KCET 2020 | KCET Year Wise Previous Years Questions

Chemistry

Mathematics

1. If $$2^x+2^y=2^{x+y}$$, then $$\frac{d y}{d x}$$ is 2. If $$f(x)=\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)$$, then $$f^{\prime}(\sqrt{3})$$ is 3. The right hand and left hand limit of the function are respectively. $$f(x)=\left\{\begin{array}{cc} \frac{e^{1 / x}-1}{ 4. If $$y=2 x^{n+1}+\frac{3}{x^n}$$, then $$x^2 \frac{d^{2 y}}{d x^2}$$ is 5. If the curves $$2 x=y^2$$ and $$2 x y=K$$ intersect perpendicularly, then the value of $$K^2$$ is 6. If $$(x e)^y=e^y$$, then $$\frac{d y}{d x}$$ is 7. If the side of a cube is increased by $$5 \%$$, then the surface area of a cube is increased by 8. The value of $$\int \frac{1+x^4}{1+x^6} d x$$ is 9. The maximum value of $$\frac{\log _e x}{x}$$, if $$x>0$$ is 10. The value of $$\int e^{\sin x} \sin 2 x d x$$ is 11. The value of $$\int_{-1 / 2}^{1 / 2} \cos ^{-1} x d x$$ is 12. If $$\int \frac{3 x+1}{(x-1)(x-2)(x-3)} d x A \log |x-1| B \log |x-2|+C \log |x-3|+C$$, then the values of $$A, B$$ and 13. Find the value of $$\int_0^1 \frac{\log (1+x)}{1+x^2} d x$$ is 14. The area of the region bounded by the curve $$y^2=8 x$$ and the line $$y=2 x$$ is 15. The value of $$\int_{-\pi / 2}^{\pi / 2} \frac{\cos x}{1+e^x} d x$$ is 16. The order of the differential equation obtained by eliminating arbitrary constants in the family of curves $$c_1 y=\left 17. The general solution of the differential equation $$x^2 d y-2 x y d x=x^4 \cos x d x$$ is 18. The area of the region bounded by the line $$y=2 x+1, X$$-axis and the ordinates $$x=-1$$ and $$x=1$$ is 19. The two vector $$\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$\hat{\mathbf{i}}+3 \hat{\mathbf{j}}+5 \hat{\ 20. If $$\mathbf{a}$$ and $$\mathbf{b}$$ are unit vectors and $$\theta$$ is the angle between $$\mathbf{a}$$ and $$\mathbf{b 21. The curve passing through the point $$(1,2)$$ given that the slope of the tangent at any point $$(x, y)$$ is $$\frac{3 x 22. If $$|\mathbf{a}+\mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2=144|\mathbf{a}|=6$$, then $$|\mathbf{b}|$$ is equal to 23. The point $$(1,-3,4)$$ lies in the octant 24. If the vectors $$2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mat 25. The distance of the point $$(1,2,-4)$$ from the line $$\frac{x-3}{2}=\frac{y-3}{3}=\frac{z+5}{6}$$ is 26. The sine of the angle between the straight line $$\frac{x-2}{3}=\frac{3-y}{-4}=\frac{z-4}{5}$$ and the plane $$2 x-2 y+z 27. If a line makes an angle of with each of $$X$$ and $$Y$$-axis, then the acute angle made by Z-axis is 28. Corner points of the feasible region determined by the system of linear constraints are $$(0,3),(1,1)$$ and $$(3,0)$$. L 29. The feasible region of an LPP is shown in the figure. If $$z=11 x+7 y$$, then the maximum value of $$Z$$ occurs at 30. A die is thrown 10 times, the probability that an odd number will come up at least one time is 31. If $$A$$ and $$B$$ are two events such that $$P(A)=\frac{1}{3}, P(B)=\frac{1}{2}$$ and $$P(A \cap B)=\frac{1}{6}$$, then 32. Events $$E_1$$ and $$E_2$$ from a partition of the sample space $$S$$. $$A$$ is any event such that $$P\left(E_1\right)= 33. The probability of solving a problem by three persons $$A, B$$ and $$C$$ independently is $$\frac{1}{2}, \frac{1}{4}$$ a 34. If $$n(A)=2$$ and total number of possible relations from Set A to set B is 1024, then $$n(B)$$ is 35. The value of $$\sin ^2 51^{\circ}+\sin ^2 39^{\circ}$$ is 36. If $$\tan A+\cot A=2$$, then the value of $$\tan ^4 A+\cot ^4 A=$$ 37. If $$A=\{1,2,3,4,5,6\}$$, then the number of subsets of A which contain at least two elements is 38. If $$z=x+i y$$, then the equation $$|z+1|=|z-1|$$ represents 39. The value of $${ }^{16} C_9+{ }^{16} C_{10}-{ }^{16} C_6-{ }^{16} C_7$$ is 40. The number of terms in the expansion of $$(x+y+z)^{10}$$ is 41. If $$P(n): 2^n 42. The two lines $$l x+m y=n$$ and $$l^{\prime} x+m^{\prime} y=n^{\prime}$$ are perpendicular if 43. If the parabola $$x^2=4$$ ay passes through the point $$(2,1)$$, then the length of the latus rectum is 44. If the sum of $$n$$ terms of an AP is given by $$S_n=n^2+n$$, then the common difference of the $$\mathrm{AP}$$ is 45. The negation of the statement "For all real numbers $$x$$ and $$y, x+y=y+x^{\prime \prime}$$ is 46. The standard deviation of the data 6, 7, 8, 9, 10 is 47. $$\lim _\limits{x \rightarrow 0}\left(\frac{\tan x}{\sqrt{2 x+4}-2}\right) \text { is equal to }$$ 48. If a relation $$R$$ on the set $$\{1,2,3\}$$ be defined by $$R=\{(1,1)\}$$, then $$R$$ is 49. Let $$f:[2, \infty) \rightarrow R$$ be the function defined $$f(x)=x^2-4 x+5$$, then the ranges of $$f$$ is 50. If $$A, B, C$$ are three mutually exclusive and exhaustive events of an experiment such that $$P(A)=2 P(B)=3 P(C)$$, the 51. The domain of the function defined by $$f(x)=\cos ^{-1} \sqrt{x-1}$$ is 52. The value of $$\cos \left(\sin ^{-1} \frac{\pi}{3}+\cos ^{-1} \frac{\pi}{3}\right)$$ is Does not exist 53. If $$A=\left(\begin{array}{lll}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{array}\right)$$ then $$A^4$$ is equal to 54. If $$A=\{a, b, c\}$$, then the number of binary operations on $$A$$ is 55. If $$\left(\begin{array}{ll}2 & 1 \\ 3 & 2\end{array}\right) A=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)$$ 56. If $$f(x)=\left|\begin{array}{ccc}x^3-x & a+x & b+x \\ x-a & x^2-x & c+x \\ x-b & x-c & 0\end{array}\right|$$, then 57. If $$A$$ and $$B$$ are square matrices of same order and $$B$$ is a skew symmetric matrix, then $$A^{\prime} B A$$ is 58. If $$A$$ is a square matrix of order 3 and $$|A|=5$$, then $$\mid A$$ adj. $$A \mid$$ is 59. If $$f(x)=\left\{\begin{array}{cc}\frac{1-\cos K x}{x \sin x}, & \text { if } x \neq 0 \\ \frac{1}{2}, & \text { if } x= 60. If $$a_1 a_2 a_3 \ldots a_9$$ are in AP, then the value of $$\left|\begin{array}{lll}a_1 & a_2 & a_3 \\ a_4 & a_5 & a_6

