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

Chemistry

1. A subshell $$n=3, l=2$$ can accommodate maximum of 2. If the work function for the photoelectron emission of a metal is 3.75 eV, then the threshold wavelength of the radiatio 3. With increasing principal quantum number, the energy difference between adjacent energy levels in $$\mathrm{H}$$-atom .. 4. The electronegativity of the given elements increases in the order. 5. The first ionisation enthalpies of $$\mathrm{Mg}$$ and $$\mathrm{Al}$$ can be expected to be ............ . 6. Which of the following statements is/are correct? 1. Mercury is the only metal that exists as liquid at room temperature 7. A covalent molecule '$$X Y^{\prime}$$' is found to have a dipole moment of $$1.5 \times 10^{-29} \mathrm{C} \cdot \mathr 8. The hybridisation of $$\mathrm{Se}$$ in $$\mathrm{SeF}_4$$ and its geometry respectively are : 9. Incorrect matching amongst the following is (according to geometry of molecules) 10. When the temperature of a gas is increased from $$30^{\circ} \mathrm{C}$$ to $$930^{\circ} \mathrm{C}$$, the root mean s 11. Three flasks of equal volume contain $$\mathrm{CH}_4, \mathrm{CO}_2$$ and $$\mathrm{Cl}_2$$ gases respectively. They wil 12. If the volume of $$15.9 \mathrm{~g}$$ of carbon tetrachloride is $$10 \mathrm{~mL}$$, calculate its density. 13. $$0.63 \mathrm{~g}$$ of oxalic acid is dissolved in order to obtain $$250 \mathrm{~cm}^3$$ of its solution. Find the nor 14. When an ideal gas expands isothermally from $$5 \mathrm{~m}^3$$ to $$10 \mathrm{~m}^3$$ at $$25^{\circ} \mathrm{C}$$ aga 15. Find the approximate value of $$(\Delta H-\Delta U)$$ in $$\mathrm{Jmol}^{-1}$$, for the formation of CO from its elemen 16. Match the following columns. .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:s 17. The pH of 0.1 M solution of acetic acid will be [degree of dissociation of acetic acid is 0.0132] 18. The main constituent of enamel on the surface of teeth is 19. $$\mathrm{H}_3 \mathrm{BO}_3$$ or $$\mathrm{B}(\mathrm{OH})_3$$ is considered as an acid because its molecule 20. The element with maximum bond energy is 21. Identify the coldest region among the following layers of atmosphere. 22. Alcohols with molecular formula $$\mathrm{C}_n \mathrm{H}_{2 n+2} \mathrm{O}$$ are isomeric with 23. $$7.8 \mathrm{~g}$$ of a compound having molecular formula $$\mathrm{C}_6 \mathrm{H}_6$$, on reacting with $$\mathrm{CH} 24. Arrange the following bases in decreasing order of basicity. 1. Aniline 2. o-nitroaniline 3. m-nitroaniline 4. p-nitroan 25. The complete combustion of one mole of benzene produces .......... grams of carbon dioxide. 26. A metal crystallises with a fcc lattice, the edge of whose unit cell is $$x \mathrm{~pm}$$. The diameter of this metal a 27. If two liquids $$A$$ and $$B$$ form a minimum boiling azeotrope at some specific composition, then which statement among 28. The vapour pressure of a solvent decreased by 20 mm of Hg when a non-volatile solute was added to the solvent. The mole 29. For a $$A+B \rightarrow$$ products, the rate of the reaction is given by rate $$=k[A][B]^2$$. The units of rate constant 30. In the electrolysis of a CuSO$$_4$$ solution, how many grames of Cu are plated out on the cathode, in the time that is r 31. For an elementary reaction, $$X(g) \longrightarrow Y(g)+Z(g)$$, the $$t_{1 / 2}$$ is $$10 \mathrm{~min}$$. In what perio 32. Which statements among the following are correct? 1. Freundlich isotherm fails at high pressure of the gas. 2. $$\Delta 33. Xenon best reacts with 34. The correct order of acidic character of the following is 35. In the following reactions (i) and (ii), the number of moles of chlorine gas released respectively are (i) $$\mathrm{MnO 36. A purple coloured compound of manganese $$(X)$$ decomposes on heating to liberate oxygen and forms compounds of manganes 37. Match the following columns and choose the correct code. .tg {border-collapse:collapse;border-spacing:0;} .tg td{borde 38. The human body does not produce 39. Identify the best suitable reagent for the following reaction. 40. The major product of the following reaction sequence is

