KCET 2017 | KCET Year Wise Previous Years Questions

Chemistry

Mathematics

1. If an LPP admits optimal solution at two consecutive vertices of a feasible region, then 2. $$ \text { } \begin{aligned} Let\,\,\,\Delta & =\left|\begin{array}{lll} A x & x^2 & 1 \\ B y & y^2 & 1 \\ C z & z^2 & 3. The total number of terms in the expansion of $(x+a)^{47}-(x-a)^{47}$ after simplification is 4. The function $f(x)=x^2+2 x-5$ is strictly increasing in the interval 5. The shaded region in the figure is the solution set of the inequations 6. The point on the curve $y^2=x$ where the tangent makes an angle of $\pi / 4$ with $X$-axis is 7. $$ \int\limits_{-\pi / 2}^{\pi / 2} \frac{d x}{e^{\sin x}+1} $$ 8. If $a$ and $\mathbf{b}$ are unit vectors, then angle between $\mathbf{a}$ and $\mathbf{b}$ for $\sqrt{3} \mathbf{a}-\mat 9. The contrapositive statement of the statement "If $x$ is prime number, then $x$ is odd" is 10. $\int\limits_{-5}^5|x+2| d x$ is equal to 11. If $\left|\begin{array}{ll}3 & x \\ x & 1\end{array}\right|=\left|\begin{array}{ll}3 & 2 \\ 4 & 1\end{array}\right|$, t 12. If $2\left|\begin{array}{ll}1 & 3 \\ 0 & x\end{array}\right|+\left|\begin{array}{ll}y & 0 \\ 1 & 2\end{array}\right|=\l 13. $$ \int\limits_0^{\pi / 2} \frac{1}{a^2 \cdot \sin ^2 x+b^2 \cdot \cos ^2 x} d x $$ 14. $$ \int \sqrt{x^2+2 x+5} d x \text { is equal to } $$ 15. A box has 100 pens of which 10 are defective. The probability that out of a sample of 5 pens drawn one by one with repla 16. The range of $\sec ^{-1} x$ is 17. $\int \frac{(x+3) e^x}{(x+4)^2} d x$ is equal to 18. $$ \text { If } y=\left|\begin{array}{ccc} f(x) & g(x) & h(x) \\ l & m & n \\ a & b & c \end{array}\right| \text {, then 19. General solution of differential equations $\frac{d y}{d x}+y=1(y \neq 1)$ is 20. If $A$ is a square matrix of order $3 \times 3$, then $|K A|$ is equal to 21. If $A=\frac{1}{\pi}\left|\begin{array}{ll}\sin ^{-1}(\pi x) & \tan ^{-1}\left(\frac{x}{\pi}\right) \\ \sin ^{-1}\left(\f 22. If ${ }^n C_{12}={ }^n C_8$, then $n$ is equal to 23. The probability distribution of $X$ is $$ \begin{array}{|c|l|c|c|c|} \hline \boldsymbol{X} & 0 & 1 & 2 & 3 \\ \hline \bo 24. The degree of the differential equation $\left[1+\left(\frac{d y}{d x}\right)^2\right]^2=\frac{d^2 y}{d x^2}$ is 25. $3+5+7+\ldots$ to $n$ terms is 26. $\int \frac{\cos 2 x-\cos 2 \theta}{\cos x-\cos \theta} d x$ is equal to 27. If $A$ and $B$ are finites sets and $A \subset B$, then 28. $$The\,\,value\,\,of\,\,\mathop {\lim }\limits_{\theta \to 0} {{1 - \cos 4\theta } \over {1 - \cos 6\theta }}\,\,is$$ 29. If $\mathbf{a}=2 \hat{\mathbf{i}}+\lambda \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\mathbf{b}=\hat{\mathbf{i}}+2 \hat{\ma 30. If $f(x)=\left\{\begin{array}{cll}k x^2 & \text { if } & x \leq 2 \\ 3 & \text { if } & x>2\end{array}\right.$ is contin 31. The area of triangle with vertices $(K, 0),(4,0)$, $(0,2)$ is 4 sq units, then value of $K$ is 32. If $\left(\frac{1+i}{1-i}\right)^m=1$, then the least positive integral value of $m$ is 33. If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are unit vectors such that $a+b+c=0$, then the value of $\mathbf{a} \cdot \mathb 34. The value of $\cos ^2 45^{\circ}-\sin ^2 15^{\circ}$ is 35. Let $f: R \rightarrow R$ be defined by $f(x)=x^4$, then 36. If $\sin x=\frac{2 t}{1+t^2}, \tan y+\frac{2 t}{1-t^2}$, then $\frac{d y}{d x}$ is equal to 37. The plane $2 x-3 y+6 z-11=0$ makes an angle $\sin ^{-1}(\alpha)$ with $X$-axis, the value of $\alpha$ is equal to 38. If $f(x)=8 x^3, g(x)=x^{1 / 3}$, then $f \circ g(x)$ is 39. If $y=\log (\log x)$, then $\frac{d^2 y}{d x^2}$ is equal to 40. $\int\limits_{0.2}^{3.5}[x] d x$ is equal to : 41. If $|x-2| \leq 1$, then 42. The perpendicular distance of the point $P(6,7,8)$ from $X Y$-plane is 43. Binary operation * on $R-\{-1\}$ defined by $a^* b=\frac{a}{b+1}$ is 44. If $y=\tan ^{-1}\left(\frac{\sin x+\cos x}{\cos x-\sin x}\right)$, then $\frac{d y}{d x}$ is equal to 45. The eccentricity of the ellipse $\frac{x^2}{36}+\frac{y^2}{16}=1$ is 46. The integrating factor of the differential equation $x \cdot \frac{d y}{d x}+2 y=x^2$ is $(x \neq 0)$ 47. The derivative of $\cos ^{-1}\left(2 x^2-1\right)$ w.r.t. $\cos ^{-1} x$ is 48. The rate of change of volume of a sphere with respect to its surface area when the radius is 4 cm is 49. $\int\limits_0^{\pi / 2} \frac{\tan ^7 x}{\cot ^7 x+\tan ^7 x} d x$ is equal to 50. The range of the function $f(x)=\sqrt{9-x^2}$ is 51. Reflexion of the point $(\alpha, \beta, \gamma)$ in $X Y$-plane is 52. The area of the region bounded by the curve $y=x^2$ and the line $y=16$ 53. If coefficient of variation is 60 and standard deviation is 24 , then Arithmetic mean is 54. Two events $A$ and $B$ will be independent if 55. Area of the region bounded by the curve $y=\cos x, x=0$ and $x=\pi$ is 56. The value of $c$ in mean value theorem for the function $f(x)=x^2$ in $[2,4]$ is 57. Equation of line passing through the point $(1,2)$ and perpendicular to the line $y=3 x-1$ 58. If $\tan ^{-1} x+\tan ^{-1} y=\frac{4 \pi}{5}$, then $\cot ^{-1} x+\cot ^{-1} y$ is equal to 59. If a matrix $A$ is both symmetric and skew symmetric, then 60. The distance of the point $(-2,4,-5)$ from the line $\frac{x+3}{3}=\frac{y-4}{5}=\frac{z+8}{6}$ is

