KCET 2018 | KCET Year Wise Previous Years Questions

Chemistry

Mathematics

1. $\int_0^1 \frac{d x}{e^x+e^{-x}}$ is equal to 2. $ \int_0^{1 / 2} \frac{d x}{\left(1+x^2\right) \sqrt{1-x^2}}$ is equal to 3. The area of the region bounded by the curve $y=\cos x$ between $x=0$ and $x=\pi$ is 4. The area bounded by the line $y=x, X$-axis and ordinates $x=-1$ and $x=2$ is 5. The degree and the order of the differential equation $\frac{d^2 y}{d x^2}=\sqrt[3]{1+\left(\frac{d y}{d x}\right)^2}$ r 6. The solution of the differential equation $x \frac{d y}{d x}-y=3$ represents a family of 7. The integrating factor of $\frac{d y}{d x}+y=\frac{1+y}{x}$ is 8. If $|\vec{a} \times \vec{b}|^2+|\vec{a} \cdot \vec{b}|^2=144$ and $|\vec{a}|=4$, then the value of $|\vec{b}|$ is 9. If $\vec{a}$ and $\vec{b}$ are mutually perpendicular unit vectors, then $(3 \vec{a}+2 \vec{b}) \cdot(5 \vec{a}-6 \vec{b 10. If the vector $a \hat{i}+\hat{j}+\hat{k} ; \hat{i}+b \hat{j}+\hat{k}$ and $\hat{i}+\hat{j}+c \hat{k}$ are coplanar $(a \ 11. If $\vec{a}=\hat{i}+\lambda \hat{j}+2 \hat{k} ; \vec{b}=\mu \hat{i}+\hat{j}-\hat{k}$ are orthogonal and $|\vec{a}|=|\vec 12. The image of the point $(1,6,3)$ in the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ is 13. The angle between the lines $2 x=3 y=-z$ and $6 x=-y=-4 z$ is 14. The value of $k$ such that the line $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-k}{2}$ lies on the plane $2 x-4 y+z=7$ is 15. The locus represented by $x y+y z=0$ is 16. The feasible region of an LPP is shown in the figure. If $z=3 x+9 y$, then the minimum value of $z$ occurs at 17. For the LPP, maximize $z=x+4 y$ subject to the constraints $x+2 y \leq 2, x+2 y \geq 8, x, y \geq 0$ 18. For the probability distribution given by $$ \begin{array}{|c|c|c|c|} \hline X=x_i & 0 & 1 & 2 \\ \hline P_i & \ 19. A bag contains 17 tickets numbered from 1 to 17. A ticket is drawn at random, then another ticket is drawn without repla 20. A flashlight has 10 batteries out of which 4 are dead. If 3 batteries are selected without replacement and tested, then 21. If $|x+5| \geq 10$, then 22. Everybody in a room shakes hands with everybody else. The total number of handshakes is 45 . The total number of persons 23. The constant term in the expansion of $\left(x^2-\frac{1}{x^2}\right)^{16}$ is 24. $P (n): 2^{2 n}-1$ is divisible by $k$ for all $n \in N^{\prime \prime}$ is true, then the value of ' $k$ ' is 25. The equation of the line parallel to the line $3 x-4 y+2=0$ and passing through $(-2,3)$ is 26. If $\left(\frac{1-i}{1+i}\right)^{96}=a+i b$, then $(a, b)$ is 27. The distance between the foci of a hyperbola is 16 and its eccentricity is $\sqrt{2}$. Its equation is 28. The number of ways in which 5 girls and 3 boys can be seated in a row so that no two boys are together is 29. If $a, b, c$ are three consecutive terms of an AP and $x, y, z$ are three consecutive terms of a GP, then the value of 30. The value