KCET 2018

If $\left[\begin{array}{cc}1 & 1 \\ -1 & 1\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{l}2 \\ 4\end{array}\right]$, then the values of $x$ and $y$ respectively are

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

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

Everybody in a room shakes hands with everybody else. The total number of handshakes is 45 . The total number of persons in the room is

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

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 events, then the probability of neither $A$ nor $B$ is

In a simultaneous throw of a pair of dice, the probability of getting a total more than 7 is

A flashlight has 10 batteries out of which 4 are dead. If 3 batteries are selected without replacement and tested, then the probability that all 3 are dead is

A bag contains 17 tickets numbered from 1 to 17. A ticket is drawn at random, then another ticket is drawn without replacing the first one. The probability that both the tickets may show even numbers is

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 $x^{b-c} \cdot y^{c-a} \cdot z^{a-b}$ is

For the probability distribution given by        
$$ \begin{array}{|c|c|c|c|} \hline X=x_i & 0 & 1 & 2 \\ \hline P_i & \frac{25}{36} & \frac{5}{18} & \frac{1}{36} \\ \hline \end{array} $$
the standard deviation $(\sigma)$ is

The equation of the line parallel to the line $3 x-4 y+2=0$ and passing through $(-2,3)$ is

The image of the point $(1,6,3)$ in the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ is

The angle between the lines $2 x=3 y=-z$ and $6 x=-y=-4 z$ is

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

The locus represented by $x y+y z=0$ is

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 $(a \neq b \neq c \neq 1)$, then the value of $a b c-(a+b+c)$ is equal to

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

If $\vec{a}$ and $\vec{b}$ are mutually perpendicular unit vectors, then $(3 \vec{a}+2 \vec{b}) \cdot(5 \vec{a}-6 \vec{b})$ is equal to

If $\vec{a}=\hat{i}+\lambda \hat{j}+2 \hat{k} ; \vec{b}=\mu \hat{i}+\hat{j}-\hat{k}$ are orthogonal and $|\vec{a}|=|\vec{b}|$, then $(\lambda, \mu)$ is equal to

In the series $L-C-R$ circuit, the power dissipation is through

In Karnataka, the normal domestic power supply AC is $220 \mathrm{~V}, 50 \mathrm{~Hz}$. Here, 220 V and 50 Hz refer to

A 100 W bulb is connected to an AC source of $220 \mathrm{~V}, 50 \mathrm{~Hz}$. Then, the current flowing through the bulb is

Which of the following, represents the variation of inductive reactance $\left(X_L\right)$ with the frequency of voltage sources $(v)$ ?

The energy equivalent to a substance of mass 1 g is

The half-life of tritium is 12.5 years. What mass of tritium of initial mass 64 mg will remain undecayed after 50 years?

The total energy of an electron revolving in the second orbit of hydrogen atom is

The period of revolution of an electron in the ground state of hydrogen atom is $T$. The period of revolution of the electron in the first excited state is

Two capacitors of $3 \mu \mathrm{~F}$ and $6 \mu \mathrm{~F}$ are connected in series and a potential difference of 900 V is applied across the combination. They are then disconnected and reconnected in parallel. The potential difference ac...

For the arrangement of capacitors as shown in the circuit, the effective capacitance between the points $A$ and $B$ is (capacitance of each capacitor is $4 \mu \mathrm{~F}$ )

The radius of the Earth is 6400 km . If the height of an antenna is 500 m , then its range is

The effective resistance between $P$ and $Q$ for the following network is

If the last band on the carbon resistor is absent, then the tolerance is

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 resistances of the devices, then

Two cells of internal resistances $r_1$ and $r_2$ and of same emf are connected in series, across a resistor of resistance $R$. If the terminal potential difference across the cells of internal resistance $r_1$ is zero, then the value of $R...

The resistance $R=\frac{V}{I}$, where $V=(100 \pm 5) \mathrm{V}$ and $I=(10 \pm 0.2) \mathrm{A}$. The percentage error in $R$ is

Five identical resistors each of resistance $R=1500 \Omega$ are connected to a 300 V battery as shown in the circuit. The reading of the ideal ammeter $A$ is

Ohm's law is applicable to

A proton and an $\alpha$-particle are accelerated through the same potential difference $V$. The ratio of their de-Broglie wavelength is

The maximum kinetic energy of emitted photoelectrons depends on

The number of photons falling per second on a completely darkened plate to produce a force of $6.62 \times 10^{-5} \mathrm{~N}$ is $n$. If the wavelength of the light falling is $5 \times 10^{-7} \mathrm{~m}$, then $n=$ $\ldots \ldots \ldot...

Two wires $A$ and $B$ are stretched by the same load. If the area of cross-section of wire $A$ is double that of $B$, then the stress on $B$ is

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 $1: 25$. Then, the current in the primary is

The magnetic flux linked with a coil varies as $\phi=3 t^2+4 t+9$. The magnitude of the emf induced at $t=2 \mathrm{~s}$ is

The work done to move a charge on an equipotential surface is

The magnitude of point charge due to which the electric field 30 cm away has the magnitude $2 \mathrm{NC}^{-1}$ will be

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

The force of repulsion between two identical positive charges when kept with a separation $r$ in air is $F$. Half the gap between the two charges is filled by a dielectric slab of dielectric constant $=4$. Then, the new force of repulsion b...

The pressure at the bottom of a liquid tank is not proportional to the

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 the Earth, the same on the space station is $\qquad$ times $v_E$.