The equivalent resistance between \(A\) and \(B\) is \(......\)

Surface tension of two liquids (having same densities), \(T_1\) and \(T_2\), are measured using capillary rise method utilizing two tubes with inner radii of \(r_1\) and \(r_2\) where \(r_1>r_2\). The measured liquid heights in these tubes are \(h_1\) and \(h_2\) respectively. [Ignore the weight of the liquid about the lowest point of miniscus]. The heights \(h _1\) and \(h _2\) and surface tensions \(T _1\) and \(T _2\) satisfy the relation :

The range of the projectile projected at an angle of \(15^{\circ}\) with horizontal is \(50\,m\). If the projectile is projected with same velocity at an angle of \(45^{\circ}\) with horizontal, then its range will be \(........\,m\)

The three charges \(q / 2, q\) and \(q / 2\) are placed at the corners \(A , B\) and \(C\) of a square of side ' \(a\) ' as shown in figure. The magnitude of electric field \((E)\) at the comer \(D\) of the square, is

Magnetic materials used for making permanent magnets \((P)\) and magnets in a transformer \((T)\) have different properties of the following, which property best matches for the type of magnet required \(?\)

Within a spherical charge distribution of charge density \(\rho \left( r \right)\), \(N\) equipotential surfaces of potential \({V_0},{V_0} + \Delta V,{V_0} + 2\Delta V,\)\(.....{V_0} + N\Delta V\left( {\Delta V > 0} \right),\) are drawn and have increasing radii \(r_0, r_1, r_2,......r_N\), respectively. If the difference in the radii of the surfaces is constant for all values of \(V_0\) and \(\Delta V\) then

A progressive wave travelling along the positive \(x-\) direction is represented by \(y(x, t) = A\,sin\,\left( {kx - \omega t + \phi } \right)\). Its snapshot at \(t = 0\) is given in the figure For this wave, the phase \(\phi \) is

The reading of the ammeter for a silicon diode in the given circuit is.......\(mA\)

The mass density of a planet of radius \(R\) varies with the distance \(r\) from its centre as \(\rho( r )=\rho_{0}\left(1-\frac{ r ^{2}}{ R ^{2}}\right) .\) Then the gravitational field is maximum at

A bat moving at \(10\,ms^{-1}\) towards a wall sends a sound signal of \(8000\,Hz\) towards it. On reflection it hears a sound of frequency \(f\). The value of \(f\) in \(Hz\) is close to (speed of sound \(= 320\,ms^{-1}\) )

A litre of dry air at \(STP\) expands adiabatically to a volume of \(3\) litres. If \(\gamma=1.40,\) the work done by air is\((3^{1.4}=4.6555)\) [Take air to be an ideal gas \(]\)

A mass of \(5\, {kg}\) is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length \(4\, {m}\) has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed? (In \({m} / {s}^{2}\))