A person is swimming with a speed of \(10\, m /s\) s at an angle of \(120^{\circ}\) with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is \('x'\) \(m / s\). The value of \('x'\) to the nearest integer is ..............

Given below are two statements. Statement \(I\) : Electric potential is constant within and at the surface of each conductor. Statement \(II\) : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point. In the light of the above statements, choose the most appropriate answer from the options give below.

The position of a particle moving on \(x\)-axis is given by \(x(t)=A \sin t+B \cos ^2 t+C t^2+D\), where \(t\) is time. The dimension of \(\frac{A B C}{D}\) is

If the \(rms\) speed of oxygen molecules at \(0^{\circ} {C}\) is \(160\; {m} / {s}\), find the rms speed of hydrogen molecules at \(0^{\circ} {C}\). (In \({m}/{s}\))

An object of mass \(m\) is suspended at the end of a massless wire of length \(L\) and area of cross\(-\)section, \(A\). Young modulus of the material of the wire is \(Y\). If the mass is pulled down slightly its frequency of oscillation along the vertical direction is

For which of the following particles will it be most difficult to experimentally verify the deBroglie relationship?

The pressure \(P_{1}\) and density \(d_{1}\) of diatomic gas \(\left(\gamma=\frac{7}{5}\right)\) changes suddenly to \(P _{2}\left(> P _{1}\right)\) and \(d _{2}\) respectively during an adiabatic process. The temperature of the gas increases and becomes \(......\) times of its initial temperature.\(\left(\right.\) given \(\left.\frac{ d _{2}}{ d _{1}}=32\right)\)

A circular table is rotating with an angular velocity of \(\omega\) \(\mathrm{rad} / \mathrm{s}\) about its axis (see figure). There is a smooth groove along a radial direction on the table. A steel ball is gently placed at a distance of \(1 \mathrm{~m}\) on the groove. All the surface are smooth. If the radius of the table is \(3 \mathrm{~m}\), the radial velocity of the ball w.r.t. the table at the time ball leaves the table is \(x \sqrt{2} \omega\) \(\mathrm{m} / \mathrm{s}\), where the value of \(x\) is _______.

An electron revolving in \(\mathrm{n}^{\text {th }}\) Bohr orbit has magnetic moment \(\mu_n\). If \(\mu_n\) \(\alpha\) \(n^x\), the value of \(x\) is _______.

A projectile is launched at an angle ' \(\alpha\) ' with the horizontal with a velocity \(20 \; ms ^{-1}\). After \(10 s\), its inclination with horizontal is ' \(\beta\) '. The value of \(\tan \beta\) will be : \(\left( g =10 \; ms ^{-2}\right)\)

Given below are two statements: Statement-\(I\): Figure shows the variation of stopping potential with frequency \((v)\) for the two photosensitive materials \(M_1\) and \(M_2\). The slope gives value of \(\frac{h}{e}\), where \(h\) is Planck's constant, \(e\) is the charge of electron. Statement-\(II\): \(M_2\) will emit photoelectrons of greater kinetic energy for the incident radiation having same frequency. In the light of the above statements, choose the most appropriate answer from the options given below.

An inductor of reactance \(100 \Omega\), a capacitor of reactance \(50 \Omega\), and a resistor of resistance \(50 \Omega\) are connected in series with an AC source of 10 V , 50 Hz. Average power dissipated by the circuit is ________ W.

Four resistances of \(15\; \Omega, 12\; \Omega, 4 \;\Omega\) and \(10\; \Omega\) respectively in cyclic order to form Wheats tone's network. The resistance that is to be connected in parallel with the resistance of \(10\; \Omega\) to balance the network is .................. \(\Omega\)