Physics

1. The value of acceleration due to gravity at a height of $$10 \mathrm{~km}$$ from the surface of earth is $$x$$. At what 2. Young's modulus of a perfect rigid body is 3. A wheel starting from rest gains an angular velocity of $$10 \mathrm{~rad} / \mathrm{s}$$ after uniformly accelerated fo 4. Iceberg floats in water with part of it submerged. What is the fraction of the volume of iceberg submerged, if the densi 5. A sphere, a cube and a thin circular plate all of same material and same mass initially heated to same high temperature 6. In an adiabatic expansion of an ideal gas the product of pressure and volume 7. A certain amount of heat energy is supplied to a monoatomic ideal gas which expands at constant pressure. What fraction 8. A tray of mass $$12 \mathrm{~kg}$$ is supported by two identical springs as shown in figure. When the tray is pressed do 9. A train whistling at constant frequency $$n$$ is moving towards a station at a constant speed $$v$$. The train goes past 10. A point charge $$q$$ is placed at the corner of a cube of side $$a$$ as shown in the figure. What is the electric flux t 11. The electric field lines on the left have twice the separation on those on the right as shown in figure. If the magnitud 12. An infinitely long thin straight wire has uniform charge density of $$\frac{1}{4} \times 10^{-2} \mathrm{~cm}^{-1}$$. Wh 13. A dipole moment $$p$$ and moment of inertia $$I$$ is placed in a uniform electric field $$\mathbf{E}$$. If it is displac 14. The difference between equivalent capacitances of two identical capacitors connected in parallel to that in series is $$ 15. Figure shows three points $$A, B$$ and $$C$$ in a region of uniform electric field $$\mathbf{E}$$. The line $$A B$$ is p 16. When a soap bubble is charged? 17. A hot filament liberates an electron with zero initial velocity. The anode potential is $$1200 \mathrm{~V}$$. The speed 18. A metal rod of length $$10 \mathrm{~cm}$$ and a rectangular cross-section of $$1 \mathrm{~cm} \times \frac{1}{2} \mathrm 19. A car has a fresh storage battery of emf $$12 \mathrm{~V}$$ and internal resistance $$2 \times 10^{-2} \Omega$$. If the 20. A potentiometer has a uniform wire of length $$5 \mathrm{~m}$$. A battery of emf $$10 \mathrm{~V}$$ and negligible inter 21. The colour code for a carbon resistor of resistance $$0.2 \mathrm{k} \Omega \pm 10 \%$$ is 22. Each resistance in the given cubical network has resistance of $$1 \Omega$$ and equivalent resistance between $$A$$ and 23. $$I-V$$ characteristic of a copper wire of length $$L$$ and area of cross-section $$A$$ is shown in figure. The slope of 24. In the given figure, the magnetic field at $$O$$. 25. The magnetic field at the origin due to a current element $$i d \mathbf{l}$$ placed at a point with vector position $$\m 26. A long cylindrical wire of radius $$R$$ carries a uniform current $$I$$ flowing through it. The variation of magnetic fi 27. A cyclotron is used to accelerate protons $$\left({ }_1^l \mathrm{H}\right)$$ deuterons $$\left({ }_1^2 \mathrm{H}\right 28. A paramagnetic sample shows a net magnetisation of $$8 \mathrm{Am}^{-1}$$ when placed in an external magnetic field of $ 29. The ratio of magnetic field at the centre of a current carrying circular coil to its magnetic moment is $$x$$, if the cu 30. In a permanent magnet at room temperature 31. A rod of length $$2 \mathrm{~m}$$ slides with a speed of $$5 \mathrm{~ms}^{-1}$$ on a rectangular conducting frame as sh 32. The current in a coil of inductance $$0.2 \mathrm{H}$$ changes from $$5 \mathrm{~A}$$ to $$2 \mathrm{~A}$$ in $$0.5 \mat 33. In the given circuit the peak voltage across $$C, L$$ and $$R$$ are $$30 \mathrm{~V}, 110 \mathrm{~V}$$ and $$60 \mathrm 34. The power factor of $$R-L$$ circuit is $$\frac{1}{\sqrt{3}}$$. If the inductive reactance is $$2 \Omega$$. The value of 35. In the given circuit, the resonant frequency is 36. A light beam of intensity $$20 \mathrm{~W} / \mathrm{cm}^2$$ is incident normally on a perfectly reflecting surface of s 37. An object approaches a convergent lens from the left of the lens with a uniform speed $$5 \mathrm{~m} / \mathrm{s}$$ and 38. The refracting angle of prism is $$A$$ and refractive index of material of prism is $$\cot \frac{A}{2}$$. The angle of m 39. The following figure shows a beam of light converging at point $$P$$. When a concave lens of focal length $$16 \mathrm{~ 40. Three polaroid sheets $$P_1, P_2$$ and $$P_3$$ are kept parallel to each other such that the angle between pass axes of 41. Two poles are separated by a distance of $$3.14 \mathrm{~m}$$. The resolving power of human eye is $$1 \mathrm{~min}$$ o 42. In Young's double slit experiment, the distance between the slits and the screen is $$1.2 \mathrm{~m}$$ and the distance 43. The de-Broglie wavelength associated with electron of hydrogen atom in this ground state is 44. The following graph represents the variation of photocurrent with anode potential for a metal surface. Here $$I_1, I_2$$ 45. The period of revolution of an electron revolving in nth orbit of $$\mathrm{H}$$-atom is proportional to 46. Angular momentum of an electron in hydrogen atom is $$\frac{3 h}{2 \pi}$$ ($$h$$ is the Planck's constant). The KE of th 47. A beam of fast moving alpha particles were directed towards a thin film of gold. The parts $$A, B$$ and $$C$$ of the tra 48. Two protons are kept at a separation of $$10 \mathrm{~nm}$$. Let $$F_n$$ and $$F_e$$ the nuclear force and the electroma 49. During a $$\beta^{-}$$-decay 50. A radio-active elements has half-life of 15 years. What is the fraction that will decay in 30 years? 51. A $$220 \mathrm{~V}$$ AC supply is connected between points $$A$$ and $$B$$ as shown in figure, what will be the potenti 52. In the following circuit what are P and Q 53. A positive hole in a semiconductor is 54. Two long straight parallel wires are a distance $$d$$ part. They carry steady equal currents flowing out of the plane of 55. A cylindrical wire has a mass $$(0.3 \pm 0.003) \mathrm{g}$$, radius $$(0.5 \pm 0.005) \mathrm{mm}$$ and length $$(6 \pm 56. At a metro station, a girl walks up a stationary escalator in $$20 \mathrm{~s}$$. If she remains stationary on the escal 57. Rain is falling vertically with a speed of $$12 \mathrm{~ms}^{-1}$$. A woman rides a bicycles with a speed of $$12 \math 58. One end of a string of length $$l$$ is connected to a particle of mass $$m$$ and the other to a small peg on a smooth ho 59. A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it a 60. A thin uniform rectangular plate of mass $$2 \mathrm{~kg}$$ is placed in $$x y$$-plane as shown in figure. The moment of

KCET 2020

MCQ (Single Correct Answer)

-0

A beam of fast moving alpha particles were directed towards a thin film of gold. The parts $$A, B$$ and $$C$$ of the transmitted and reflected beams corresponding to the incident parts $$A, B$$ and $$C$$ of the beam are shown in the adjoining diagram. The number of alpha particles in

KCET 2020 Physics - Atoms and Nuclei Question 6 English