of $\lim \limits_{x \rightarrow 0} \frac{[x]}{x}$ is : 31. Let $f(x)=x-\frac{1}{x}$, then $f(-1)$ is 32. The negation of the statement " 72 is divisible by 2 and $3^{\prime \prime}$ is 33. The probability of happening of an event $A$ is 0.5 and that of $B$ is 0.3 . If $A$ and $B$ are mutually exclusive event 34. In a simultaneous throw of a pair of dice, the probability of getting a total more than 7 is 35. If $A$ and $B$ are mutually exclusive events, given that $P(A)=\frac{3}{5}, P(B)=\frac{1}{5}$, then $P(A$ or $B)$ is 36. Let $f, g: R \rightarrow R$ be two functions defined as $f(x)=|x|+x$ and $g(x)=|x|-x \forall x \in R$. Then $(f \circ g) 37. A is a set having 6 distinct elements. The number of distinct functions from $A$ to $A$ which are not bijections is 38. If $\sin ^{-1} x+\cos ^{-1} y=\frac{2 \pi}{5}$, then $\cos ^{-1} x+\sin ^{-1} y$ is 39. The value of the expression $\tan \left(\frac{1}{2} \cos ^{-1} \frac{2}{\sqrt{5}}\right)$ is 40. If $A=\left[\begin{array}{cc}2 & -2 \\ -2 & 2\end{array}\right]$, then $A^n=2^k A$, where $k$ is equal to 41. If $\left[\begin{array}{cc}1 & 1 \\ -1 & 1\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{ 42. If $A=\left[\begin{array}{cc}\cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha\end{array}\right]$, then $A A^{\pri 43. If $x, y, z \in R$, then the value of determinant $\left|\begin{array}{lll}\left(5^x+5^{-x}\right)^2 & \left(5^x-5^{-x}\ 44. The value of determinant $\left|\begin{array}{lll}a-b & b+c & a \\ b-a & c+a & b \\ c-a & a+b & c\end{array}\right|$ is 45. If $\left(x_1, y_1\right),\left(x_2, y_2\right)$ and $\left(x_3, y_3\right)$ are the vertices of a triangle whose are is 46. Let $A$ be a square matrix of order $3 \times 3$, then $|5 A|$ is equal to 47. If $f(x)=\left\{\begin{array}{clc}\frac{\sqrt{1+k x}-\sqrt{1-k x}}{x} & \text { if }-1 \leq x is continuous at $x=0$, th 48. If $\cos y=x \cos (a+y)$ with $\cos a \neq \pm 1$, then $\frac{d y}{d x}$ is equal to 49. If $f(x)=|\cos x-\sin x|$, then $f^{\prime}\left(\frac{\pi}{6}\right)$ is equal to 50. $$ \text { If } y=\sqrt{x+\sqrt{x+\sqrt{x+\ldots \infty}}} \text {, then } \frac{d y}{d x} \text { is equal } $$ to 51. If $f(x)=\left\{\begin{array}{cl}\frac{\log _e x}{x-1} & ; x \neq 1 \\ k & ; x=1\end{array}\right.$ is continuous at $x 52. Approximate change in the volume $V$ of a cube of side $x$ metres caused by increasing the side by $3 \%$ is 53. The maximum value of $\left(\frac{1}{x}\right)^x$ is 54. $f(x)=x^x$ has stationary point at 55. The maximum area of a rectangle inscribed in the circle $(x+1)^2+(y-3)^2=64$ is 56. $\int \frac{1}{1+e^x} d x$ is equal to 57. $\int \frac{1}{\sqrt{3-6 x-9 x^2}} d x$ is equal to 58. $\int e^{\sin x} \cdot\left(\frac{\sin x+1}{\sec x}\right) d x$ is equal to 59. $\int_{-2}^2|x \cos \pi x| d x$ is equal to 60. Let $f: R \rightarrow R$ be defined by $f(x)=\left\{\begin{array}{lc}2 x ; & x > 3 \\ x^2 ; & 1 $$ f(-1)+f(2)+f(4) \tex

