KCET 2019 | KCET Year Wise Previous Years Questions

Chemistry

Mathematics

1. The inverse of the matrix $$\left[\begin{array}{ccc}2 & 5 & 0 \\ 0 & 1 & 1 \\ -1 & 0 & 3\end{array}\right]$$ is 2. If $$P$$ and $$Q$$ are symmetric matrices of the same order then $$P Q-Q P$$ is 3. If $$3 A+4 B^{\prime}=\left[\begin{array}{ccc}7 & -10 & 17 \\ 0 & 6 & 31\end{array}\right]$$ and $$2 B+3 A^{\prime}\left 4. If $$A=\left[\begin{array}{ll}1 & 3 \\ 4 & 2\end{array}\right], B=\left[\begin{array}{cc}2 & -1 \\ -1 & 2\end{array}\rig 5. If the value of a third order determinant is 16, then the value of the determinant formed by replacing each of its eleme 6. $$\int x^3 \sin 3 x d x=$$ 7. The area of the region above $$X$$-axis included between the parabola $$y^2=x$$ and the circle $$x^2+y^2=2 x$$ in square 8. The area of the region bounded by $$Y$$-axis, $$y=\cos x$$ and $$y=\sin x, 0 \leq x \leq \frac{\pi}{2}$$ is 9. The integrating factor of the differential equation $$\left(2 x+3 y^2\right) d y=y d x(y>0)$$ is 10. The equation of the curve passing through the point $$(1,1)$$ such that the slope of the tangent at any point $$(x, y)$$ 11. Foot of the perpendicular drawn from the point $$(1,3,4)$$ to the plane $$2 x-y+z+3=0$$ is 12. Acute angel between the line $$\frac{(x-5)}{2}=\frac{y+1}{-1}=\frac{z+4}{1}$$ and the plane $$3 x-4 y-z+5=0$$ is 13. The distance of the point $$(1,2,1)$$ from the line $$\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-3}{2}$$ is. 14. $$X Y$$ plane divides the line joining the points $$A(2,3,-5)$$ and $$B(-1,-2,-3)$$ in the ratio 15. The shaded region in the figure is the solution set of the inequations. 16. The constant term in the expansion of $$\left|\begin{array}{ccc}3 x+1 & 2 x-1 & x+2 \\ 5 x-1 & 3 x+2 & x+1 \\ 7 x-2 & 3 17. If $$[x]$$ represents the greatest integer function and $$f(x)=x-[x]-\cos x$$, then $$f^{\prime}\left(\frac{\pi}{2}\righ 18. If $$f(x)=\left\{\begin{array}{cl}\frac{\sin 3 x}{e^{2 x}-1} ; & x \neq 0 \\ k-2 ; & x=0\end{array}\right.$$ is continuo 19. If $$f(x)=\sin ^{-1}\left(\frac{2^{x+1}}{1+4^x}\right)$$ then $$f^{\prime}(0)=$$ 20. If $$x=a \sec ^2 \theta$$ & $$y=a \tan ^2 \theta$$, then $$\frac{d^2 y}{d x^2}=$$ 21. If $$\alpha$$ and $$\beta$$ are roots of the equation $$x^2=x+1=0$$, then $$\alpha^2+\beta^2$$ is 22. The number of 4 digit numbers without repetition that can be formed using the digits $$1,2,3,4,5,6,7$$ in which each num 23. The number of terms in the expansion of $$\left(x^2+y^2\right)^{25}-\left(x^2-y^2\right)^{25}$$ after simplification is 24. The third term of a GP is 9. The product of its first five terms is 25. A line cuts off equal intercepts on the co-ordinate axes. The angle made by this line with the positive direction of $$X 26. The eccentricity of the ellipse $$9 x^2+25 y^2=225$$ is 27. $$\sum_\limits{r=1}^n(2 r-1)=x$$ then, $$ \lim _\limits{n \rightarrow \infty}\left[\frac{1^3}{x^2}+\frac{2^3}{x^2}+\frac 28. The negative of the statement "All continuous functions are differentiable." 