KCET 2024

The equation of parabola whose focus is $(6,0)$ and directrix is $x=-6$ is

A die is thrown 10 times. The probability that an odd number will come up at least once is

A random variable $X$ has the following probability distribution:

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If a random variable $X$ follows the binomial distribution with parameters $n=5, p$ and $P(X=2)=9 P(X=3)$, then $p$ is equal to

If $\triangle A B C$ is right angled at $C$, then the value of $\tan A+\tan B$ is

If $A M$ and GM of roots of a quadratic equation are 5 and 4 , respectively, then the quadratic equation is

If $S_n$ stands for sum to $n$-terms of a GP with $a$ as the first term and $r$ as the common ratio, then $S_n: S_{2 n}$ is

Two finite sets have $m$ and $n$ elements respectively. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of $m$ and $n$, respectively are

Let $A=\{2,3,4,5, \ldots, 16,17,18\}$. Let $R$ be the relation on the set $A$ of ordered pairs of positive integers defined by $(a, b) R(c, d)$ if and only if $a d=b c$ for all $(a, b),(c, d)$ in $A \times A$. Then, the number of ordered pa...

Let $a, b, c, d$ and $e$ be the observations with mean $m$ and standard deviation $S$. The standard deviation of the observations $a+k$, $b+k, c+k, d+k$ and $e+k$ is

The angle between the line $x+y=3$ and the line joining the points $(1,1)$ and $(-3,4)$ is

The sine of the angle between the straight line $\frac{x-2}{3}=\frac{y-3}{4}=\frac{4-z}{-5}$ are the plane $2 x-2 y+z=5$ is

The distance between the two planes $2 x+3 y+4 z=4$ and $4 x+6 y+8 z=12$ is

If lines $\frac{x-1}{-3}=\frac{y-2}{2 k}=\frac{z-3}{2}$ and $\frac{x-1}{3 k}=\frac{y-5}{1}=\frac{z-6}{-5}$ are mutually perpendicular, then $k$ is equal to

The equation $x y=0$ in three-dimensional space represents

The plane containing the point $(3,2,0)$ and the line $\frac{x-3}{1}=\frac{y-6}{5}=\frac{z-4}{4}$ is

The volume of the parallelopiped whose co terminous edges are $\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+\hat{\mathbf{j}}$ is

The vectors $\mathbf{A B}=3 \hat{\mathbf{i}}+4 \hat{\mathbf{k}}$ and $\mathbf{A C}=5 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$ are the sides of a $\triangle A B C$, The length of the median through $A$ is

Let $\mathbf{a}$ and $\mathbf{b}$ be two unit vectors and $\theta$ is the angle between them. Then, $\mathbf{a}+\mathbf{b}$ is a unit vector, if

If $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are three non-coplanar vectors and $p, q$ and $r$ are vectors defined by $\mathbf{p}=\frac{\mathbf{a} \times \mathbf{c}}{[\mathbf{a b c}]}, \mathbf{q}=\frac{\mathbf{c} \times \mathbf{a}}{[\mathbf...

Which of the following combinations should be selected for better tuning of an $L-C-R$ circuit used for communication?

The figure shows variation of $R, X_L$ and $X_C$ with frequency $f$ in a series $L-C-R$ circuit. Then, for what frequency point is the circuit capacitive?

In an $L-C-R$ series circuit, the value of only capacitance $C$ is varied. The resulting variation of resonance frequency $f_0$ as a function of $C$ can be represented as

Consider the nuclear fission reaction ${ }_0^1 n+{ }_{92}^{235} \mathrm{U} \longrightarrow{ }_{56}^{144} \mathrm{Ba}+{ }_{36}^{89} \mathrm{Kr}+3{ }_0^1 n$. Assuming all the kinetic energy is carried away by the fast neutrons only and total ...

The ratio of area of first excited state to ground state of orbit of hydrogen atom is

The ratio of volume of $\mathrm{Al}^{27}$ nucleus to its surface area is (Given, $R_0=1.2 \times 10^{-15} \mathrm{~m}$)

In alpha particle scattering experiment, if $v$ is the initial velocity of the particle, then the distance of closest approach is $d$. If the velocity is doubled, then the distance of closest approach becomes

The natural logarithm of the activity $R$ of a radioactive sample varies with time $t$ as shown. At $t=0$, there are $N_0$ undecayed nuclei. Then, $N_0$ is equal to [Take $e^2=7.5$ ]

A capacitor of capacitance $5 \mu \mathrm{~F}$ is charged by a battery of emf 10 V . At an instant of time, the potential difference across the capacitors is 4 V and the time rate of change of potential difference across the capacitor is $0...

