A ball is thrown vertically upwards with an initial velcoity \(u\) reaches maximum height in \(5 \mathrm{~s}\). The ratio of distance travelled by the ball in the 2 nd and 7 th second is (assume, \(g=10\) \(\mathrm{m} / \mathrm{s}^2\) )

A series LCR circuit is connected to an ac source of voltage \(150 \sin (80 \pi t)\) volt. If the resistance of the resistor in the circuit is \(25 \Omega\) and the impedance in the circuit is \(75 \Omega\), the average power dissipated per cycle in the circuit is

The dielectric constant of a medium is 8 and its relative permeability is 200. If an electromagnetic wave of frequency 100 MHz travels in this medium, then its wavelength is

The Brewster angle for air to glass transition of light is (Refractive index of glass \(=1.5\) ).

Two charges are \(+10 \mu C\) and \(-10 \mu C\) are separated by \(10 \mathrm{~cm}\). The magnitude of force acting on another charge \(5 \mu \mathrm{C}\) placed at the midpoint of the line joining the two charges will be [Use \(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\) in SI unit]

An electromagnetic wave is propagating in vacuum along $-\hat{\mathrm{j}}$ direction. The magnetic field of the wave is given by $\overrightarrow{B}=\left(2\times {10}^{-8}\right)\cos \left[\pi \times {10}^{15}\left(t+\frac{y}{c}\right)\right] \hat{\mathrm{k}} \mathrm{T}$. The electric field $\overrightarrow{E}$ of this wave is ($c=$ speed of light)

Match the following table. \begin{array}{|c|c|c|c|} \hline & List-I & & List-II \ \hline A. & \begin{array}{l}\text { Michelson-Morley } \ \text { experiment }\end{array} & I. & \begin{array}{l}\text { The existence of } \ \text { anti-matter }\end{array} \ \hline B. & \begin{array}{l}\text { Stern-Gerlach } \ \text { experiment }\end{array} & II. & \begin{array}{l}\text { The existence of } \ \text { de-Broglie matter waves }\end{array} \ \hline C. & \begin{array}{l}\text { Davisson-Germer } \ \text { experiment }\end{array} & III. & Electrons have spins \ \hline D. & \begin{array}{l}\text { Anderson discovery } \ \text { of positron }\end{array} & \mathrm{IV}. & \begin{array}{l}\text { The non-existence of } \ \text { ether }\end{array} \ \hline \end{array} \(\begin{array}{llll}A & B & C & D\end{array}\)

At what temperature is the root mean square (rms) speed of Neon gas atoms is equal to the rms speed of Helium gas atom at \(-33^{\circ} \mathrm{C}\) ? (atomic mass of \(\mathrm{Ne}=2.02 \mathrm{u}\), and that of \(\mathrm{He}=4.0 \mathrm{u}\) )

A current $I=5\mathrm{A}$flows along a thin wire shaped as shown in figure. The radius of curved part of the wire is equal to $R=100\mathrm{mm}$, the angle $2\varphi =90°$. The magnitude of magnetic field at the point $O$is approximately
$\left[\text{Use},\frac{{\mu }_0}{4\pi }={10}^{-7}\mathrm{T}\mathrm{m}{\mathrm{A}}^{-1}\right]$

The work done in blowing a soap bubble of diameter 3 cm is (Surface tension of soap solution \(=0.035 \mathrm{Nm}^{-1}\) )

A gas is suddenly compressed such that its absolute temperature is doubled. If the ratio of the specific heat capacities of the gas is 1.5, then the percentage decrease in the volume of the gas is

Which of the following statements are true in the context of a Compound Microscope? (A) Each lens produces a virtual and inverted image. (B) The objective has a very short focal length. (C) The eyepiece is used as a simple magnifying glass. (D) The objective and eyepiece are convex and concave lenses respectively.

A moving particle collides with a stationary particle of mass $\frac{1}{n}$ times the mass of moving particle, the fraction of its kinetic energy transferred to the stationary particle is