29. Mean and standard deviation of 100 items are 50 and 4 , respectively. The sum of all squares of the items is 30. Two letters are chosen from the letters of the word 'EQUATIONS'. The probability that one is vowel and the other is cons 31. $$f: R \rightarrow R$$ and $$g:[0, \infty) \rightarrow R$$ is defined by $$f(x)=x^2$$ and $$g(x)=\sqrt{x}$$. Which one o 32. If $$A=\{x \mid x \in N, x \leq 5\},B=\left\{x \mid x \in Z, x^2-5 x+6=0\right\}$$, then the number of onto functions fr 33. On the set of positive rational, a binary operation * is defined by $$a * b=\frac{2 a b}{5}$$. If $$2 * x=3^{-1}$$, then 34. $$\cos \left[2 \sin ^{-1} \frac{3}{4}+\cos ^{-1} \frac{3}{4}\right]=$$ 35. If $$a+\frac{\pi}{2} 36. If $$|3 x-5| \leq 2$$ then 37. A random variable '$$X$$' has the following probability distribution .tg {border-collapse:collapse;border-spacing:0;} 38. If $$A$$ and $$B$$ are two events of a sample space $$S$$ such that $$P(A)=0.2, P(B)=0.6$$ and $$P(A \mid B)=0.5$$ then 39. If '$$X$$' has a binomial distribution with parameters $$n=6, p$$ and $$P(X=2)=12$$, $$P(X=3)=5$$ then $$P=$$ 40. A man speaks truth 2 out of 3 times. He picks one of the natural numbers in the set $$S=\{1,2,3,4,5,6,7\}$$ and reports 41. The order of the differential equation $$y=C_1 e^{C_2+x}+C_3 e^{C_4+x}$$ is 42. If $$|\mathbf{a}|=16,|\mathbf{b}|=4$$, then $$\sqrt{|\mathbf{a} \times \mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2}=$$ 43. If the angle between $$\mathbf{a}$$ & $$\mathbf{b}$$ is $$\frac{2 \pi}{3}$$ and the projection of $$\mathbf{a}$$ in the 44. A unit vector perpendicular to the plane containing the vector $$\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$$ 45. $$[\mathbf{a}+2 \mathbf{b}-\mathbf{c}, \mathbf{a}-\mathbf{b}, \mathbf{a}-\mathbf{b}-\mathbf{c}]=$$ 46. $$\sqrt[3]{y} \sqrt{x}=\sqrt[6]{(x+y)^5}$$, then $$\frac{d y}{d x}=$$ 47. Rolle's theorem is not applicable in which one of the following cases? 48. The interval in which the function $$f(x)=x^3-6 x^2+9 x+10$$ is increasing in 49. The sides of an equilateral triangle are increasing at the rate of $$4 \mathrm{~cm} / \mathrm{sec}$$. The rate at which 50. The value of $$\sqrt{24.99}$$ is 51. $$\int_\limits{-3}^3 \cot ^{-1} x d x=$$ 52. $$\int \frac{1}{\sqrt{x}+x \sqrt{x}} d x=$$ 53. $$\begin{aligned} & \int \frac{2 x-1}{(x-1)(x+2)(x-3)} d x \\ & \quad=A \log |x-1|+B \log |x+2|+C \log |x-3|+K \end{alig 54. $$\int_\limits0^2\left[x^2\right] d x=$$ 55. $$\int_\limits0^1 \sqrt{\frac{1+x}{1-x}} d x=$$ 56. If $$U$$ is the universal set with 100 elements; $$A$$ and $$B$$ are two set such that $$n(A)=50, n(B)=60, n(A \cap B)=2 57. The domain of the function $$f: R \rightarrow R$$ defined by $$f(x)=\sqrt{x^2-7 x+12}$$ is 58. If $$\cos x=|\sin x|$$ then, the general solution is 59. $$\sqrt{3} \operatorname{cosec} 20^{\circ}-\sec 20^{\circ}=$$ 60. If $$P(n): 2^n