Mathematics

1. Let $$f(x)=(x+2)^2-2, x \geq-2$$. Then, $$f^{-1}(x)$$ is equal to 2. If $$f$$ is the greatest integers function defined on $$R$$ as $$f(x)=[x]$$ and $$g$$ is the modulus function defined on 3. If $$f: R \rightarrow R$$ and $$g: R \rightarrow R$$ are two functions defined by $$f(x)=a x+b(a \neq 0), \forall x \in 4. Using mathematical induction, the numbers $$a_n^{\prime}$$ s are defined by $$a_0=1, a_{n+1}=3 n^2+n+a_n (n \geq 0)$$, t 5. If $$k \in R$$ and $$\operatorname{det} A=\left|\begin{array}{lll}a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\ 6. If $$A=\left[\begin{array}{llll}\sqrt{2020} & \sqrt{2021} & \sqrt{2021} & \sqrt{2023} \\ \sqrt{4040} & \sqrt{4042} & \sq 7. If $$\left|\begin{array}{lll}x & x^2 & 1+x^3 \\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3\end{array}\right|=0$$ and $$x, y$$ an 8. Let A be a $$n\times n$$ matrix such that A is upper-triangular. Then, $$adj (A)$$ is equal to 9. Let $$Z_1, Z_2$$ and $$Z_3$$ be three non zero complex numbers such that $$a=\left|Z_1\right|, b=\left|Z_2\right|$$ and 10. If $$\left|z_1+z_2\right|^2=\left|z_1\right|^2+\left|z_2\right|^2$$, where $$z_1$$ and $$z_2$$ are two complex numbers, 11. A real value of $$x$$ will satisfy the equation, $$\left(\frac{3-4 i x}{3+4 i x}\right)=\alpha-i \beta,(\alpha, \beta$$ 12. What is the value of $$(1-i \sqrt{3})^9$$ is equal to 13. $$\left(\frac{\sqrt{6}-\sqrt{2}}{4}+\frac{\sqrt{6}+\sqrt{2}}{4} i\right)^{2020}$$ is equal to 14. If $$f(10-x)=3 x^2+4 x-5$$ and $$f(x)=p x^2+q x+r$$, then $$p+q+r$$ is equal to 15. For $$a\ne b$$, if the equation $$x^2+ax+b=0$$ and $$x^2+bx+a=0$$ have a common root, then the value of $$a+b$$ is equal 16. If the product of the roots of $$9x^3+112x^2-120x+a=0$$ is 12, then the value of $$a$$ is 17. $$2+\sqrt{5}, 1$$ are roots of the cubic equation given by 18. A set contains 11 elements. The number of subsets of the set which contain at most 5 elements is 19. If $$\begin{aligned} \frac{2 x^4-x^3+3 x^2-x+4}{x^2-3 x+2} =f(x)+\frac{A}{x-1}+\frac{B}{x-2}\end{aligned}$$, then 20. Let $$\theta$$ be an angle in the standard position such that the point $$(-5,12)$$ lies on its terminal side, then 21. If $$\cos \frac{\pi}{4} \cos \frac{\pi}{8} \cos \frac{\pi}{16} \cos \frac{\pi}{32}=2^m \operatorname{cosec} \frac{\pi}{n 22. If $$A+B+C=\frac{3 \pi}{2}$$, then $$\cos 2 A+\cos 2 B+\cos 2 C$$ is equal to 23. $$\tan ^{-1}(-2)-\tan ^{-1}(3)$$ is equal to 24. $$\sinh (x+y) \cosh (x-y)$$ is equal to 25. What is the value of $$(a-b)^2 \cos ^2 \frac{c}{2}+(a+b)^2 \sin ^2 \frac{c}{2}$$ 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 $$r 27. If in $$\triangle A B C, a \tan A+b \tan B=(a+b). \tan \left(\frac{A+B}{2}\right)$$, then which of the following holds? 