The equivalent resistance between the points \(A\) and \(B\) in the following circuit is \(\frac{x}{5} \Omega\). The value of \(x\) is ___________.

A 400 g solid cube having an edge of length 10 cm floats in water. How much volume of the cube is outside the water ?
(Given : density of water \(=1000 \mathrm{~kg} \mathrm{~m}^{-3}\) )

In the given figure, a mass \(M\) is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is \(k\). The mass oscillates on a frictionless surface with time period \(T\) and amplitude \(A\). When the mass is in equilibrium position, as shown in the figure, another mass \(m\) is gently fixed upon it. The new amplitude of oscillation will be

A compound microscope consists of an objective lens of focal length \(1 \,cm\) and an eye piece of focal length \(5 \,cm\) with a separation of \(10 \,cm\) The distance between an object and the objective lens, at which the strain on the eye is minimum is \(\frac{ n }{40}\, cm .\) The value of \(n\) is\(....\)

The transfer characteristic curve of a transistor, having input and output resistance \(100\,\Omega \) and \(100\,k\Omega \) respectively, is shown in the figure. The Voltage and Power gain, are respectively

Your friend is having eye sight problem. She is not able lo see clearly a distant uniform window mesh and it appears to her as non-uniform and distorted. The doctor diagnosed the problem as

The time period of a simple harmonic oscillator is \(T =2 \pi \sqrt{\frac{ k }{ m }}\). The measured value of mass (m) of the object is 10 g with an accuracy of 10 mg , and time for 50 oscillations of the spring is found to be 60 s using a watch of 2 s resolution. Percentage error in determination of spring constant( \(k\) ) is ___________ %.

A rocket has to be launched from each in such a way that it never returns. If \(E\) is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have if the same rocket is to be launched from the surface of the moon ? Assume that the density of the earth and the moon are equal and that the earth’s volume is \(64\) times the volume of the moon.

A metal wire of uniform mass density having length \(L\) and mass \(M\) is bent to form a semicircular arc and a particle of mass \(m\) is placed at the centre of the arc. The gravitational force on the particle by the wire is _______.

One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston system. The cross-section area of the cylinder is \(4\) cm\(^2\). The gas is heated slowly to raise the temperature by \(1.2\,^\circ\)C during which the piston moves by \(25\) mm. The amount of heat supplied to the gas is ________ J. (Atmospheric pressure \(=100\) kPa, \(R=8.3\) J/mol·K) (Neglect mass of the piston)

In the below circuit the current in each resistance is