Two long parallel plates $A$ and $B$ are separated by a distance of $4 \mathrm{cm}$ with an electric field of $45.5{\mathrm{Vm}}^{-1}$ between the plates directed normally from plate $A$ to plate $B,$ as shown in the figure. An electron is projected from plate $A$ with velocity $v$ at an angle of $30°$ with the
surface of plate $A$. The maximum value of $v$ so that the electron does not hit plate $B$ is
$($Assume gravity free space, charge of electron $=1.6\times {10}^{-19}\mathrm{C}$ and mass of electron $\left.=9.1\times {10}^{-31} \mathrm{kg}\right)$

A circular coil has $100$ turns, radius $3 \mathrm{cm}$ and resistance $4\mathrm{\Omega }$. This coil is co-axial with a solenoid of $200$ turns/cm and diameter $4 \mathrm{cm}$. If the solenoid current is decreased from $2 \mathrm{A}$ to zero in $0.04 \mathrm{s}$, then the current induced in the coil is

\(5 \mathrm{~g}\) of steam at \(100^{\circ} \mathrm{C}\) is mixed with \(5 \mathrm{~g}\) of ice at \(0^{\circ} \mathrm{C}\). What is the final temperature of the mixture?

Two polaroids are placed in the path of unpolarised light beam of intensity \(I_0\) such that no light is emitted from the second polaroid. If a third polaroid whose polarisation axis makes an angle \(\theta\) with that of the first polaroid is placed between the polaroids, then intensity of light emerging from the last polaroid is

In an amplitude modulation with modulation index 0.5, the ratio of the amplitude of the carrier wave to that of the side band in the modulated wave is

A body whose momentum is constant must have constant

Four resistors \(A, B, C\) and \(D\) form a Wheatstones bridge. The bridge is balanced, when \(C=100 \Omega\). If \(A\) and \(B\) are interchanged, the bridge balances for \(C=121 \Omega\). The value of \(D\) is

90. If the dipole moment of a short bar magnet is \(1.25 \mathrm{~A}-\mathrm{m}^2\), find the magnetic field on its axis at a distance of \(0.5 \mathrm{~m}\) from the centre of the magnet.

For any value of \(\theta\), if the straight lines \(x \sin \theta+(1-\cos \theta) y=a \sin \theta\) and \(x \sin \theta-(1+\cos \theta) y+a \sin \theta=0\) intersect at \(P(\theta)\), then the locus of \(P(\theta)\) is a

Which of the following reactions are not feasible?
I. \(\mathrm{CH}_3 \mathrm{CH}=\mathrm{CH}_2 \frac{\mathrm{HCl}}{\left(\mathrm{C}_6 \mathrm{H}_5 \mathrm{CO}\right)_2 \mathrm{O}_2} \longrightarrow \mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{Cl}\)
II. \(\mathrm{C}_6 \mathrm{H}_6+\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{Cl} \stackrel{\mathrm{AlCl}_3}{\longrightarrow} \mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}\left(\mathrm{CH}_3\right)_2\)
III. \(\mathrm{CH}_3 \mathrm{CHClCH}_2 \mathrm{Cl} \underset{\Delta}{\stackrel{\mathrm{KOH}}{\longrightarrow}} \mathrm{CH}_3 \mathrm{C} \equiv \stackrel{+}{\mathrm{CH}}\)
IV. \(\mathrm{CH}_3 \mathrm{CH}=\mathrm{CHCH}_3 \stackrel{\mathrm{KMnO}_4 / \mathrm{H}^{+}}{\longrightarrow} \mathrm{CH}_3 \mathrm{COOH}\)

If \((3,-1)\) is one end of a diameter of the circle \(x^2+y^2-2 x+4 y=0\), then the equation of the tangent at the other end of that diameter is

The bond order of dioxygen is ' \(m\) '. The bond order values of \(\mathrm{N}_2^{+}\)and \(\mathrm{C}_2^{2-}\) are respectively

The angle between the axes of a polariser and an analyser is \(45^{\circ}\). If the intensity of the unpolarized light incident on the polariser is 1 , then the intensity of the light emerged from the analyser is