{-1}$$, then $$\left[\begin{array}{cc}z_1 & z_2 \\ -\bar{z}_2 & \bar{ 8. What is the value of $$\left|\begin{array}{ccc}a & b & c \\ a-b & b-c & c-a \\ b+c & c+a & a+b\end{array}\right|$$ ? 9. The radius of the circle represented by $$(1+i)(1+3i)(1+7i)=x+iy$$ is $$(i=\sqrt{-1})$$. 10. If $$1, \alpha_1, \alpha_2, \alpha_3$$ and $$\alpha_4$$ are the roots of $$z^5-1=0$$ and $$\omega$$ is a cube root of un 11. If $$a > 0$$ and $$z=x+i y$$, then $$\log _{\cos ^2 \theta}|z-a|>\log _{\cos ^2 \theta}|z-a i|,(\theta \in R)$$ implies 12. If one root of the equation $$i x^2-2(i+1) x+(2-i)=0$$ is $$(2-i)$$, then the other root is 13. If $$\alpha$$ and $$\beta$$ are the roots of the quadratic equation $$x^2+x+1=0$$, then the equation whose roots are $$\ 14. If $$2, 1$$ and $$1$$ are roots of the equation $$x^3-4 x^2+5 x-2=0$$, then the roots of $$\left(x+\frac{1}{3}\right)^3- 15. If $$f(x)=2x^3+mx^2-13x+n$$ and 2, 3 are the roots of the equation $$f(x)=0$$, then the values of m and n are 16. The value of $${ }^6 P_4+4 \cdot{ }^6 P_3$$ is 17. The number of ways in which 3 boys and 2 girls can sit on a bench so that no two boys are adjacent is 18. In how many ways can 5 balls be placed in 4 tins if any number of balls can be placed in any tin? 19. Given, $$\frac{3 x-2}{(x+1)^2(x+3)}=\frac{A}{x+1} +\frac{B}{(x+1)^2}+\frac{C}{x+3}$$, then $$4 A+2 B+4 C$$ is equal to 20. What is the value of $$\cos \left(22 \frac{1}{2}\right)^{\circ}$$ ? 21. If $$\cos \theta=-\sqrt{\frac{3}{2}}$$ and $$\sin \alpha=\frac{-3}{5}$$, where '$$\theta$$' does not lie in the third qu 22. If $$\tan \beta=\frac{\tan \alpha+\tan \gamma}{1+\tan \alpha \tan \gamma}$$, then $$\frac{\sin 2 \alpha+\sin 2 \gamma}{1 23. If $$\sin \left(\frac{\pi}{4} \cos \theta\right)=\cos \left(\frac{\pi}{4} \tan \theta\right)$$, then $$\theta$$ is equal 24. If $$x=\sin \left(2 \tan ^{-1} 2\right), y=\cos \left(2 \tan ^{-1} 3\right)$$ and $$z=\sec \left(3 \tan ^{-1} 4\right)$$ 25. In $$\triangle A B C$$, medians $$A D$$ and $$B E$$ are drawn. If $$A D=4, \angle D A B=\frac{\pi}{6}$$ and $$\angle A B 26. In a $$\triangle A B C, 2 \Delta^2=\frac{a^2 b^2 c^2}{a^2+b^2+c^2}$$, then the triangle is 27. The sides of a triangle inscribed in a given circle subtend angles $$\alpha, \beta, \gamma$$ at the center. The minimum 28. The position vectors of the points $$A$$ and $$B$$ with respect to $$O$$ are $$2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\ha 29. Let $$\mathbf{u}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{v}=-3 \hat{\mathbf{i}}+2 \hat{\mathbf{j 30. If the lines, $$\frac{x-3}{2}=\frac{y-2}{3}=\frac{z-1}{\lambda}$$ and $$\frac{x-2}{3}=\frac{y-3}{2}=\frac{z-2}{3}$$ are 31. If a = (1, 1, 0) and b = (1, 1, 1), then unit vector in the plane of a and b and perpendicular to a is 