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Given both vector A & B have the same magnitude of 1 unit. Find $\overrightarrow{c}$ such that $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=0$?

1. 282

If the effective capacity between $x$ and $y$ is $c$ in the given circuit, the capacity of the condenser $\text{P}$ is

A magnetic field $(4\times {10}^{-3}\hat{k})\text{T}$ exerts a force $(4\hat{i}+3\hat{j})\times {10}^{-10}\text{N}$ on a particle having a charge ${10}^{-9}\text{C}$ and going in the $x-y$ plane. The velocity $\left(\text{in m/s}\right)$ of the particle is

A block of mass $m$ rests on a rough horizontal surface with a rope tied to it. The co-efficient of friction between the surface and the block is $\mu$. A monkey of the same mass climbs at the free end of the rope. The maximum acceleration with which the monkey can climb without moving the block is

In an atom, two electrons move around the nucleus in circular orbits of radii $R$ and $4R$. The ratio of the time taken by them to complete one revolution is :

(neglect electric interaction)

The magnetic field in a region is given by $B=2r$, where $r$ is the perpendicular distance from the $\text{x-axis}$. The direction of the magnetic field is along the positive $\text{z -axis}$. A conducting rod of length $1\text{m}$ lies parallel to the $\text{y-axis}$ as shown in the figure. If the rod moves with the velocity $v=8\text{m/s}$ along the positive x-axis, find the emf induced between the ends of the rod.

Find the value of wave number $\left(\overline{\nu }\right)$ in terms of Rydberg's constant $\left(R\right)$, when transition of electron takes place between two levels of $H{e}^{+}$ ion whose sum is $4$ and difference is $2$.

A steel wire of mass $8\text{g}$ and length $160\text{cm}$ is fixed at two ends. The tension in the wire is $50\text{N}$. Find the frequency and wavelength of the fourth harmonic.

Two capacitors are first connected in parallel and then in series. If the equivalent capacitance in the two cases are $16\text{F}$ and $3\text{F}$ respectively, then capacitance of each capacitor is

Find the angle between the lines $\overrightarrow{r}=3\hat{i}-2\hat{j}+6\hat{k}+\lambda (2\hat{i}+\hat{j}+2\hat{k})and\overrightarrow{r}=(2\hat{j}-5\hat{k})+\mu (6\hat{i}+3\hat{j}+2\hat{k}).$

A narrow monochromatic beam of light of intensity I is incident on a glass plate. Another identical glass plate is kept parallel to it. Each glass plate reflects 25% of the light incident on it and transmits the remaining. Then the ratio of the maximum to minimum intensities in the interference pattern formed by the two beams obtained after one reflection at each plate is approximately.

A straight rope of length ‘L’ is kept on a frictionless horizontal surface and a force ‘F’ is applied to one end of the rope in the direction of its length and away from that end. The tension in the rope at a distance ${}^{\prime }{l}^{\prime }$ from that end is

The truth table for the given circuit is

Two Radioactive substances X and Y emit particles respectively. Their disintegration constants are in the ratio 2 : 3. To have equal rate of disintegration of getting emission of particles., the ratio of number of atoms of X to that of Y at any time instant is

The figure below shows the snapshot of two waves $A$ and $B$ at a time instant $t$. The equation for $A$ is,

$y=A\sin (kx-\omega t-\varphi )$

and for $B$ is,

$y=A\sin (kx-\omega t)$.

It is clearly shown in the figure that wave $A$ is ahead of $B$ by a distance $\frac{\varphi }{k}$.



The motion of a single point in time, i.e. $y$ versus $t$ for two waves is best represented by,

Which of the following nuclei shown in the graph is light and stable?

1. 14.86

The acceleration due to gravity on the moon is only one sixth that of earth. If the earth and moon are assumed to have the same density, the ratio of radii of moon and earth will be

The correct order of dipole moment among the following:

Two coherent sources of light of wavelength $\lambda$ in the same phase are placed parallel to each other at a small separation of $2\lambda$. The path difference at point $\text{P}$ is

An external pressure $P$ is applied on a cube at $0^{o}C$ so that it is equally compressed from all sides. $K$ is the bulk modulus of the material of the cube and $\alpha$ is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by

The forward path transfer function of a unity negative feedback system is given by $G\left(s\right)=\frac{K}{(s+2)(s-1)}$

The value of $K$ which will place both the poles of the closed-loop system at the same location is

1. 2.25

A vernier callipers has 25 divisions on its vernier scale for every 35 divisions on its main scale. If 1 cm on the main scale is split into 12 units, the least count of the callipers will be