The \(SI\) unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be ..............

The first three spectral lines of \(H\) -atom in the Balmer series are given \(\lambda_{1}, \lambda_{2}, \lambda_{3}\) considering the Bohr atomic model, the wave lengths of first and third spectral lines \(\left(\frac{\lambda_{1}}{\lambda_{3}}\right)\) are related by a factor of approximately 'x' \(\times 10^{-1}\). The value of \(x\), to the nearest integer, is

In thermodynamics, heat and work are

Four particles \(A, B, C, D\) of mass \(\frac{\mathrm{m}}{2}, \mathrm{~m}, 2 \mathrm{~m}, 4 \mathrm{~m}\), have same momentum, respectively. The particle with maximum kinetic energy is _______.

A spherical ball of radius \(1 \times 10^{-4} \mathrm{~m}\) and density \(10^5\) \(\mathrm{kg} / \mathrm{m}^3\) falls freely under gravity through a distance \(h\) before entering a tank of water, If after entering in water the velocity of the ball does not change, then the value of \(h\) is approximately _______. (The coefficient of viscosity of water is \(9.8 \times 10^{-6}\) \(\left.\mathrm{N} \mathrm{s} / \mathrm{m}^2\right)\)

The ratio of 10.Powers of two motors is \(\frac{3 \sqrt{x}}{\sqrt{x}+1}\), that are capable of raising \(300\,kg\) water in \(5\) minutes and \(50\,kg\) water in \(2\) minutes respectively from a well of \(100\,m\) deep. The value of \(x\) will be

A conductor lies along the \(z-\)axis \(a\) \(-1.5\)\( \le Z < 1.5\,m\) carries a fixed current of \(10.0\ A\) in \( - {\hat a_z}\) direction (see figure). For a field \(\vec B\) \(=\) \(3.0 \times  10^{-4}\)  \(e^{-0.2x}\) \({\hat a_y}\,T\) find the power required to move the conductor at constant speed to \(x = 2.0\ m, y = 0\ m\) in \(5 \times 10^{-3}\ s\). Assume parallel motion along the \(x-\)axis........\( W\)

'\(n\)' moles of an ideal gas undergoes a process \(A \rightarrow B\) as shown in the figure. The maximum temperature of the gas during the  process will be

Which of the following phenomena can not be explained by wave theory of light ?

Five equal resistances are connected in a network as shown in figure. The net resistance between the points \(A\) and \(B\) is

A spherical ball of mass \(2\) kg falls from a height of \(10\) m and is brought to rest after penetrating \(10\) cm into sand. The average force exerted by sand on the ball is _______ N. (Take \(g = 10\) m/s\(^2\))

From a tower of height \(H\), a particle is thrown vertically upwards with a speed \( u\). The time taken by the particle, to hit the ground, is \(n\) times that taken by it to reach the highest point of its path. The relation between \(H, u\) and \(n\) is:

For designing a voltmeter of range \(50\,V\) and an ammeter of range \(10\,mA\) using a galvanometer which has a coil of resistance \(54\,\Omega\) showing a full scale deflection for \(1\,mA\) as in figure. \((A)\) for voltmeter \(R \approx 50\,k\Omega\) \((B)\) for ammeter \(r \approx 0.2\,\Omega\) \((C)\) for ammeter \(r \approx 6\,\Omega\) \((D)\) for voltmeter \(R \approx 5\,k \Omega\) \((E)\) for voltmeter \(R \approx 500 \Omega\) Choose the correct answer from the options given below