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Match the percentages with the fractions.

If instead of dropping, I threw a ball down at some velocity u,near the surface of the earth, the ratio of the distances covered in the 1st , 2nd and 3rd second (not after n seconds) will be ?

Two parallel metallic plates have surface charge densities ${\sigma }_1$ and ${\sigma }_2$ as shown in figure. Match the following.





Table-1
Table-2

An open cylindrical tube of cross-sectional area $A$ has two air tight frictionless pistons at its two ends. The pistons are tied with a straight piece of metallic wire. The tube contains a gas at atmospheric pressure $P_0$ and temperature $T_0$ in between the pistons. If temperature of the gas is doubled, then the tension in the wire is

(Assume that metallic wire is rigid)

The force which opposes an external force acting on a body while it is still at rest is called:

The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe $L$ metre long. The length of the open pipe will be

A body of mass 0.01 kg executes simple harmonic motion (SHM) about x = 0 under the influence of a force show below.

The time period of the SHM is approximately

1. 468.77

Equation of progressive wave is given by $y=0.2\cos \pi (0.04t+0.02x-\frac{\pi }{6})$. The distance is expressed in cm and time in second. What will be the minimum distance between two particles having the phase difference of $\frac{\pi }{2}$?

A particle of mass m and charge q is released from rest in a uniform electric field E. The kinetic energy attained by the particle after moving a distance x along the electric field is

A
cylinder of mass 10 kg and radius 15 cm is rolling perfectly on a
plane of inclination 30°.
The coefficient of static friction µ_s
= 0.25.

(a) How
much is the force of friction acting on the cylinder?

(b) What
is the work done against friction during rolling?

(c) If
the inclination θ
of
the plane is increased, at what value of θ does
the cylinder begin to skid, and not roll perfectly?

Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance $\left(\frac{R}{2}\right)$ from the earth's centre, where $R$ is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period:

A $4\text{kg}$ block is on a smooth horizontal table. The block is connected to a second block of mass $1\text{kg}$ by a massless flexible taught cord that passes over a frictionless pulley. The $1\text{kg}$ block is $1\text{m}$ above the floor. The two blocks are released from rest. With what speed (in $\text{m/s}$) does the $1\text{kg}$ block hit the ground?

The speed of a projectile at its maximum height is $\frac{\sqrt{3}}{2}$ times of its initial speed. If range of projectile is $p$ times the maximum height reached by it, then find the value of $p$.

A person stands on a spring balance at the equator. If the speed of earth's rotation increased by such an amount that the balance reading is half the true weight, what will be the length of the day in this case(approximately)?

Match $\text{List I}$ with the $\text{List II}$ and select the correct answer using the code given below the lists :



$\begin{array}{cccc}& \text{List I}& & \text{List II}\\ \text{(A)}& \text{Volume of parallelepiped determined by vectors}\overrightarrow{a},\overrightarrow{b}\text{and}\overrightarrow{c}\text{is}2.\text{Then the volume}& \text{(P)}& 100\\ & \text{of the parallelepiped determined by vectors}2(\overrightarrow{a}\times \overrightarrow{b}),3(\overrightarrow{b}\times \overrightarrow{c})\text{and}(\overrightarrow{c}\times \overrightarrow{a})\text{is}& & \\ \text{(B)}& \text{Volume of parallelepiped determined by vectors}\overrightarrow{a},\overrightarrow{b}\text{and}\overrightarrow{c}\text{is}5.\text{Then the volume}& \text{(Q)}& 30\\ & \text{of the parallelepiped determined by vectors}3(\overrightarrow{a}+\overrightarrow{b}),(\overrightarrow{b}+\overrightarrow{c})\text{and}2(\overrightarrow{c}+\overrightarrow{a})\text{is}& & \\ \text{(C)}& \text{Area of a triangle with adjacent sides determined by vectors}\overrightarrow{a},\overrightarrow{b}\text{is}20.\text{Then the}& \text{(R)}& 24\\ & \text{area of the triangle with adjacent sides determined by vectors}(2\overrightarrow{a}+3\overrightarrow{b})\text{and}(\overrightarrow{a}-\overrightarrow{b})\text{is}& & \\ \text{(D)}& \text{Area of a parallelogram with adjacent sides determined by vectors}\overrightarrow{a}\text{and}\overrightarrow{b}\text{is}30.& \text{(S)}& 60\\ & \text{Then the area of the parallelogram with adjacent sides determined by vectors}& & \\ & (\overrightarrow{a}+\overrightarrow{b})\text{and}\overrightarrow{a}\text{is}& & \end{array}$



Which of the following is the only CORRECT combination?

A soap film is formed on a frame of area $4\times {10}^{-3}{\text{m}}^2$. If the area of the film is reduced to half, what is the change in its potential energy?
(Surface tension $=40\times {10}^{-3}\text{N/m}$)

The internal resistance of a cell is to be determined using a potentiometer. In an experiment, an external resistance of $\text{R}$ $=$ $60\Omega$ is used across the given cell. When the key $K_1$ is closed and $K_2$ is open, the balance point is found at a length of $72$ $\text{cm}$. The balance length on the potentiometer is found at $60$ $\text{cm}$ when both the keys are closed. Calculate the internal resistance of the cell.

Which of the following step/event is required to increase the intracellular concentration of $C{O}_2$ ensuring minimal oxygenase activity in dry tropical plants?

If $97.52$ is divided by $2.54$, the correct result in terms of significant figures is

There is an electric field $E$ in the $\text{x-}$direction. If the work done by electric field in moving a charge of $0.2\text{C}$ through a distance of $2\text{m}$ along a line making an angle ${60}^{\circ }$ with the $\text{x-}$axis is $4\text{J}$, then what is the value of $E$ ?

A ball is thrown vertically upwards, and it rises to a height of $10\text{m}$. The velocity with which it was thrown upwards is -

The momentum $P$ and kinetic energy $E$ of a body of mass $m$ are related as:

Two inductances connected in parallel are equivalent to a single inductance of $1.5\text{H}$ and when connected in series are equivalent to a single inductance of $8\text{H}.$ The difference in their inductance is-

Two cars having masses $m_{1}and{m}_2$ move in circles of radii $r_{1}and{r}_2$ respectively. If they complete the circle in equal time, the ratio of their angular speeds $\frac{{\omega }_1}{{\omega }_2}$ is _______

A particle is moving in a circle of radius $R$ with constant speed. The time period of the particle is $T$. In a time $t=\frac{T}{6}$, the magnitude of average velocity of the particle is

Two long parallel wires situated at a distance $2a$ are carrying equal current ‘$i$’ in opposite direction as shown in figure. The value of magnetic field at a point $P$ situated at equal distance $\left(r\right)$ from both the wires is

An angular structure $\text{ABC}$ with side $AB=BC=L$ is made up of two thin rods $\text{AB}$ of mass $m$ and $\text{BC}$ of mass $2m$. The structure when hanged from point $A$ stays in equilibrium with side $BC$ horizontal. Find the value of angle $\theta$.

When an object travels the same distance in equal intervals of time, then it is moving with a/an ________speed.