Physics

1. Which one of the following nuclei has shorter mean life? 2. The conductivity of semiconductor increases with increase in temperature because 3. For a transistor amplifier, the voltage gain 4. In the following circuit, what are P and Q? 5. An antenna uses electromagnetic waves of frequency $$5 \mathrm{~MHz}$$. For proper working, the size of the antenna shou 6. A magnetic needle has a magnetic moment of $$5 \times 10^{-2} \mathrm{~Am}^2$$ and moment of inertia $$8 \times 10^{-6} 7. A toroid has 500 turns per meter length. If it carries a current of $$2 \mathrm{A}$$, the magnetic energy density inside 8. Consider the situation given in figure. The wire $$A B$$ is slid on the fixed rails with a constant velocity. If the wir 9. The frequency of an alternating current is $$50 \mathrm{~Hz}$$. What is the minimum time taken by current to reach its p 10. The readings of ammeter and voltmeter in the following circuit are respectively 11. Two metal plates are separated by $$2 \mathrm{~cm}$$. The potentials of the plates are $$-10 \mathrm{~V}$$ and $$+30 \ma 12. The equivalent capacitance between A and B is 13. A capacitor of capacitance $$C$$ charged by an amount $$Q$$ is connected in parallel with an uncharged capacitor of capa 14. Though the electron drift velocity is small and electron charge is very small, a conductor can carry an appreciably larg 15. Masses of three wires of copper are in the ratio $$1: 3: 5$$ and their lengths are in the ratio $$5: 3: 1$$. The ratio o 16. If $$P, Q$$ and $$R$$ are physical quantities having different dimensions, which of the following combinations can never 17. The given graph shows the variation of velocity $$v$$ with position $$x$$ for a particle moving along a straight line W 18. The trajectory of a projectile projected from origin is given by the equation $$y=x-\frac{2 x^2}{5}$$. The initial veloc 19. An object with mass $$5 \mathrm{~kg}$$ is acted upon by a force, $$\mathbf{F}=(-3 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}) \ 20. During inelastic collision between two objects, which of the following quantity always remains conserved? 21. In Rutherford experiment, for head-on collision of $$\alpha$$-particles with a gold nucleus, the impact parameter is 22. Frequency of revolution of an electron revolving in $$n$$th orbit of $$\mathrm{H}$$-atom is proportional to 23. A hydrogen atom is ground state absorbs $$10.2 \mathrm{~eV}$$ of energy. The orbital angular momentum of the electron is 24. The end product of decay of $${ }_{90} \mathrm{Th}^{232}$$ is $${ }_{82} \mathrm{~Pb}^{208}$$. The number of $$\alpha$$ 25. Two protons are kept at a separation of $$10 \mathrm{~nm}$$. Let $$F_n$$ and $$F_e$$ be the nuclear force and the electr 26. Two particles which are initially at rest move towards each other under the action of their mutual attraction. If their 27. A particle is moving uniformly along a straight line as shown in the figure. During the motion of the particle from $$A$ 28. A satellite is orbiting close to the earth and has a kinetic energy $$K$$. The minimum extra kinetic energy required by 29. A wire is stretched such that its volume remains constant. The poission's ratio of the material of the wire is 30. A cylindrical container containing water has a small hole at height of $$H=8 \mathrm{~cm}$$ from the bottom and at a dep 31. A transparent medium shows relation between $$i$$ and $$r$$ as shown. If the speed of light in vacuum is $$c$$, the Brew 32. If Young's double slit experiment, using monochromatic light of wavelength $$\lambda$$, the intensity of light at a poin 33. Due to Doppler's effect the shift in wavelength observed is $$0.1 \mathop A\limits^o$$ for a star producing wavelength $ 34. An electron is moving with an initial velocity $$\mathbf{v}=v_0 \hat{\mathbf{i}}$$ and is in a uniform magnetic field $$ 35. Light of certain frequency and intensity incident on a photosensitive material causes photoelectric effect. If both the 36. A certain charge $$2 Q$$ is divided at first into two parts $$q_1$$ and $$q_2$$. Later the charges are placed at a certa 37. A particle of mass $$m$$ and charge $$q$$ is placed at rest in uniform electric field $$E$$ and then released. The kinet 38. An electric dipole is kept in non-uniform electric field. It generally experiences 39. The figure gives the electric potential $$V$$ as a function of distance through four regions on $$x$$-axis. Which of the 40. A system of two charges separated by a certain distance apart stores electrical potential energy. If the distance betwee 41. In a cyclotron a charged particle 42. The number of turns in a coil of galvanometer is tripled, then 43. A circular current loop of magnetic moment $$M$$ is in a arbitrary orientation in an external uniform magnetic field $$\ 44. In a permanent magnet at room temperature 45. Coersivity of a magnet where the ferromagnet gets completely demagnetized is $$3 \times 10^3 \mathrm{~Am}^{-1}$$. The mi 46. An inductor of inductance $$L$$ and resistor $$R$$ are joined together in series and connected by a source of frequency 47. An electromagnetic wave is travelling in $$x$$-direction with electric field vector given by, $$\mathbf{E}_y=E_0 \sin (k 48. The phenomenon involved in the reflection of radio-waves by ionosphere is similar to 49. A point object is moving uniformly towards the pole of a concave mirror of focal length $$25 \mathrm{~cm}$$ along its ax 50. A certain prism is found to produce a minimum deviation of $$38^{\circ}$$. It produce a deviation of $$44^{\circ}$$ when 51. In the given circuit, the current through 2$$\Omega$$ resistor is 52. Kirchhoff 's junction rule is a reflection of 53. The variation of terminal potential difference $$V$$ with current flowing through a cell is as shown. The emf and intern 54. In a potentiometer experiment, the balancing point with a cell is at a length $$240 \mathrm{~cm}$$. On shunting the cell 55. The magnetic fields at the centre O in the given figure is 56. An aluminium sphere is dipped into water. Which of the following is true? 57. A thermodynamic system undergoes a cyclic process $$A B C$$ as shown in the diagram. The work done by the system per cyc 58. One mole of $$\mathrm{O}_2$$ gas is heated at constant pressure starting at $$27^{\circ} \mathrm{C}$$. How much energy m 59. A piston is performing S.H.M. in the vertical direction with a frequency of $$0.5 \mathrm{~Hz}$$. A block of $$10 \mathr 60. The equation of a stationary wave is $$y=2 \sin \left(\frac{\pi x}{15}\right) \cos (48 \pi t)$$. The distance between a