Physics

1. The energy equivalent to a substance of mass 1 g is 2. The half-life of tritium is 12.5 years. What mass of tritium of initial mass 64 mg will remain undecayed after 50 years? 3. In a CE amplifier, the input AC signal to be amplified is applied across 4. If $A=1$ and $B=0$, then in terms of Boolean algebra, $A+\bar{B}=$ 5. The density of electron-hole pair in a pure germanium is $3 \times 10^{16} \mathrm{~m}^{-3}$ at room temperature. On dop 6. The DC common emitter current gain of an $n-p-n$ transistor is 50 . The potential difference applied across the collecto 7. The radius of the Earth is 6400 km . If the height of an antenna is 500 m , then its range is 8. A space station is at a height equal to the radius of the Earth. If ' $v_E$ ' is the escape velocity on the surface of t 9. A particle shows distance-time curve as shown in the figure. The maximum instantaneous velocity of the particle is aroun 10. Which of the following graphs correctly represents the variation of $g$ on the Earth? 11. A cup of tea cools from $65.5^{\circ} \mathrm{C}$ to $62.5^{\circ} \mathrm{C}$ in 1 min in a room at $22.5^{\circ} \math 12. The dimensions of the ratio of magnetic flux $(\phi)$ and permeability $(\mu)$ are 13. A mass $m$ on the surface of the Earth is shifted to a target equal to the radius of the Earth. If $R$ is the radius and 14. First overtone frequency of a closed pipe of length $l_1$ is equal to the second harmonic frequency of an open pipe of l 15. The resistance $R=\frac{V}{I}$, where $V=(100 \pm 5) \mathrm{V}$ and $I=(10 \pm 0.2) \mathrm{A}$. The percentage error i 16. A block rests on a rough inclined plane making an angle of $30^{\circ}$ with the horizontal, The coefficient of static f 17. Two particles of masses $m_1$ and $m_2$ have equal kinetic energies. The ratio of their momentum is 18. The pressure at the bottom of a liquid tank is not proportional to the 19. A Carnot engine takes 300 calories of heat from a source at 500 K and rejects 150 calories of heat to the sink. The temp 20. Pressure of an ideal gas is increased by keeping temperature constant. The kinetic energy of molecules 21. A man weighing 60 kg is in a lift moving down with an acceleration of $1.8 \mathrm{~ms}^{-2}$. The force exerted by the 22. Moment of inertia of a body about two perpendicular axes $X$ and $Y$ in the plane of lamina are $20 \mathrm{~kg}-\mathrm 23. Two wires $A$ and $B$ are stretched by the same load. If the area of cross-section of wire $A$ is double that of $B$, th 24. The magnitude of point charge due to which the electric field 30 cm away has the magnitude $2 \mathrm{NC}^{-1}$ will be 25. A mass of 1 kg carrying a charge of 2 C is accelerated through a potential of 1 V . The velocity acquired by it is 26. The force of repulsion between two identical positive charges when kept with a separation $r$ in air is $F$. Half the ga 27. For the arrangement of capacitors as shown in the circuit, the effective capacitance between the points $A$ and $B$ is ( 28. The work done to move a charge on an equipotential surface is 29. Two capacitors of $3 \mu \mathrm{~F}$ and $6 \mu \mathrm{~F}$ are connected in series and a potential difference of 900 30. Ohm's law is applicable to 31. If the last band on the carbon resistor is absent, then the tolerance is 32. The effective resistance between $P$ and $Q$ for the following network is 33. Five identical resistors each of resistance $R=1500 \Omega$ are connected to a 300 V battery as shown in the circuit. Th 34. Two cells of internal resistances $r_1$ and $r_2$ and of same emf are connected in series, across a resistor of resistan 35. The $I-V$ graphs for two different electrical appliances $P$ and $Q$ are shown in the diagram: If $R_P$ and $R_Q$ be the 36. The correct Biot-Savart law in vector form is 37. An electron is moving in a circle of radius $r$ in a uniform magnetic field $B$. Suddenly, the field is reduced to $\fra 38. A charge $q$ is accelerated through a potential difference $V$. It is then passed normally through a uniform magnetic fi 39. A cyclotron's oscillator frequency is 10 MHz and the operating magnetic field is 0.66 T . If the radius of its dees is 6 40. Needles $N_1, N_2$ and $N_3$ are made of a ferromagnetic, a paramagnetic and adiamagnetic substance, respectively. A mag 41. The strength of the Earth's magnetic field is 42. A jet plane having a wing-span of 25 m is travelling horizontally towards East with a speed of $3600 \mathrm{~km} / \mat 43. Which of the following, represents the variation of inductive reactance $\left(X_L\right)$ with the frequency of voltage 44. The magnetic flux linked with a coil varies as $\phi=3 t^2+4 t+9$. The magnitude of the emf induced at $t=2 \mathrm{~s}$ 45. A 100 W bulb is connected to an AC source of $220 \mathrm{~V}, 50 \mathrm{~Hz}$. Then, the current flowing through the b 46. In the series $L-C-R$ circuit, the power dissipation is through 47. In Karnataka, the normal domestic power supply AC is $220 \mathrm{~V}, 50 \mathrm{~Hz}$. Here, 220 V and 50 Hz refer to 48. A step-up transformer operates on a 230 V "ne and a load current of 2 A . The ratio of primary and secondary windings is 49. The number of photons falling per second on a completely darkened plate to produce a force of $6.62 \times 10^{-5} \math 50. An object is placed at the principal focus of a convex mirror. The image will be at 51. An object is placed at a distance of 20 cm from the pole of a concave mirror of focal length 10 cm . The distance of the 52. A candle placed 25 cm from a lens forms an image on a screen placed 75 cm on the other side of the lens. The focal lengt 53. A plane wavefront of wavelength $\lambda$ is incident on a single slit of width $a$. The angular width of principal maxi 54. In a Fraunhofer diffraction at a single slit, if yellow light illuminating that slit is replaced by blue light, then dif 55. In Young's double slit experiment, two wavelengths $\lambda_1=780 \mathrm{~nm}$ and $\lambda_2=520 \mathrm{~nm}$ are use 56. In Young's double slit experiment, slits are separated by 2 mm and the screen is placed at a distance of 1.2 m from the 57. The maximum kinetic energy of emitted photoelectrons depends on 58. A proton and an $\alpha$-particle are accelerated through the same potential difference $V$. The ratio of their de-Brogl 59. The total energy of an electron revolving in the second orbit of hydrogen atom is 60. The period of revolution of an electron in the ground state of hydrogen atom is $T$. The period of revolution of the ele