Physics

1. A coil of inductive reactance $1 / \sqrt{3} \Omega$ and resistance $1 \Omega$ is connected to a $200 \mathrm{~V}, 50 \ma 2. A car moving with a velocity of $20 \mathrm{~ms}^{-1}$ stopped at a distance of 40 m . If the same car is travelling at 3. The particle emitted in the decay of ${ }_{92}^{238} \mathrm{U}$ to ${ }_{92}^{234} \mathrm{U}$ 4. Of the following graphs, the one that correctly represents the $I-V$ characteristics of a 'Ohmic device' is 5. The susceptibility of a ferromagnetic substance is 6. The working of magnetic braking of trains is based on 7. A substance of mass 49.53 g occupies $1.5 \mathrm{~cm}^3$ of volume. The density of the substance (in $\mathrm{g} \mathr 8. From the following graph of photo current against collector plate potential, for two different intensities of light $I_1 9. Two balls are thrown simultaneously in air. The acceleration of the centre of mass of the two balls when in air 10. If $\mathbf{E}$ and $\mathbf{B}$ represent electric and magnetic field vectors of an electromagentic wave, the direction 11. A body of the mass 50 kg is suspended using a spring balance inside a lift at rest. If the lift starts falling freely, t 12. Two point charges $A=+3 \mathrm{nC}$ and $B=+1 \mathrm{nC}$ are placed 5 cm apart in air. The work done to move charge $ 13. A proton, a deuteron and an $\alpha$-particle are projected perpendicular to the direction of a uniform magnetic field w 14. The S.I. unit of specific heat capacity is 15. In the three parts of a transistor, 'Emitter' is of 16. A bar magnet is allowed to fall vertically through a copper coil placed in a horizontal plane. The magnet falls with a n 17. For which combination of working temperatures, the efficiency of Carnot's engine is the least? 18. A basic communication system consists of (i) Transmitter (ii) Information sources (iii) User of information (iv) Channel 19. According to Huygens' principle, during refraction of light from air to a denser medium 20. A galvanometer of resistance $50 \Omega$ is connected to a battery of $3 \cdot \mathrm{~V}$ along with a${ }^{\text { }} 21. In the A.C. circuit shown, keeping ' $K$ ' pressed, if an iron rod inserted into the coil, the bulb in the circuit, 22. A magnetic dipole of magnetic moment $6 \times 10^{-2}$ A-m ${ }^2$ and moment of inertia $12 \times 10^{-6} \mathrm{~kg 23. $4 \times 10^{10}$ electrons are removed from a neutral metal sphere of diameter 20 cm placed in air. The magnitude of t 24. The mass defect of ${ }_2^4 \mathrm{He}$ is 0.03 u . The binding energy per nucleon of helium (in MeV) is 25. A cylindrical conductor of diameter 0.1 mm carries a current of 90 mA . The current density ( in $\mathrm{Am}^{-2}$ ) is 26. Which of the following properties is 'False' for a bar magnet? 27. According to cartesian sign convention, in ray optics 28. A linear object of height 10 cm is kept in front of a concave mirror of radius of curvature 15 cm , at a distance of 10 29. The energy gap in case of which of the following is less than 3 eV ? 30. The minimum value of effective capacitance that can be obtained by combining 3 capacitors of capacitances $1 \mathrm{pF} 31. Two spheres of electric charges +2 nC and -8 nC are placed at a distance $d$ apart. If they are allowed to touch each ot 32. The value of acceleration due to gravity at a depth of 1600 km is equal to 33. Two simple pendulums $A$ and $B$ are made to oscillate simultaneously and it is found that $A$ completes 10 oscillations 34. A motor pump lifts 6 tonnes of water from a well of depth 25 m to the first floor of