KCET 2019

MCQ (Single Correct Answer)

-0

$$\begin{aligned} & \int \frac{2 x-1}{(x-1)(x+2)(x-3)} d x \\ & \quad=A \log |x-1|+B \log |x+2|+C \log |x-3|+K \end{aligned}$$

Then $$A, B, C$$ are respectively

$$\frac{1}{6}, \frac{-1}{3}, \frac{1}{3}$$

$$\frac{-1}{6}, \frac{1}{3}, \frac{1}{3}$$

$$\frac{-1}{6}, \frac{-1}{3}, \frac{1}{2}$$

$$\frac{1}{6}, \frac{1}{3}, \frac{1}{5}$$

KCET 2019

MCQ (Single Correct Answer)

-0

$$\int_\limits0^2\left[x^2\right] d x=$$

$$5-\sqrt{2}+\sqrt{3}$$

$$5-\sqrt{2}-\sqrt{3}$$

$$-5-\sqrt{2}-\sqrt{3}$$

$$5+\sqrt{2}-\sqrt{3}$$

KCET 2019

MCQ (Single Correct Answer)

-0

$$\int_\limits0^1 \sqrt{\frac{1+x}{1-x}} d x=$$

$$\frac{\pi}{2}$$

$$\frac{\pi}{2}-1$$

$$\frac{1}{2}$$

$$\frac{\pi}{2}+1$$

KCET 2019

MCQ (Single Correct Answer)

-0

If $$U$$ is the universal set with 100 elements; $$A$$ and $$B$$ are two set such that $$n(A)=50, n(B)=60, n(A \cap B)=20$$ then $$n\left(A^{\prime} \cap B^{\prime}\right)=$$

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