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Correct Bernoulli’s equation is: [Symbols have their usual meaning]

Average force exerted on a non-reflecting surface at normal incidence is \( 2.4 \times 10^{-4} \, \text{N} \). If \( 360 \, \text{W}/\text{cm}^{2} \) is the light energy flux during span of \( 1 \) hour \( 30 \) minutes. Then the area of the surface is:

A clock has \( 75 \, \text{cm} \), \( 60 \, \text{cm} \) long second hand and minute hand respectively. In \( 30 \) minutes duration the tip of second hand will travel \( x \) distance more than the tip of minute hand. The value of \( x \) in meter is nearly. [Take : \( \pi = 3.14 \)]

Paramagnetic substances.
A. Align themselves along the directions of external magnetic field.
B. Attract strongly towards external magnetic field.
C. Has susceptibility little more than zero.
D. Move from a region of strong magnetic field to weak magnetic field.
Choose the most appropriate answer from the options given below:

Two planets \( A \) and \( B \) having masses \( m_{1} \) and \( m_{2} \) move around the sun in circular orbits of \( r_{1} \) and \( r_{2} \) radii respectively. If angular momentum of \( A \) is \( L \) and that of \( B \) is \( 3L \), the ratio of time period \( \left( \frac{T_A}{T_B} \right) \) is:

Young's modulus is determined by the equation given by \( Y = 49000 \, \frac{m}{l} \, \text{dyne} / \text{cm}^2 \) where \( M \) is the mass and \( l \) is the extension of wire used in the experiment. Now error in young modules (\( Y \)) is estimated by taking data from \( M\text{–}l \) plot in graph paper. The smallest scale divisions are \( 5 \, \text{g} \) and \( 0.02 \, \text{cm} \) along load axis and extension axis respectively. If the value of \( M \) and \( l \) are \( 500 \, \text{g} \) and \( 2 \, \text{cm} \) respectively then percentage error of \( Y \) is:

A \( \text{LCR} \) circuit is at resonance for a capacitor \( C \), inductance \( L \) and resistance \( R \). Now the value of resistance is halved keeping all other parameters same. The current amplitude at resonance will be now:

Two charged conducting spheres of radii \( a \) and \( b \) are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:

Three bodies \( A \), \( B \) and \( C \) have equal kinetic energies and their masses are \( 400 \, \text{g} \), \( 1.2 \, \text{kg} \) and \( 1.6 \, \text{kg} \) respectively. The ratio of their linear momenta is:

A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature \( 27^{\circ}\text{C} \). The ratio of specific heat of gases at constant volume respectively is:

A stationary particle breaks into two parts of masses \( m_A \) and \( m_B \) which move with velocities \( v_A \) and \( v_B \) respectively. The ratio of their kinetic energies \( (K_B : K_A) \) is:

A player caught a cricket ball of mass \( 150 \, \text{g} \) moving at a speed of \( 20 \, \text{m/s} \). If the catching process is completed in \( 0.1 \, \text{s} \), the magnitude of force exerted by the ball on the hand of the player is:

Critical angle of incidence for a pair of optical media is \( 45^\circ \). The refractive indices of first and second media are in the ratio:

The diameter of a sphere is measured using a vernier caliper whose \( 9 \) divisions of main scale are equal to \( 10 \) divisions of vernier scale. The shortest division on the main scale is equal to \( 1 \, \text{mm} \). The main scale reading is \( 2 \, \text{cm} \) and second division of vernier scale coincides with a division on main scale. If mass of the sphere is \( 8.635 \, \text{g} \), the density of the sphere is:

The output \( Y \) of following circuit for given inputs is:

Binding energy of a certain nucleus is \( 18 \times 10^{8} \, \text{J} \). How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus:

Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P–V diagram. The relation between the ratio \( \dfrac{V_a}{V_d} \) and the ratio \( \dfrac{V_b}{V_c} \) is:

In the given circuit, the terminal potential difference of the cell is:

In an expression \( a \times 10^{b} \).

Three vectors \( \overrightarrow{OP} \), \( \overrightarrow{OQ} \) and \( \overrightarrow{OR} \) each of magnitude \( A \) are acting as shown in figure. The resultant of the three vectors is \( A\sqrt{x} \). The value of \( x \) is _______.

A liquid column of height \( 0.04 \, \text{cm} \) balances excess pressure of a soap bubble of certain radius. If density of liquid is \( 8 \times 10^{3} \, \text{kg m}^{-3} \) and surface tension of soap solution is \( 0.28 \, \text{N m}^{-1} \), then diameter of the soap bubble is ______ \( \text{cm} \).
[If \( g = 10 \, \text{m s}^{-2} \)]

In an alpha particle scattering experiment distance of closest approach for the \( \alpha \) particle is \( 4.5 \times 10^{-14} \, \text{m} \). If target nucleus has atomic number \( 80 \), then maximum velocity of \( \alpha \)-particle is ______ \( \times 10^{5} \, \text{m} / \text{s} \) approximately.
[\( \dfrac{1}{4\pi \varepsilon_{0}} = 9 \times 10^{9} \) SI unit, mass of \( \alpha \) particle \( = 6.72 \times 10^{-27} \, \text{kg} \)]

A square loop \( PQRS \) having \( 10 \) turns, area \( 3.6 \times 10^{-3} \, \text{m}^{2} \) and resistance \( 100 \, \Omega \) is slowly and uniformly being pulled out of a uniform magnetic field of magnitude \( B = 0.5 \, \text{T} \) as shown. Work done in pulling the loop out of the field in \( 1.0 \, \text{s} \) is ______ \( \times 10^{-6} \, \text{J} \).

A parallel beam of monochromatic light of wavelength \( 600 \, \text{nm} \) passes through single slit of \( 0.4 \, \text{mm} \) width. Angular divergence corresponding to second order minima would be ______ \( \times 10^{-3} \, \text{rad} \).

An electron with kinetic energy \( 5 \, \text{eV} \) enters a region of uniform magnetic field of \( 3 \, \mu \text{T} \) perpendicular to its direction. An electric field \( E \) is applied perpendicular to the direction of velocity and magnetic field. The value of \( E \), so that electron moves along the same path, is ______ \( \text{N C}^{-1} \).
[Given, mass of electron \( = 9 \times 10^{-31} \, \text{kg} \), electric charge \( = 1.6 \times 10^{-19} \, \text{C} \)]

Resistance of a wire at \( 0^\circ \text{C} \), \( 100^\circ \text{C} \) and \( t^\circ \text{C} \) is found to be \( 10 \, \Omega \), \( 10.2 \, \Omega \) and \( 10.95 \, \Omega \) respectively. The temperature \( t \) in Kelvin scale is ______.

A uniform thin metal plate of mass \( 10 \, \text{kg} \) with dimensions is shown. The ratio of x and y coordinates of center of mass of plate is \( \frac{n}{9} \). The value of \( n \) is ______.

An electronic field, $\vec{E} = \frac{2\hat{i} + 6\hat{j} + 8\hat{k}}{\sqrt{6}}$ passes through the surface of $4\text{ m}^2$ area having unit vector $\hat{n} = \left(\frac{2\hat{i} + \hat{j} + \hat{k}}{\sqrt{6}}\right)$. The electric flux for that surface is ______ $\text{V m}$.

A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is \( \left( \dfrac{a-1}{a} \right) \) then the value of \( a \) is ______.