32. The line passing through $$(1,1,-1)$$ and parallel to the vector $$\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$ 33. Let $$\mathbf{a}=\hat{\mathbf{i}}$$ and $$\mathbf{b}=\hat{\mathbf{j}}$$, the point of intersection of the lines $$\mathb 34. The mean deviation from the mean of the set of observation $$-1,0,4$$ is 35. Let an angle of a triangle is 60$$^\circ$$. If the variance of the angles of the triangle is 1014$$^\circ$$, then the ot 36. One card is selected at random from 27 cards numbered form 1 to 27. What is the probability that the number on the card 37. Nine balls one drawn simultaneously from a bag containing 5 white and 7 black balls. The probability of drawing 3 white 38. The probabilities that $$A$$ and $$B$$ speak truth are $$\frac{4}{5}$$ and $$\frac{3}{4}$$ respectively. The probability 39. The mean and variance of a binomial variable X are 2 and 1 respectively. The probability that X takes values greater tha 40. For the random variable X with probability distribution is given by the table .tg {border-collapse:collapse;border-spa 41. The locus of a point, which is at a distance of 4 units from $$(3,-2)$$ in $$x y$$-plane is 42. When the axes are rotated through an angle 45$$^\circ$$, the new coordinates of a point P are (1, $$-$$1). The coordinat 43. Find the equation of a straight line passing through $$(-5,6)$$ and cutting off equal intercepts on the coordinate axes. 44. Line has slope $$m$$ and $$y$$-intercept 4 . The distance between the origin and the line is equal to 45. The equation of the base of an equilateral triangle is $$x+y=2$$ and one vertex is $$(2,-1)$$, then the length of the si 46. The equation of a straight line which passes through the point $$\left(a \cos ^3 \theta, a \sin ^3 \theta\right)$$ and p 47. The acute angle between lines $$6 x^2+11 x y-10 y^2=0$$ is 48. If the lines, joining the origin to the points of intersection of the curve $$2 x^2-2 x y+3 y^2+2 x-y-1=0$$ and the line 49. The equation of bisector of the angle between the lines represented by $$3 x^2-5 x y+4 y^2=0$$ is 50. If the bisectors of the pair of lines $$x^2-2 m x y-y^2=0$$ is represented by $$x^2-2 n x y-y^2=0$$, then 51. Find the equation of the circle which passes through origin and cuts off the intercepts $$-$$2 and 3 over the $$X$$ and 52. The angle between the pair of tangents drawn from $$(1,1)$$ to the circle $$x^2+y^2+4 x+4 y-1=0$$ is 53. If the circle $$x^2+y^2-4 x-8 y-5=0$$ intersects the line $$3 x-4 y-m=0$$ in two distinct points, then the number of int 54. Let $$C$$ be the circle center $$(0,0)$$ and radius 3 units. The equation of the locus of the mid-points of the chords o 55. The length of the common chord of the circles $$x^2+y^2+3x+5y+4=0$$ and $$x^2+y^2+5x+3y+4=0$$ is __________ units. 