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A cube of weight $20N$ rests on a rough inclined plane having angle of inclination ${37}^{\circ }$. The minimum force necessary to prevent the cube from sliding down the plane is $(\mu =0.5)$

Work function of metal $A$ is $4.2\text{eV}$. Find the threshold frequency of metal $B$, having work function equal to $80\%$ that of metal $A$.

As shown in the figure, the rod is moving with velocity, $2\text{m/s}$. What will the value of velocity $v$ after time $t$ ? (Given: $B=3\text{T}$, and length of rod $=1\text{m}$, mass of rod $=m)$.

A particle of specific charge $\alpha$ enters region with a uniform magnetic field $\overrightarrow{B}=-B_0\hat{k}$ with velocity $\overrightarrow{V}=V_0\hat{i}$ from origin. If the value of $\alpha$ is $\frac{\pi }{3},B_0=1\text{T}$ and $V_0=2\text{m/s}$, then the position vector of particle w.r.t origin at $t=1\text{sec}$ will be:

Find the maximum magnifying power of a compound microscope having a $25$ diopter lens as the objective, a $5$ diopter lens as the eyepiece and the separation $30\text{cm}$ between the two lenses. The least distance for clear vision is $25\text{cm}$.

The angle between the two vectors $\overrightarrow{A}=3\hat{i}+4\hat{j}+5\hat{k}$ and $\overrightarrow{B}=3\hat{i}+4\hat{j}-5\hat{k}$ will be

In a cricket match, Sachin hit a 1 kg ball thrown at him at 126 km/hr exactly in the opposite direction with the exact same speed. Find the impulse that his bat imparted on the ball in the short duration for which they were in contact.

Two springs $A$ and $B$ are stretched by applying forces of equal magnitudes. If the energy stored in $A$ is E, then the energy stored in B will be-

(Given relation between spring constants of $A$ and $B$ is $(k_A=2k_B)$)

The equivalent resistance between points $A$ and $B$ is

The radius of Krypton, the home planet of the famous D.C comic super-hero Superman, is 12 times the radius of earth. If the capacitance of earth is C, the capacitance of Krypton will be .

In the given circuit, the current through the Zener Diode is close to

$(V_Z=10\text{volts}\text{for the Zener diode})$

A block of mass $m$ slides along a floor while a force of magnitude $F$ is applied to it at an angle $\theta$ as shown in figure. The coefficient of kinetic friction is ${\mu }_K$. Then, the block's acceleration ${}^{\prime }{a}^{\prime }$ is given by: ($g$ is acceleration due to gravity)

A ball rolls down from the top of a staircase with horizontal velocity $36\text{m/s}$. If each step is $4\text{m}$ high and $3\text{m}$ wide, the ball just hits the edge of the $n^{th}$ step where $n=\frac{1152}{\alpha g}$ , then $\alpha$ is :

[$g$ is the acceleration due to gravity]

Two discs $A$ and $B$ having moment of inertia $I$ and $2I$ respectively, rotating initially with angular velocity $2\omega$ and $\omega$ are placed together coaxially on a vertical axle as shown in figure. Find the loss in kinetic energy of combination of discs, considering interaction between discs to be gentle.

A capacitor of capacitance $C$ is charged by connecting it to a battery of emf $E$. The capacitor is now disconnected and reconnected to the battery with the polarity reversed. The heat developed in the connecting wires is:

Four identical rods AB, CD, CF and DE are joined as shown in figure. The length, cross -sectional area and thermal conductivity of each rod are l, A and K respectively. The ends A, E and F are maintained at temperatures $T_1,T_2$ and $T_3$ respectively. Assuming no loss of heat to the atmosphere, find the temperature at B.

If the speed of the particle is $v=4t^3-6t^2+5\text{m/s}$, the distance of the particle as a function of time $t$ is

Rank in order, from highest to lowest, the liquid heights $h_a,h_b,h_c\&h_d$ . The air flow is from left to right. The liquid columns are not drawn to scale but pipe diameter is drawn to scale.

A particle of mass $1\text{mg}$ and having charge $1\mu \text{C}$ is moving in a magnetic field, $\overrightarrow{B}=(2\hat{i}+3\hat{j}+\hat{k})\text{T}$ with velocity $\overrightarrow{v}=(2\hat{i}+\hat{j}$$-\hat{k})$$\text{km/s}$. Find the magnitude of acceleration.

As shown in fig, a bob of mass ‘m’ is attached by one end of string of length 1 metre and makes an angle ${60}^{\circ }$ with vertical. When it is released it strikes perfectly elastically with block of mass ‘3m’ (which is rest on smooth horizontal table). The height of table is also 1 metre. The range obtained by ‘3m’ block from vertical side ‘CD’ of table will be…………….

Find the potential difference $V_a-V_b$ in the circuits shown if figure (32-E12).

Figure 32 - E12

The image of the line $20x=15(y-3)=12z$ in the plane $ax+by+cz=d$ is $\frac{100x}{3}+21=25y-54=20z-21$. The distance of the plane from the origin is $\frac{3\sqrt{2}}{20}$. If $a,b,c\&d$ are integer then the value of $a+b+c+d$ is

The P-V diagram here shows six curved paths (connected by vertical paths) that can be followed by a gas. Which two of the curved paths should be part of a closed cycle (those curved paths plus connecting vertical paths) if the net work done by the gas during the cycle is to be at its maximum positive value?

A large box is given velocity $u$ up the inclined plane and during its motion this box has acceleration $6m/s^2$ down the inclined plane. At the time of projection of box a particle is also projected from point $P$ with speed $10m/s$ making an angle $74°$ with horizontal as shown in fig. Value of $u$ so that particle hits the point $Q(PQ=10m)$



Diagram

A man observed the pressure amplitude in a sound wave from a wireless receiver as $4\times {10}^{-2}{\text{N/m}}^2$ and the intensity at a point as ${10}^{-6}{\text{W/m}}^2$. If by turning the volume knob, the pressure amplitude is increased to $5\times {10}^{-2}{\text{N/m}}^2$, evaluate the intensity.

A progressive wave of frequency $500\text{Hz}$ is travelling with a velocity $360{\text{ms}}^{-1}$. How far are two points, ${60}^{\circ }$ out of phase with each other ?

If $\overrightarrow{a}=3\hat{i}+4\hat{j}$ and $\overrightarrow{b}=7\hat{i}+24\hat{j}$, then find the vector having the same magnitude as $\overrightarrow{b}$ and same direction as $\overrightarrow{a}$.

In the given circuit, $R_1=10\Omega ,R_2=20\Omega ,$$C_1=1\mu \text{F},C_2=2\mu \text{F}$ and $E=6\text{V}$. Find the charge on each capacitor in the steady state.

The de broglie wavelength of neutrons in thermal equlibrium at temperature $T$ is