An athlete runs along a circular track of diameter 80 m . The distance travelled and the magnitude of displacement of the athlete when he covers $3 / 4$ th of the circle is (in m )

E is the electric field inside a conductor whose material has conductivity $\sigma$ and resistivity $\rho$. The current density inside the conductor is $\mathbf{J}$. The correct form of Ohm's law is

An electric blub of $60 \mathrm{~W}, 120 \mathrm{~V}$ is to be connected to 220 V source. What resistance should be connected in series with the bulb, so that the bulb glows properly?

In the circuit shown, the end $A$ is at potential $V_0$ and end $B$ is grounded. The electric current $I$ indicated in the circuit is

The $I-V$ graph for a conductor at two different temperatures $100^{\circ} \mathrm{C}$ and $400^{\circ} \mathrm{C}$ is as shown in the figure. The temperature coefficient of resistance of the conductor is about (in per degree Celsius)

The electric current flowing through a given conductor varies with time as shown in the graph below. The number of free electrons which flow through a given cross-section of the conductor in the time interval $0 \leq t \leq 20 \mathrm{~s}$ ...

In an experiment to determine the temperature coefficient of resistance of a conductor, a coil of wire $X$ is immersed in a liquid. It is heated by an external agent. A meter bridge set up is used to determine resistance of the coil $X$ at ...

Light of energy $E$ falls normally on a metal of work function $\frac{E}{3}$. The kinetic energies $K$ of the photo electrons are

The photoelectric work function for photo metal is 2.4 eV . Among the four wavelengths, the wavelength of light for which photoemission does not take place is

A thick metal wire of density $\rho$ and length $L$ is hung from a rigid support. The increase in length of the wire due to its own weight is ( $Y=$ Young's modulus of the material of the wire)

An induced current of 2 A flows through a coil. The resistance of the coil is $10 \Omega$. What is the change in magnetic flux associated with the coil in 1 ms ?

A square loop of side length $a$ is moving away from an infinitely long current carrying conductor at a constant speed $v$ as shown. Let $x$ be the instantaneous distance between the long conductor and side $A B$. The mutual inductance $M$ ...

In the figure, a conducting ring of certain resistance is falling towards a current carrying straight long conductor. The ring and conductor are in the same plane. Then, the

Electromagnetic waves are incident normally on a perfectly reflecting surface having surface area $A$. If $I$ is the intensity of the incident electromagnetic radiation and $c$ is the speed of light in vacuum, the force exerted by the elect...

A body has a charge of $-3.2 \mu \mathrm{C}$. The number of excess electrons will be

A point charge $A$ of $+10 \mu \mathrm{C}$ and another point charge $B$ of $+20 \mu \mathrm{C}$ are kept 1 m apart in free space. The electrostatic force on $A$ due to $B$ is $F_1$ and the electrostatic force on $B$ due to $A$ is $\mathbf{F...

The total electric flux through a closed spherical surface of radius $r$ enclosing an electric dipole of dipole moment $2 a q$ is (Give $\varepsilon_0=$ permittivity of free space)

A uniform electric field $E=3 \times 10^5 \mathrm{NC}^{-1}$ is acting along the positive $Y$-axis. The electric flux through a rectangle of area $10 \mathrm{~cm} \times 30 \mathrm{~cm}$ whose plane is parallel to the ZX -plane is

Under electrostatic conditien of a charged conductor, which among the following statements is true?

A cube of side 1 cm contains 100 molecules each having an induced dipole moment of $0.2 \times 10^{-6} \mathrm{C}-\mathrm{m}$ in an external electric field of $4 \mathrm{NC}^{-1}$. The electric susceptibility of the materials is ..............

Water flows through a horizontal pipe of varying cross-section at a rate of $0.314 \mathrm{~m}^3 \mathrm{~s}^{-1}$. The velocity of water at a point where the radius of the pipe is 10 cm is