56. Find the equation of the circle which passes through the point $$(1,2)$$ and the points of intersection of the circles $ 57. The coordinates of the focus of the parabola described parametrically by $$x=5t^2+2$$ and $$y=10t+4$$ (where t is a para 58. If $$\tan \theta_1, \tan \theta_2=\frac{-a^2}{b^2}$$, then the chord joining 2 points $$\theta_1$$ and $$\theta_2$$ one 59. If one focus of a hyperbola is $$(3,0)$$, the equation of its directrix is $$4 x-3 y-3=0$$ and its eccentricity $$e=5 / 60. If the vertices of the triangles are (1, 2, 3), (2, 3, 1), (3, 1, 2) and if H, G, S and I respectively denote its orthoc 61. A(2, 3, 4), B(4, 5, 7), C(2, $$-$$6, 3) and D(4, $$-$$4, k) are four points. If the line AB is parallel to CD, then k is 62. If the direction cosines of two lines are $$\left( {{2 \over 3},{2 \over 3},{1 \over 3}} \right)$$ and $$\left( {{5 \ove 63. $$\mathop {\lim }\limits_{n \to \infty } {{n{{(2n + 1)}^2}} \over {(n + 2)({n^2} + 3n - 1)}}$$ is equal to 64. If the function $$f(x)$$, defined below, is continuous on the interval $$[0,8]$$, then $$f(x)=\left\{\begin{array}{cc}x^ 65. If $$f(x)$$, defined below, is continuous at $$x=4$$, then $$f(x) = \left\{ {\matrix{ {{{x - 4} \over {|x - 4|}} + a} 66. If $$f(x)=2x^2+3x-5$$, then the value of $$f'(0)+3f'(-1)$$ is equal to 67. If $$y=\left(1+\frac{1}{x}\right)\left(1+\frac{2}{x}\right)\left(1+\frac{3}{x}\right) \ldots\left(1+\frac{n}{x}\right)$$ 68. $$\frac{d}{d x}\left\{\sin ^2\left(\cot ^{-1} \sqrt{\frac{1+x}{1-x}}\right)\right\}$$ is equal to 69. If $$y=\tan ^{-1}\left\{\frac{a x-b}{b x+a}\right\}$$, then $$y^{\prime}$$ is equal to 70. If $$y=4 x-6$$ is a tangent to the curve $$y^2=a x^4+b$$ at $$(3,6)$$, then the values of $$a$$ and $$b$$ are 71. Find the positive value of $$a$$ for which the equality $$2 \alpha+\beta=8$$ holds, where $$\alpha$$ and $$\beta$$ are t 72. If the radius of a sphere is measured as 9 cm with an error of 0.03 cm, then find the approximate error in calculating i 73. The diameter and altitude of a right circular cone, at a certain instant, were found to be 10 cm and 20 cm respectively. 74. $$\int \frac{\sin \alpha}{\sqrt{1+\cos \alpha}} d \alpha$$ is equal to 75. If $$\int \frac{\cos 4 x+1}{\cot x-\tan x}=k \cos 4 x+C$$, then $$k$$ is equal to 76. If $$\int\left[\cos (x) \cdot \frac{d}{d x}(\operatorname{cosec}(x)] d x=f(x)+g(x)+c\right.$$ then $$f(x) \cdot g(x)$$ i 77. If $$\int \frac{(2 x+1)^6}{(3 x+2)^8} d x=P\left(\frac{2 x+1}{3 x+2}\right)^Q+R$$, then $$\frac{P}{Q}$$ is equal to 78. If $$\int_0^a {{{dx} \over {4 + {x^2}}} = {\pi \over 8}} $$, then the value of a is equal to 79. $$\int_1^2 {{{{x^3} - 1} \over {{x^2}}}} $$ is equal to 80. The solution of the differential equation $$2x\left(\frac{dy}{dx}\right)-y=4$$ represents a family of