28. If $$\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{ 29. Let $$u=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}$$ and $$v=3 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}$$. Consider three points $$P 30. The point of intersection of the lines joining points $$\hat{\mathbf{i}}+2 \hat{\mathbf{j}}, 2 \hat{\mathbf{i}}-\hat{\ma 31. The value of $$\frac{(\mathbf{a} \times \mathbf{b})^2+(\mathbf{a} \cdot \mathbf{b})^2}{2(\mathbf{a})^2(\mathbf{b})^2}$$ 32. Let $$\mathbf{a}=\hat{\mathbf{i}}-\hat{\mathbf{j}}, \mathbf{b}=\hat{\mathbf{j}}-\hat{\mathbf{k}}$$ and $$\mathbf{c}=\hat 33. Let $$u$$ and $$v$$ be two non-zero vectors in $$R^3$$ with the intermediate angle $$45^{\circ}$$. Then $$|\mathbf{u} \t 34. The equation of the plane passing through $$3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}$$ and parallel to t 35. Given, $$\mathbf{a}=3 \hat{\mathbf{i}}-\hat{\mathbf{j}}, \mathbf{b}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-3 \hat{\mathbf{k 36. If the mean of a data x is 10 and if all the observations are multiplied by 2, then the mean of new data is 37. A coin is tossed until a head appears or it has been tossed thrice. Given that head doesn’t appear on the first toss, th 38. Box-I contains 3 cards bearing numbers 1, 2, 3 , Box II contains 5 cards bearing numbers 1 , 2, 3, 4, 5 and Box III cont 39. The range of a random variable $$X$$ is $$\{1,2,3, \ldots\}$$ and $$P(X=x)=\frac{C^x}{x !}$$. for $$x=1,2,3$$, ... Then, 40. Tom and Jerry play a game of alternately throwing an unfair coin. First one to get head wins. If Tom starts the game, he 41. A point moves so that the sum of its distances from $$(a e, 0)$$ and $$(-a e, 0)$$ is $$2 a$$, then the equation to its 42. The point to which the origin should be shifted in order to eliminate the $$x$$ and $$y$$ terms from the equation $$9 x^ 43. If $$A(1,3)$$ and $$C(7,5)$$ are two opposite vertices of a square, then find the equation of a side passing through $$A 44. $$C$$ is the centroid of the triangle with vertices $$(3,-1),(1,3)$$ and $$(2,4)$$. Let $$P$$ be the point of intersecti 45. The distance of the point $$(1,2)$$ from the line $$x+y+5=0$$ measured along the line parallel to $$3 x-y=7$$ is equal t 46. Find the equation of a line which passes through $$\left(2 \cos ^3(\theta), 2 \sin ^3(\theta)\right)$$ and is perpendicu 47. The value of $$p$$ for which the equation $$x^2+p x y+y^2-5 x-7 y+6=0$$ represents a pair of straight lines is 48. If one of the line represented by $$-a x^2+2 h x y+b y^2=0$$ passes through $$(2,3)$$ and the other passes through $$(4, 49. The equation of the pair of straight lines parallel to $$x$$-axis and touching the circle $$x^2+y^2-6 x-4 y-12=0$$ is 50. If the lines represented by the equation $$2 x^2-p x y+2 y^2=0$$ are real, then the value of $$p$$ lies in the interval 51. The points where the circle $$x^2+y^2-3 x -4 y+2=0$$ cuts the $$X$$-axis are 52. The center and radius of the circle $$x^2+y^2+8 x+10 y-8=0$$ respectively are and units 53. The poles of the tangents to the circle $$x^2+y^2=4$$ with respect to the circle $$(x+2)^2+y^2=8$$, lie on 54. If