height 35 m from the ground floor i 35. The waves set up in a closed pipe are 36. In the figure shown, if the diode forward voltage drop is 0.2 V , the voltage difference between $A$ and $B$ is 37. If $\mathbf{A}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+8 \hat{\mathbf{k}}$ is perpendicular to $\mathbf{B}=4 \hat{\mathbf{ 38. The angle between velocity and acceleration of a particle describing uniform circular motion is 39. A straight wire of length 50 cm carrying a current of 2.5 A is suspended in mid-air by a uniform magnetic field of 0.5 T 40. 'Young's modulus' is defined as the ratio of 41. Which of the following semi-conducting device is used as voltage regulator? 42. Which of the following logic gate is universal gate 43. A particle is dropped from a height $H$. The de-Broglie wavelength of the particle depends on height as 44. Three point charges of $+2 q,+2 q$ and $-4 q$ are placed at the corners $A, B$ and $C$ of an equilateral triangle $A B C 45. In a system of two crossed polarisers, it is found that the intensity of light from the second polariser is half from th 46. A piece of copper is to be shaped into a conducting wire of maximum resistance. The suitable length and diameter are ... 47. During scattering of light, the amount of scattering in inversely proportional to................ of wavelength of light 48. A jet plane of wing span 20 m is travelling towards west at a speed of $400 \mathrm{~ms}^{-1}$. If the earth's total mag 49. The energy (in eV ) required to excite an electron from $n=2$ to $n=4$ state in hydrogen atom is 50. 'Hydraulic lift' works on the basis of 51. In a nuclear reactor, the function of the moderator is to decreases 52. The scientist who is credited with the discovery of 'nucleus' in an atom is 53. A system of two capacitors of capacitance $2 \mu \mathrm{~F}$ and $4 \mu \mathrm{~F}$ is connected in series across a po 54. In meter bridge experiment, with a standard resistance in the right gap and a resistance coil dipped in water (in a beak 55. The power dissipated in $3 \Omega$ resistance in the following circuit is 56. The mean energy of a molecule of an ideal gas is 57. The magnetic field at the centre of a current carrying loop of radius 0.1 m is $5 \sqrt{5}$ times that at a point along 58. $$ \text { The value of } I \text { in the figure shown below is } $$ 59. In Young's double-slit experiment, if yellow light is replaced by blue light, the interference fringes becomes 60. The output of a step down transformers is measured to be 48 V when connected to a 12 W bulb. The value of peak current i

KCET 2017

MCQ (Single Correct Answer)

-0

If $A=\frac{1}{\pi}\left|\begin{array}{ll}\sin ^{-1}(\pi x) & \tan ^{-1}\left(\frac{x}{\pi}\right) \\ \sin ^{-1}\left(\frac{x}{\pi}\right) & \cot ^{-1}(\pi x)\end{array}\right|$

$B=\left|\begin{array}{cc}-\cos ^{-1}(\pi x) & \tan ^{-1}\left(\frac{x}{\pi}\right) \\ \sin ^{-1}\left(\frac{x}{\pi}\right) & -\tan ^{-1}(\pi x)\end{array}\right|$,

then $A-B$ is :

$\frac{1}{2}$ I

$/$

$2!$

KCET 2017

MCQ (Single Correct Answer)

-0

If ${ }^n C_{12}={ }^n C_8$, then $n$ is equal to

KCET 2017

MCQ (Single Correct Answer)

-0

The probability distribution of $X$ is

$$ \begin{array}{|c|l|c|c|c|} \hline \boldsymbol{X} & 0 & 1 & 2 & 3 \\ \hline \boldsymbol{P}(\boldsymbol{X}) & 0.3 & k & 2 k & 2 k \\ \hline \end{array} $$

$$ \text { The value of } k \text { is } $$

0.7

0.3

0.14

KCET 2017

MCQ (Single Correct Answer)

-0

The degree of the differential equation $\left[1+\left(\frac{d y}{d x}\right)^2\right]^2=\frac{d^2 y}{d x^2}$ is