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An object of mass $4kg$ is sliding with a constant velocity of $8m/s$ on a frictionless horizontal table. The force required to keep the object moving with same velocity is

A particle is performing S.H.M. Its total energy is $E$. When the displacement of the particle is half of its amplitude, its K.E will be

A point on the rim of a disc starts circular motion from rest and after time $t$, it gains an angular acceleration given by $\alpha =3t-t^2$. The angular velocity after $2\text{sec}$ is:

Only one product D is produced in the country. Its output during the year 2014 and 2015 was 200 and 220 units respectively. The market price of the product during the year was Rs 100 and Rs 110 per unit respectively. Calculate the percentage change in real GDP and nominal GDP in year 2015 using 2014 as the base year.

The relationship between kinematic viscosity $\left(v\right)$ and dynamic viscosity $\left(\mu \right)$ is

If ${\epsilon }_0\text{and}{\mu }_0$ represent the permittivity and permeability of vacuum and $\epsilon \text{and}\mu$ represent the permittivity and permeability of medium, the refractive index of the medium is given by

If the unit of force and length each be increased by four times, then the unit of energy is increased by

A block of mass m moves with a speed v towards the right block in equilibrium with a spring. If the surface is frictionless and collistions are elastic, the frequency of collisions between the masses will be :

Find the thickness fo a plate which will produce a change in optical path equal to half th ewavelength $\lambda$ of the light passing through it normally. The refractive
index of the plate is $\mu$

Observe the graph given below.

The equation of the line representing the relationship between Time spent and Payment is represented by ______.

In an AC generator, a coil with $N$ turns, all of them has same area $A$ and total resistance $R$, rotates with an angular frequency $\omega$ in a magnetic field $B$. The peak value of current in the coil is-

Two capacitors $C_1$ and $C_2$ are charged to $120\text{V}$ and $200\text{V}$ respectively. It is found that by connecting them together, the potential difference on each one can be made zero. Then:

A block of mass ‘m’ is kept over a fixed smooth wedge. Block is attached to a sphere of same mass through fixed massless pullies $P_1$ and $P_2$. Sphere is dipped inside the water as shown. If specific gravity of sphere is 2, find the acceleration of sphere.

During a tennis match, a player serves at $23.6{\text{ms}}^{-1}$, the ball leaving the racquet horizontally $2.37\text{m}$ above the court surface. By how much does the ball clear the net which is $12\text{m}$ away and $0.9\text{m}$ high?
(Take $g=10m/s^2$)

When stopping potential is applied in an experiment on photoelectric effect, no photocurrent is observed. This means that

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Let $\overrightarrow{p}$ and $\overrightarrow{q}$ be the position vectors of points $P$ and $Q$ respectively with respect to origin $\left(O\right)$ and $|\overrightarrow{p}|=p,|\overrightarrow{q}|=q.$ If $R,S$ divide $PQ$ internally and externally in the ratio $2:3$ respectively. If $\overrightarrow{OR}$ and $\overrightarrow{OS}$ are perpendicular, then

A block of mass $10\text{kg}$ is kept on a rough inclined plane as shown in the figure. A force of $3\text{N}$ is applied on the block. The coefficient of static friction between the plane and the block is $0.6$. What should be the minimum value of force $P$, such that the block does not move downward? $\text{(take}g=10{\text{ms}}^{-2})$

In a hollow spherical shell, potential (V) changes with respect to distance (r) from centre as

A boat moves perpendicular to the bank of a stream with a velocity of $7.2\text{km/h}$. The current carries it $150\text{m}$ downstream, the time required to cross the river is

(The width of the river is $0.5\text{km}$)

A particle performs simple harmonic motion with amplitude A and time period T. The mean velocity of the particle over the time internal during which it travels a distance of A/2 starting from extreme position is

The value of $\frac{d}{dx}\underset{1}{\overset{x^4}{\int }}\sec tdt$ is

Ratio of the longest wavelength corresponding to Lyman and Balmer series, in the hydrogen spectrum, is-

Ratio of moment of inertia, $I_1:I_2$ of a uniform square plate about shown axes is

when a magnet needle is placed in a non uniform magnetic field it experiences_____________.

A parallel plate condenser has a capacitance 50μF in air and 110μF when immersed in an oil. The dielectric constant of the oil is?

A body of mass $18\text{kg}$ initially at rest explodes into three fragments with masses in the ratio of $2:1:3$. If smaller fragments fly in mutually perpendicular directions and their velocities are $10\text{m/s}$ and $5\text{m/s}$ respectively, then what is the speed of the heaviest fragment?

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of $\frac{C_p}{C_v}$ for the gas is:

A point charge of +12$\text{μC}$ is at a distance $6\text{cm}$ vertically above the centre of a square of side $12\text{cm}$ as shown in figure. The magnitude of the electric flux through the square will be $\times {10}^3{\text{Nm}}^2/\text{C}$

Three rods made of the same material and having the same cross-section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at $0^{\circ }C$ and ${90}^{\circ }C$ respectively. The temperature of junction of the three rods will be

A point source of light B is placed at a distance 'L' in front of the center of a mirror of width 'd' hung vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror at a distance '2L' from it as shown in the figure. The greatest distance over which he can see the image of the light source in the mirror is

Two masses $m_1=1\text{kg}$ and $m_2=0.5\text{kg}$ are suspended together by a massless spring of spring constant $12.5\text{N/m}$. When masses are in equilibrium, $m_1$ is removed without disturbing the system. New amplitude of oscillation will be

A simple pendulum has a time period of 3.0 s. If the point of suspension of the pendulum starts moving vertically upward with a velocity v = kt where $k=4.4m{s}^{-2}$, the new time period will be (Take g = 10 $m{s}^{-2}$