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If Rajesh moves along a circular path from point $A(0,0)$ as shown in the figure and reaches diametrically opposite point $B(10,0)$, what is his displacement vector? Given: radius of circle is $5\text{m}$.

Different stages of power transmission and distribution are given in the following chart:

Arrange the given terms in the above boxes in the correct order.

Power generator, Substation, Star connection, Power transformer, Distribution transformer, Household connection.

Which of the following is correctly matched?

A body starts rotating from rest under the influence of a variable torque $\tau =10{\cos }^2\theta$ where, $\tau$ is in $\text{J}$. Find the total work done by the torque to rotate the body from $0^{\circ }$ to ${180}^{\circ }$.

The x-t graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at $t=\frac{4}{3}s$ is

The dimension of $LC$, where $L$ is the inductance and $C$ is the capacitance, is -

The wheel of a car accelerated uniformly from rest, rotates through $1.5\text{rad}$ during the first $\text{second}$. The angle rotated during the next $\text{second}$ will be :

In the given figure, find the displacement of the block $A$ in the $x$-axis in the time interval of $3s$ (String is massless and inextensible)

1. -2

Two strings $1$ and $2$ make a junction of partly reflected and partly transmitted waves. The linear mass density of string $2$ is four times that of string $1$, and the boundary between the two strings is at $x=0$. The expression for the incident wave is $y_i=A_i\cos (k_{1}x-{\omega }_{1}t)$. Which of the following relations is correct, if average power carried by the incident wave, transmitted wave and reflected wave are $P_i,P_t\&P_r$ respectively? [Assume tension in string $1$ and $2$ to be the same]

For the figure given below, the total magnetic induction at point O (due to curved and straight portion) will be

Calculate energy of one mole of photons of radiation whose frequency as 5 $\times$ ${10}^{14}$Hz.

Two conductors having same width and length, thickness $d_1$ and $d_2$, thermal conductivity $K_1$ and $K_2$ are placed one above the another. Find the equivalent thermal conductivity parallel to the contact surface such that the temperature difference across both the faces of both the conductors are same.

If 2 moles of an ideal monoatomic gas at temperature $T_0$ is mixed with 4 moles of another ideal monoatomic gas at temperature $2T_0$ in a closed vessel, then the temperature of the mixture is

Find the maximum force $F$ to be applied for the system shown, so that the two blocks move together. Take $g=10{\text{m/s}}^2$.

Which of the following correctly represents the $FBD$ of mass $m$.

A man of mass $60\text{kg}$ is pulling a mass $M$ by an inextensible light rope passing through a smooth and massless pulley as shown. $\mu$ between the ground and the man is $0.5$. Find the maximum value of $M$ that can be pulled slowly by the man without slipping on the ground.

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights $h_{\text{sph}}$ and $h_{\text{cyl}}$ on the incline. The ratio $\frac{h_{\text{sph}}}{h_{\text{cyl}}}$ is given by

A metallic spherical solid ball of radius $r$ has capacitance ${}^{\prime }{C}^{\prime }$ , then metallic spherical hollow ball of radius $2r$ has capacitance equal to

Match the column - I with column - II, for an ideal gas going through following processes.

If a parallel plate capacitor of capacitance $50\text{pF}$ has a breakdown voltage of $200\text{V}$, when an electric field of $500\text{N/C}$ is applied. Calculate the area of the plates in this case which can store the required charges.

Between the plates of a parallel plate capacitor a dielectric plate is introduced just to fill the space between the plates. The capacitor is charged and later disconnected from the battery. The dielectric plate is slowly drawn out of the capacitor parallel to the plates. The plot of the potential difference across the plates and the length of the dielectric plate drawn out is

Why photoelectric effect is not explained in terms of wave theory of light?

Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity. In one such system, dimensions of different quantities are given in terms of a quantity X as follows: [position] = [$X^{\alpha }$] ; [speed] = [$X^{\beta }$] ; [acceleration] =[$X^p$] ; [linear momentum] = [$X^q$] ; [force] = [$X^r$]. Then ,

An object is lying at a distance of $2\text{m}$ from a spherical interface as shown in the figure. If the radius of the interface is $\frac{2}{3}\text{m}$ and refractive index of the medium is $\mu =1.4$, calculate the magnification of the image formed by the interface.

For a body on a horizontal surface, coefficients of static and kinetic frictions are $0.4$ and $0.2$, respectively. When the body is in uniform motion on the surface, a horizontal force equal in magnitude to limiting friction is applied on it. The acceleration produced is

A particle moves from position, ${\overrightarrow{r}}_1=3\hat{i}+2\hat{j}-6\hat{k}$ to position ${\overrightarrow{r}}_2=14\hat{i}+13\hat{j}-9\hat{k}$ under the action of force $(4\hat{i}+\hat{j}+3\hat{k})$ $\text{N}$. Calculate the work done.

A plate of area $2{\text{m}}^2$ is made to move horizontally with a speed of $2\text{m/s}$ by applying a horizontal tangential force over the free surface of a liquid having depth of $1\text{m}$. If the coefficient of viscosity of liquid is $0.01\text{Poise}$, find the tangential force needed to move the plate.

A siren producing a sound of frequency $750\text{Hz}$ moves away from an observer at rest towards a cliff at a speed of $30\text{m/s}$. The frequency of echo heard by the observer reflected from the cliff is
[speed of sound in air $=330\text{m/s})$

The potential energy of the system of two identically charged spherical shell as shown in the figure is equal to (Assume the charge distribution to be uniform on surface)

Two capacitors $\text{A}$ and $\text{B}$ with capacitances $15\mu \text{F}$ and $5\mu \text{F}$ are charged to potential difference of $5\text{V}$ and $9\text{V}$ respectively. Consider a wire connected to each cepacitor as shown (with free ends). An uncharged capacitor $5\mu \text{F}$ with lead wire falls on the free ends to complete the circuit. Find how much amount of heat produced in the circuit?