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

Three point charges of $+2 q,+2 q$ and $-4 q$ are placed at the corners $A, B$ and $C$ of an equilateral triangle $A B C$ of side $x$. The magnitude of the electric dipole moment of this system is

$2 q x$

$3 \sqrt{2} q x$

$3 q x$

$2 \sqrt{3} q x$

KCET 2017

MCQ (Single Correct Answer)

-0

In a system of two crossed polarisers, it is found that the intensity of light from the second polariser is half from that of first polariser. The angle between their pass axes is

$60^{\circ}$

$30^{\circ}$

$0^{\circ}$

$45^{\circ}$

KCET 2017

MCQ (Single Correct Answer)

-0

A piece of copper is to be shaped into a conducting wire of maximum resistance. The suitable length and diameter are ......................and............................respectively.

$2 L$ and $d / 2$

$L / 2$ and $2 d$

Landd

$2 L$ and $d$

KCET 2017

MCQ (Single Correct Answer)

-0

During scattering of light, the amount of scattering in inversely proportional to................ of wavelength of light.

square

fourth power

half

cube