The output $F$of the logic circuit given below is

The maximum length of water column that can stay without falling in a vertically held capillary tube of diameter 1 mm and open at both the ends is
(Acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\) and surface tension of water \(=0.07 \mathrm{Nm}^{-1}\) )

An object is placed at a distance of $40 \mathrm{cm}$ in front of a concave mirror of focal length $20 \mathrm{cm}$. The image produced is

An infinitely long straight conductor is bent into the shape as shown below. It carries a current of I ampere and the radius of the circular loop is R metre. Then, the magnitude of magnetic induction at the centre of the circular loop is

A rifle of \(20 \mathrm{~kg}\) mass can fire 4 bullets per second. The mass of each bullet is \(35 \times 10^{-3} \mathrm{~kg}\) and its final velocity is \(400 \mathrm{~ms}^{-1}\). Then what force must be applied on the rifle so that it does not move backwards while firing the bullets ?

If \(A\) is the areal velocity of a planet of mass \(M\), its angular momentum is

A cell of emf \(10 \mathrm{~V}\) and internal resistance \(3 \Omega\) is connected in parallel with another cell of emf \(7 \mathrm{~V}\) and internal resistance \(\frac{3}{5} \Omega\), such that their positive terminals are joined together and so their are negative terminals. Their positive terminals are joined with the negative terminal and their negative terminal is joined with the positive terminal of a third cell of emf \(20 \mathrm{~V}\) with internal resistance \(2 \Omega\). The combination can be replaced by a battery of emf \(E\) and internal resistance \(r\), then the values of \(E\) and \(R\) are respectively

If $E$ and $E_0$ denote energies at time $t$ and $t_0$ respectively, and $L$ and $L_0$ distance from some point at $t$ and $t_0$ respectively, then which of the following equations can be declared to be incorrect on dimensional grounds (A) $E=\frac{2E_{0}L}{L_0}$ (B) $E=E_0{e}^{-\frac{2L}{L_0}}$ (C) $E=2L{e}^{\frac{-L}{E_0}}$ (D) $E=2\left(\frac{E_0}{L_0}\right)\times e^{\frac{-L}{L_0}}$

The magnetised wire of moment \(M\) and length \(l\) is bent in the form of semicircle of radius \(r\). Then its magnetic moment is

A solid sphere of mass 2 kg and radius 0.5 m is rolling without slipping on a horizontal surface. The ratio of the rotational and translational kinetic energies of the sphere is

Three identical vessels are filled up to the same height with three different liquids \(A, B\) and \(C\) of densities \(\rho_{\mathrm{A}^{\prime}} \rho_{\mathrm{B}}\) and \(\rho_{\mathrm{C}}\), then the pressure at the bottom of the vessels is

Two wires of the same material and length but diameters in the ratio \(1: 2\) are stretched by the same force. The elastic potential energy per unit volume for the wires, when stretched by the same force will be in the ratio.

A monoatomic gas does $100 \mathrm{J}$ of work when it is expanded isobarically. How much of heat is given to the gas in the process