the power of the point $$(1,6)$$ with respect to the circle $$x^2+y^2+4 x-6 y-a=0$$ is $$-16$$ then $$a$$ equals 55. The equation of radical axis of the circles $$x^2+y^2+4 x+6 y+7=0$$ and $$4 x^2+4 y^2+8 x+12 y-9=0$$ is 56. The radical axis of the circles $$S_1: x^2+y^2-4 x+6 y-10=0$$ and $$S_2 : x^2+y^2+2 x-6 y+2=0$$, cut the circle $$S_1$$ 57. The point of intersection of the latus rectum and axis of the parabola $$y^2+4 x+2 y-8=0$$ is 58. If the focal chord of the hyperbola subtends a right angle at the center, then its eccentricity is 59. The direction cosines of the line joining the points $$(-2,4,-5)$$ and $$(1,2,3)$$ are 60. The points (2, 3, 4), ($$-$$1, $$-$$2, 1) and (5, 8, 7) are 61. The sum of intercepts of the plane $$4 x+3 y+2 z=2$$ on the coordinate axes is 62. If $$\lim _\limits{x \rightarrow 0}\left(\frac{11 x^3-3 x+4}{13 x^3-5 x^2-7}\right)=\frac{a}{b}$$, then the value of $$a 63. $$\lim _\limits{x \rightarrow 1} \frac{(1-x)\left(1-x^2\right) \ldots\left(1-x^{2 n}\right)}{\left\{(1-x)\left(1-x^2\rig 64. If $$f(x)=\frac{\log _e\left(1+x^2(\tan x)\right)}{\sin x^3}, x \neq 0$$ is to be continuous at $$x=0$$, then $$f(0)$$ m 65. If $$x=\sec \theta-\cos \theta$$ and $$y=\sec ^n \theta-\cos ^n \theta$$, then $$\left(x^2+4\right)\left(\frac{d y}{d x} 66. If $$f(x)=\left|\begin{array}{ccc}x & x^2 & x^3 \\ 1 & 2 x & 3 x^2 \\ 0 & 2 & 6 x\end{array}\right|$$, then the ratio $$ 67. If $$y=\log _{\cot x} \tan x-\log _{\tan x} \cot x +\tan ^{-1}\left(\frac{4 x}{4-x^2}\right)$$, then $$\frac{d y}{d x}$$ 68. If $$y=\sin (\sin x)$$ and $$y^{\prime \prime}+f(x) \cdot y^{\prime}+g(x) \cdot y=0$$, then $$f(x) \cdot g(x)$$ is equal 69. A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thickness, which melts at a rate of 50 cm 70. Find the minimum value of $$2x+3y$$, when $$xy=6$$. 71. The volume of a spherical balloon is increasing at the rate of $$30 \mathrm{~cm}^3$$ per minute. Find the rate of change 72. If $$g(x)=\frac{1}{6} f\left(3 x^2-1\right)+\frac{1}{2} f\left(1-x^2\right), \forall x \in R$$, where $$f^{\prime \prime 73. If the function $$f(x)=2 x^3-9 a x^2+12 a^2 x+1$$ attains its maximum and minimum at $$p$$ and $$q$$ respectively, such 74. If $$f^{\prime}(x)=x+\frac{1}{x}$$, then $$f(x)$$ is equal to 75. If $$f(x)=\frac{1}{\left(\cos ^2 x\right) \sqrt{1+\tan x}}$$, then its antiderivative $$F(x)=$$ ........, given, $$F(0)= 76. If the primitive of $$\cos (\log x)$$ is $$f(x)\{\cos (g(x))+\sin (h(x))\}$$, then which among the following is true? 77. $$\int \frac{\sec x}{\sqrt{\sin (2 x+\theta)+\sin \theta}} d x$$ is equal to 78. If $$\int_\limits0^\pi \log (\sin x) d x=8 k$$, then $$\int_\limits0^{\frac{\pi}{4}} \log (1+\tan x) d x$$ is equal to 79. If $$\int_\limits0^1 x^m(1-x)^n d x=k \int_\limits0^1 x^n(1-x)^m d x$$, then the value of $k$ equals 80. The equation of the curve passing through the point $$\left(0, \frac{\pi}{4}\right)$$ and satisfying the differential eq