Physics

1. The displacement of a particle starting from rest at $$t=0$$ is given by $$s=9 t^2-2 t^3$$. The time in seconds at which 2. The range of a projectile is 100 m. Its kinetic energy will be maximum after covering a distance of 3. Two cars A and B are moving with a velocity of 30 km/h in the same direction. They are separated by 10 km. The speed of 4. A book is lying on a table. What is the angle between the normal reaction acting on the book on the table and the weight 5. A boy throws a cricket ball from the boundary to the wicket keeper. If the frictional force due to air $$(f_a )$$ cannot 6. When a force F = 17 $$-$$ 2x + 6x$$^2$$N acts on a body of mass 2 kg and displaces it from x = 0 m to x = 8 m, the work 7. A rifle bullet loses $$\left(\frac{1}{25}\right)$$th of its velocity in passing through a plank. The least number of suc 8. A uniform chain has a mass m and length $$l$$. It is held on a frictionless table with one-sixth of its length hanging o 9. A sphere and a hollow cylinder without slipping, roll down two separate inclined planes A and B, respectively. They cove 10. Four spheres each of diameter $$2 a$$ and mass $$m$$ are placed in a way that their centers lie on the four corners of a 11. If an energy of 684 J is needed to increase the speed of a flywheel from 180 rpm to 360 rpm, then find its moment of ine 12. A particle executing simple harmonic motion along a straight line with an amplitude A, attains maximum potential energy 13. The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscilla 14. The gravitational potential energy is maximum at 15. A geostationary satellite is taken to a new orbit, such that its distance from centre of the earth is doubled. Then, fin 16. A body of mass 10 kg is attached to a wire of 0.3 m length. The breaking stress is 4.8 $$\times$$ 10$$^7$$ Nm$$^{-2}$$. 17. A glass flask weighting 390 g, having internal volume 500 cc just floats when half of it is filled with water. Specific 18. Water does not wet an oily glass because 19. Boiling water is changing into steam. The specific heat of boiling water is 20. If the volume of a block of metal changes by $$0.12 \%$$ when heated through $$20^{\circ} \mathrm{C}$$, then find its co 21. Isothermal process is the graph between 22. For a monoatomic ideal gas is following the cyclic process ABCA shown in the U versus p plot, identify the incorrect opt 23. The pressure of a gas is proportional to 24. A string fixed at both ends vibrate in 5 loops as shown in the figure. The total number of nodes and anti-nodes respecti 25. The position of the direct image obtained at O, when a monochromatic beam of light is passed through a plane transmissio 26. What is the electric flux for Gaussian surface $$A$$ that encloses the charged particles in free space? [Given, $$q_1=-1 27. Two charges 8 $$\mu$$C each are placed at the corners A and B of an equilateral triangle of side 0.2 m in air. The elect 28. A 60 $$\mu$$F parallel plate capacitor whose plates are separated by 6 mm is charged to 250 V, and then the charging sou 29. Five current carrying conductors meet at a point P. What is the magnitude and direction of the current in the fifth cond 30. A wire of length $$L$$ metre carrying a current $$I$$ ampere is bent in the form of a circle. Magnitude of its magnetic 31. What is the net force on the square coil? 32. A paramagnetic sample showing a net magnetisation of $$0.8 \mathrm{~A} \mathrm{~m}^{-1}$$, when placed in an external ma 33. The induced emf cannot be produced by 34. Assertion (A) When plane of coil is perpendicular to magnetic field, magnetic flux linked with the coil is minimum, but 35. A 20 V AC is applied to a circuit consisting of a resistor and a coil with negligible resistance. If the voltage across 36. The electric and the magnetic fields associated with an electromagnetic wave propagating along the $$z$$-axis, can be re 37. The graph between the maximum speed $$(v_{max})$$ of a photoelectron and frequency $$(\nu)$$ of the incident radiation, 38. The angular momentum of the orbital electron is integral multiple of 39. Which of the following values is the correct order of nuclear density? 40. The truth table given below corresponds to logic gate.

AP EAPCET 2021 - 20th August Morning Shift

MCQ (Single Correct Answer)

-0

Find the positive value of $$a$$ for which the equality $$2 \alpha+\beta=8$$ holds, where $$\alpha$$ and $$\beta$$ are the points of maximum and minimum, respectively, of the function $$f(x)=2 x^3-9 a x^2+12 a^2 x+1$$.

$$\frac{1}{4}$$

AP EAPCET 2021 - 20th August Morning Shift

MCQ (Single Correct Answer)

-0

If the radius of a sphere is measured as 9 cm with an error of 0.03 cm, then find the approximate error in calculating its surface area.

2.16 $$\pi$$ cm$$^2$$

21.6 $$\pi$$ cm$$^2$$

216 $$\pi$$ cm$$^2$$

0.216 $$\pi$$ cm$$^2$$

AP EAPCET 2021 - 20th August Morning Shift

MCQ (Single Correct Answer)

-0

The diameter and altitude of a right circular cone, at a certain instant, were found to be 10 cm and 20 cm respectively. If its diameter is increasing at a rate of 2 cm/s, then at what rate must its altitude change, in order to keep its volume constant?

4 cm/s

6 cm/s

$$-$$4 cm/s

$$-$$8 cm/s

AP EAPCET 2021 - 20th August Morning Shift

MCQ (Single Correct Answer)

-0

$$\int \frac{\sin \alpha}{\sqrt{1+\cos \alpha}} d \alpha$$ is equal to

$$-2 \sqrt{2} \cos \left(\frac{\alpha}{2}\right)+C$$

$$2 \sqrt{2} \cos \left(\frac{\alpha}{2}\right)+C$$

$$\sqrt{2} \cos \left(\frac{\alpha}{2}\right)+C$$

$$-\sqrt{2} \cos \left(\frac{\alpha}{2}\right)+C$$

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