A helicopter reises from rest on the ground vertically upwards with a constant acceleration \(g.\) A food packet is dropped from the helicopter when it is a height \(h\). The time taken by the packet to reach the ground is close to \([ g\) is the acceleration due to gravity]

The root mean square speed of smoke particles of mass \(5 \times 10^{-17}\,kg\) in their Brownian motion in air at NTP is approximately \(.......\,mm\,s ^{-1}\) [Given \(k =1.38 \times 10^{-23}\,J\,K ^{-1}\) ]

Consider a modified Bernoulli equation.
\(\left( P +\frac{ A }{ Bt ^2}\right)+\rho g ( h + Bt )+\frac{1}{2} \rho V^2=\) constant
If \(t\) has the dimension of time then the dimensions of A and B are _________ , _________ respectively.

The rain drop of mass \(1\) g, starts with zero velocity from a height of \(1\) km. It hits the ground with a speed of \(5\) m/s. The work done by the unknown resistive force is _______ J. (take \(g = 10\) m/s\(^2\))

In a photoelectric experiment, increasing the intensity of incident light :

A tightly wound long solenoid carries a current of 1.5 A . An electron is executing uniform circular motion inside the solenoid with a time period of 75 ns . The number of turns per metre in the solenoid is ________.
[Take mass of electron \(\mathrm{m}_{\mathrm{e}}=9 \times 10^{-31} \mathrm{~kg}\), charge of electron \(\left|\mathrm{q}_{\mathrm{e}}\right|=1.6 \times 10^{-19} \mathrm{C}\),
\(\left.\mu_0=4 \pi \times 10^{-7} \frac{\mathrm{~N}}{\mathrm{~A}^2}, 1 \mathrm{~ns}=10^{-9} \mathrm{~s}\right]\)

Light enters from air into a given medium at an angle of \(45^{\circ}\) with interface of the air-medium surface. After refraction, the light ray is deviated through an angle of \(15^{\circ}\) from its original direction. The refractive index of the medium is.

The magnetic field inside a 200 turns solenoid of radius 10 cm is \(2.9 \times 10^{-4} \mathrm{Tesla}\). If the solenoid carries a current of 0.29 A , then the length of the solenoid is ________ \(\pi \mathrm{cm}\).

An electron is made to enter symmetrically between two parallel and equally but oppositely charged metal plates, each of 10 cm length. The electron emerges out of the electric field region with a horizontal component of velocity \(10^6 \mathrm{~m} / \mathrm{s}\). If the magnitude of the electric field between the plates is \(9.1 \mathrm{~V} / \mathrm{cm}\), then the vertical component of velocity of electron is (mass of electron \(=9.1 \times 10^{-31} \mathrm{~kg}\) and charge of electron \(=1.6 \times 10^{-19} \mathrm{C}\) )

Projectiles \(A\) and \(B\) are thrown at angles of \(45^{\circ}\) and \(60^{\circ}\) with vertical respectively from top of a \(400 \mathrm{~m}\) high tower. If their ranges and times of flight are same, the ratio of their speeds of projection \(v_A: v_B\) is _______.

The torque of a force \(5 \hat{i}+3 \hat{j}-7 \hat{k}\) about the origin is \(\tau\). If the force acts on a particle whose position vector is \(2 \hat{i}+2 \hat{j}+\hat{k}\), then the value of \(\tau\) will be.

A flask contains Hydrogen and Argon in the ratio \(2: 1\) by mass. The temperature of the mixture is \(30^{\circ} C\). The ratio of average kinetic energy per molecule of the two gases ( \(K\) argon/ \(K\) hydrogen) is: (Given: Atomic Weight of \(Ar = 39.9\))

A swimmer wants to cross a river from point \(A\) to point \(B\). Line \(A B\) makes an angle of \(30^{\circ}\) with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle \(\theta\) with the line \({AB}\) should be \(^{\circ}\), so that the swimmer reaches point \({B}\).