Physics

1. Which year was declared as the International year of Physics? 2. One angstrom $$(\mathop A\limits^o )$$ is equal to 3. An object is moving with a uniform acceleration which is parallel to its instantaneous direction of motion. The displace 4. A hiker stands on the edge of a cliff $$490 \mathrm{~m}$$ above the ground and throws a stone horizontally with an initi 5. Two paper screens $$A$$ and $$B$$ are separated by $$150 \mathrm{~m}$$. A bullet pierces $$A$$ and than $$B$$. The hole 6. A 30 kg slab B rests on a frictionless floor as shown in the figure. A 10 kg block A rests on top of the slab B. The coe 7. A ball of mass 3 kg, moving with a speed of 100 ms$$^{-1}$$, strikes a wall at an angle 60$$^\circ$$ (as shown in figure 8. An engine develops 20 kW of power. How much time will it take to lift a mass of 200 kg to a height of 40 m? (g = 10 ms$$ 9. Two bodies having kinetic energy in the ratio 4 : 1, are moving with same linear velocity. The ratio of their masses is 10. Water is falling on the blades of a turbine from a height of $$25 \mathrm{~m}$$ and $$3 \times 10^3 \mathrm{~kg}$$ of wa 11. As solid sphere of mass $$M$$ and radius $$R$$ spins about an axis passing through its centre making $$600 \mathrm{~rpm} 12. Two fly wheels $$A$$ and $$B$$ are mounted side by side with frictionless bearings on a common shaft. Their moments of i 13. In case of a forced vibration, the resonance wave becomes very sharp when the 14. If the Earth stops rotating in its orbit about the sun, there will be variation in the weight of our bodies at 15. At what depth below surface of the Earth, the acceleration due to gravity will be half of its value that at $$1600 \math 16. The dimensions of stress is 17. What causes the free surface of a liquid to have minimum area? 18. Assertion (A) The upper surface of the wing of an aeroplane is made convex and the lower surface is made concave. Reason 19. A glass vessel of volume $$V_o$$ is completely filled with a liquid and its temperature is raised by $$\Delta T$$. What 20. A Carnot engine whose heat sink is at 27$$^\circ$$C has an efficiency of 40%. By how much should its source temperature 21. A diatomic gas is heated at constant pressure, what fraction of the heat energy is used to increase the internal energy? 22. An ideal gas is taken from state-1 to state- 2 through optional path $$A, B, C$$ and $$D$$ as shown in the $$p$$ - $$V$$ 23. When the temperature of an ideal gas is increased from 27$$^\circ$$C to 127$$^\circ$$C. Calculate the percentage increas 24. Two waves are represented by $$x_1=A \sin \left(\omega t+\frac{\pi}{6}\right) \text { and } x_2=A \cos \omega t \text {. 25. Assertion (A) The focal length of lens does not change when red light is replaced by blue light. Reason (R) The focal le 26. The wavefront is a surface in which 27. Two charges $$10 ~\mu \mathrm{C}$$ and $$-10 ~\mu \mathrm{C}$$ are placed at points $$A$$ and $$B$$ separated by a dista 28. When a number of charged liquid drops coalesce, which of the following quantity does not change? 29. What is the angle between maximum value of potential gradient and equipotential surface? 30. The conductivity of a conductor decreases with temperature because, on heating 31. Torque required to hold a small circular coil of 10 turns, area of $$2 \times 10^{-4} \mathrm{~m}^2$$ area of carrying 0 32. Two concentric coils each of radius equal to $$4 \pi ~\mathrm{cm}$$ are placed at right angles to each other. If $$10 \m 33. An AC generator consists of a coil of 100 turns and is of cross-sectional area $$3 \mathrm{~m}^2$$. It is rotating at a 34. Assertion (A) Magnetic flux is a vector quantity. Reason (R) Value of magnetic flux can be positive negative or zero. 35. The output current versus time curve of a rectifier is shown in the figure. The average value of output current in this 36. The shortest wavelength of X-rays emitted from an X-ray tube depends upon ........... . 37. If a photocell is illuminated with a radiation of 1240 $$\mathop A\limits^o $$, the stopping potential is found to be 8V 38. The wavelength of the first spectral line of the Lyman series of hydrogen spectrum is 39. Which of the following nuclear reactions is possible? 40. A change of $$0.04 \mathrm{~V}$$ takes place between the base and the emitter when an input signal is connected to the c

AP EAPCET 2021 - 20th August Evening Shift

MCQ (Single Correct Answer)

-0

$$\int \frac{\sec x}{\sqrt{\sin (2 x+\theta)+\sin \theta}} d x$$ is equal to

$$\sqrt{(\tan x+\tan \theta) \sec \theta}+c$$

$$\sqrt{2(\tan x+\tan \theta) \sec \theta}+c$$

$$\sqrt{2(\sin x+\tan \theta) \sec \theta}+c$$

$$\sqrt{2(\cos x+\tan \theta) \sec \theta}+c$$

AP EAPCET 2021 - 20th August Evening Shift

MCQ (Single Correct Answer)

-0

If $$\int_\limits0^\pi \log (\sin x) d x=8 k$$, then $$\int_\limits0^{\frac{\pi}{4}} \log (1+\tan x) d x$$ is equal to

$$k$$

$$-k$$

$$\frac{k}{2}$$

$$4 k$$

AP EAPCET 2021 - 20th August Evening Shift

MCQ (Single Correct Answer)

-0

If $$\int_\limits0^1 x^m(1-x)^n d x=k \int_\limits0^1 x^n(1-x)^m d x$$, then the value of $k$ equals

$$m$$

$$n$$

$$\frac{1}{\mathrm{mn}}$$

$$1$$

AP EAPCET 2021 - 20th August Evening Shift

MCQ (Single Correct Answer)

-0

The equation of the curve passing through the point $$\left(0, \frac{\pi}{4}\right)$$ and satisfying the differential equation $$\left(e^x \tan y\right) d x\left.+\left(1+e^x\right) \sec ^2 y\right) d y=0$$ is given by

$$\left(1+e^x\right) \tan y=2$$

$$1+e^x=2 \tan y$$

$$1+e^x=2 \sec y$$

$$\left(1+e^x\right) \tan y=k$$

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