KCET 2018

MCQ (Single Correct Answer)

-0

If $\left(x_1, y_1\right),\left(x_2, y_2\right)$ and $\left(x_3, y_3\right)$ are the vertices of a triangle whose are is ' $k$ ' square units, then $\left|\begin{array}{lll}x_1 & y_1 & 4 \\ x_2 & y_2 & 4 \\ x_3 & y_3 & 4\end{array}\right|^2$ is

$32 k^2$

$16 k^2$

$64 k^2$

$48 k^2$

KCET 2018

MCQ (Single Correct Answer)

-0

Let $A$ be a square matrix of order $3 \times 3$, then $|5 A|$ is equal to

$5|A|$

$125|\mathrm{~A}|$

$25|\mathrm{~A}|$

$15|\mathrm{~A}|$

KCET 2018

MCQ (Single Correct Answer)

-0

If $f(x)=\left\{\begin{array}{clc}\frac{\sqrt{1+k x}-\sqrt{1-k x}}{x} & \text { if }-1 \leq x<0 \\ \frac{2 x+1}{x-1} & \text { if } 0 \leq x \leq 1\end{array}\right.$

is continuous at $x=0$, then the value of $k$ is

$k=1$

$k=-1$

$k=0$

$k=2$

KCET 2018

MCQ (Single Correct Answer)

-0

If $\cos y=x \cos (a+y)$ with $\cos a \neq \pm 1$, then $\frac{d y}{d x}$ is equal to

$\frac{\sin a}{\cos ^2(a+y)}$

$\frac{\cos ^2(a+y)}{\sin a}$

$\frac{\cos a}{\sin ^2(a+y)}$