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An alternating voltage $V=140sin\left(50t\right)$ (in Volts) is applied to a resistor of resistance $10$$\Omega$. This voltage produces $\Delta$$H$ heat in the resistor in time interval $\Delta$$t$. To produce the same amount of heat in the same time interval, required DC current is approximately equal to

A ray is incident on a plane mirror at an angle of incidence i and the angle of deviation of reflected ray is D. Then choose the most appropriate plot of |D| versus |i|.

A small sphere of radius $r$ and mass $m$ oscillates back and forth on a smooth concave surface of radius $R$ as shown in figure. Find the time period of small oscillations.

An eye can distinguish between two points of an object if they are separated by more than 0.22 mm when the object is placed at 25 cm from the eye. The object is now seen by a compound microscope having a 20 D objective and 10 D eyepiece separated by a distance of 20 cm. The final image is formed at 25 cm from the eye. What is the minimum separation between two points of the object which can now be distinguished?

Suppose the distance between the atoms of a diatomic gas remains constant. Its specific heat at constant volume per mole is

Point charges $Q_1=5m-C$ (milli-coulomb) and $Q_2=6m-C$ (milli-coulomb) are at a separation of 100m from each other. What is the magnitude of force on any one of the charge?

The graph shows the extension $\left(\Delta f\right)$ of a wire of length $1\text{m}$, suspended from the top of a roof at one end, with a load $W$ connected to the other end. If the cross-sectional area of the wire is ${10}^{-6}{\text{m}}^2$, Young's modulus of the material of the wire is

A bead 'B' is threaded on a smooth circular wire frame of radius $r$. The radius at a certain position of the bead makes an angle $\theta$ with the vertical axis. The entire frame is rotated with an angular speed $\omega$ about the vertical axis. The distance of the bead from the vertical axis is $R$. If the bead is in equilibrium (with respect to the rotating frame), then identify the correct statements:

A man of mass $60\text{kg}$ is standing on a platform of mass $140\text{kg}$ kept on a smooth horizontal surface. The man starts moving on the platform with a velocity $2\text{m/s}$ relative to the platform. Find the recoil velocity of the platform.

The equation of projectile is y=ax-bx^2 then horizontal range is

Ratio of amplitude of two waves is $1:16$. The ratio of maximum to minimum intensity when the waves interfere is

What will be the modulus of rigidity for water, considering it to be ideal fluid ?

Find the total energy of the particle executing linear SHM and show graphically the variation of P.E and K.E with respect to position.

In $v-t$ graph shown in fig. the distance travelled by the body in $5$ seconds will be

Two wires of the young's modulii $Y$ and $2Y$ having lengths $2L,L$ and radii $2R,R$ respectively, are joined end to end as shown in the image. The elastic potential energy stored in the system in equilibrium, is


[Assume the wires are massless and $w$ is the weight hung at the bottom]

on turning a corner a car driver driving at 36 km per hour find the side on the road 55m ahead he immediately applies brakes so as to stop within 5 M of the child calculate the retardation produced and the time taken by the car to stop

An electron with a speed of 1.8 x 10⁶ m/s is moving in a circular orbit in a uniform magnetic field of 10^-4 Wb/m², the radius of the circular path of the electron is

Power dissipation is maximum

Mass of spacecraft varies with time as $m=5000e^{-t}\text{kg}$. Find the rate of fuel ejection after $5\text{s}$. (Take $e=2.718$)

A boy of $50$ kg mass is running with a velocity of $2$ $\frac{m}{s}$. He jumped into a stationary cart of $2$ kg while running. Find the velocity of the cart after the boy jumped into it. (in $\frac{m}{s}$)

Two sound waves move in the same diretion in the same medium. The pressure amplitudes of the waves are equal but the wavelength of the first wave is double the second. Let the average power transmitted across a cross saection by the first wave be $P_1$ and that by the second wave be $P_2$ . Then

Which of the following quantity remains constant during the uniform circular motion?

When momentum of a body increases by 200% its Kinetic energy increases by?

The notes of frequency equal to or an integral multiple of fundamental frequency are called

F-centres are

The work done in moving a charge of 1C between two points on an equipotential surface is

The pressure at the bottom of a tank of water is $3P$ where $P$ is the atmospheric pressure. If the water is drawn out till the level of water is lowered by one-fifth, the pressure at the bottom of the tank will now be:

A body moves in a circle of radius $1m$. Its speed is given by $v=2t^2$. FInd the net acceleration at $t=2$ seconds.

If we can throw a ball upto a maximum height $H$, the maximum horizontal distance to which we can throw it is

Two sound sources $S_1$ and $S_2$ emit pure sinusoidal waves in phase. If the speed of sound is $330\text{m/s}$, then for what frequencies does constructive interference occur at P?

Figure shows a combination of logic gates. To what single gate is this combination equivalent?

If the tension in the cable of 1000 kg elevator is

A string of length 20 cm and linear mass density $0.40gc{m}^{-1}$ is fixed at both ends and is kept under a tension of 16N. A wave pulse is produced at t = 0 near an end as shown in figure, which travels towards the otherend. When will the string have the shape shown in the figure again?

A cricket player catches a ball of mass 0.1 kg, moving with a speed of 10m $s^{-1}$ in 0.1s. Magnitude of the force exerted by him is (N)

An object of density $\rho =500{\text{kg/m}}^3$ is hanging from a thin steel wire. The fundamental frequency of transverse standing wave on the wire is $200\text{Hz}$. The set up is now immersed in water, so that one third of the object's volume is submerged. The new fundamental frequency (in $\text{Hz}$) is

If the momentum of an electron is increased by $\Delta p$, then the de-Broglie wavelength associated with it changes by 0.50%. The initial momentum of the electron will be

When the ratio of the minimum velocity to the maximum velocity is $\frac{1}{\sqrt{2}}$ in a projectile motion, the angle of projection of projectile is

An object $A$ is moving with $10m/s$ and $B$ is moving with $5m/s$ in the same direction as shown. Initially $A$ is $100m$ behind $B$ as shown. Find the time taken by $A$ to meet $B$

Velocity of a car as a function of time is given by $v\left(t\right)=(4t^3+e^t)$ in $\text{m/s}$. The displacement in $\left(m\right)$ of the car as a function of time $t$ is

A rail-road car is moving towards the right with acceleration $a$ and a dog of mass $m$ is chasing a man $\left(A\right)$ with an acceleration $\frac{a}{3}$ relative to the car and the man $\left(A\right)$ is accelerating towards left with an acceleration of magnitude $\frac{a}{3}$ with respect to the car as shown in the figure. If an observer $B$ on the ground is observing both the dog and man $\left(A\right)$, then the net force experienced by the dog as seen by observer $B$ is

If the length of second's pendulum is decreased by $2\%$, how many seconds it will loose per day ?

A SONAR system fixed in a submarine operates at a frequency 40.0 kHz. An enemy submarine moves towards the SONAR with a speed of 360 km/hr. What is the frequency of sound reflected by the submarine? Take the speed of sound in water to be 1450 m/s.