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A person has a near point at $80\text{cm}$. Find the power of the lens he should use while reading at $25\text{cm}$.

1. 500

The de-Broglie wavelength of proton travelling at velocity $v$ is same as the wavelength of an alpha particle. What is the velocity of the alpha particle ?

1 kg ice at $-{10}^{\circ }C$ is mixed with 1 kg of water at ${50}^{\circ }C$. When the mixture attains equilibrium, find the mass of ice in final mixture.
$[L_f=80kcal/kg;Sice=\frac{1}{2}kcal/k{g}^{\circ }C;S_{water}=1kcal/k{g}^{\circ }C]$

The density of water at the surface of the ocean is $\rho$. If the bulk modulus of water is $B$, what is the density of ocean water at a depth where the pressure is $n{P}_0$ [$P_0$ is the atmospheric pressure]?

The P-V diagram for a cyclic process is a triangle ABC drawn in order. The co-ordinates of A, B and C are $(4,1),(2,4),$ and $(2,1)$ respectively. Calculate the work done in the complete cycle.

In common emitter amplifier, the current gain is $62$. The collector resistance and input resistance are $5\text{k}\Omega$ and $500\Omega$ respectively. If the input voltage is $0.01\text{V}$, the output voltage will be

In circular motion, suppose $\overrightarrow{a}$ is the acceleration of particle,

$\overrightarrow{v}$ its linear velocity and $\overrightarrow{\omega }$ its angular velocity.

$$\begin{array}{cc}& \\ \text{Column-I}& \text{Column-II}\\ \text{(a)}|\overrightarrow{a}\times \overrightarrow{v}|& \text{(p) positive}\\ \text{(b)}\overrightarrow{a}.\overrightarrow{v}& \text{(q) Negative}\\ \text{(c)}\overrightarrow{\omega }.\overrightarrow{v}& \text{(r) zero}\\ \text{(d)}|\overrightarrow{\omega }\times \overrightarrow{a}|& \text{(s) Undefined}\end{array}$$

Air is streaming past a horizontal air plane wing such that its speed is 120m/s over the upper surface and 90 m/s at the lower surface. If the density of air is 1.3 kg per $metr{e}^3$ and the wing is 10 m long and has an average width of 2 m, then the difference of the pressure on the two sides of the wing is

A luminous object is placed at a distance of $30\text{cm}$ from the convex lens of focal length $20\text{cm}$. At what distance from the lens, a convex mirror of radius of curvature $10\text{cm}$ should be placed in order to have an upright image of the object coincident with it ?

Power supplied to a particle of mass $2\text{kg}$ varies with time as $P=\frac{3t^2}{2}$ watt. Here $t$ is in second. If velocity of particle at $t=0$ is $v=0$. The velocity of particle at time $t=2$ s will be

An object is places at a distance 40 cm from a thin converging lens of focal length; 10cm. Calculate the image distance.

Let a force $\overrightarrow{F}$ be acting on a body free to rotate about a point $O$ and let $\overrightarrow{r}$ be the position vector of any point $P$ on the line of action of the force. Then torque $\overrightarrow{\tau }$ of this force about point $O$ is defined as :
$\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}$
Given, $\overrightarrow{F}=(2\hat{i}+3\hat{j}-\hat{k})N$ and $\overrightarrow{r}=(\hat{i}-\hat{j}+6\hat{k})m$. Find the torque of this force.

A soil sphere of mass $M$ and radius $R$ is divided into two unequal parts. The first part has a mass of $\frac{7M}{8}$ and is converted into a uniform disc of radius $2R.$ The second part is converted into a uniform solid sphere. Let $I_1$ be the moment of inertia of disc about its axis and $I_2$ is moment of inertia of new sphere about its axis. The ratio $\frac{I_1}{I_2}$ is given by

In the derivation of electric field due to an electric dipole on an equatorial line, why do we put cos $\theta =\frac{a}{\sqrt{2}+r^2}$

Consider a circular coil of wire carrying current $I$, forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by ${\varphi }_i$. The magnetic flux through the area of the circular coil area is given by ${\varphi }_0$. Which of the following option is correct?

Starting from rest, a body slides down a ${45}^{\circ }$ inclined plane in twice the time it takes to slide down the same distance in the absence of friction. The coefficient of kinetic friction between the body and the inclined plane is

In the following hexagons, made up of two different material P and Q, current enters and leaves from points X and Y respectively. In which of the following case the magnetic field at its centre is not zero?

For sound waves in air with frequency 1000 Hz, a displacement amplitude of $1.2\times {10}^{-8}$ m produces a pressure amplitude of $3.0\times {10}^{-2}$ Pa. What is the wavelength of these waves? (Provided Bulk modulus of Air = $1.42\times {10}^{5}Pa$)

The coefficient of static friction is $0.2$ between block $A$ of mass $2\text{kg}$ and the table as shown in the figure. What would be the maximum mass value of block $B$ so that the two blocks do not move? The string and the pulley are assumed to be smooth and massless $(g=10{\text{m/s}}^2)$

If the terminal speed of a sphere of gold (density $=19.5{\text{kg/m}}^3$) is $0.2\text{m/s}$ in a viscous liquid (density $=1.5{\text{kg/m}}^3$), find the terminal speed of a sphere of silver (density $=10.5{\text{kg/m}}^3$) of the same size in the same liquid

Under the condition of dim light, the pupils __________.

In locomotives, the secondary force is equal to the centrifugal force produced by an equivalent crank running at twice the speed and having an equivalent radius

A storage battery is connected to a charger for charging with a voltage of $12.5\text{V}.$ The internal resistance of the storage battery is $1\Omega .$ When the charging current is $0.5A,$ the emf of the storage battery is

If $\frac{\sin \theta }{x}=\frac{\cos \theta }{y}$, then $\sin \theta -\cos \theta$ is