The logic gate equivalent to the given logic circuit is

Two charges \(q\) and \(3 q\) are separated by a distance ' \(r\) ' in air. At a distance \(x\) from charge \(q\), the resultant electric field is zero. The value of \(x\) is _______.

The focal length of the objective and the eyepiece of a telescope are \(50\,cm\) and \(5\,cm\) respectively. If the telescope is focussed for distinct vision on a scale distant \(2\,m\) from its objective, then its magnifying power will be

A \(10\,\mu C\) charge is divided into two parts and placed at \(1\,cm\) distance so that the repulsive force between them is maximum. The charges of the two parts are :

The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors \(\overrightarrow{ a }, \overrightarrow{ b }\) and \(\overrightarrow{ c }\) respectively. Then choose the correct relation for these vectors.

A uniform conducting wire of length is \(24 {a}\), and resistance \({R}\) is wound up as a current carrying coil in the shape of an equilateral triangle of side \('a'\) and then in the form of a square of side \('a'.\) The coil is connected to a voltage source \({V}_{0}\). The ratio of magnetic moment of the coils in case of equilateral triangle to that for square is \(1: \sqrt{y}\) where \(y\) is ..... .

The distance between object and its two times magnified real image as produced by a convex lens is \(45 \mathrm{~cm}\). The focal length of the lens used is _______ \(\mathrm{cm}\).

Following plots show Magnetization \((M)\) \(vs\) Magnetising field \((H)\) and Magnetic susceptibility \((\chi)\) vs temperature \((T)\) graph : Which of the following combination will be represented by a diamagnetic material?

Given below are two statements :
Statement I : In a vernier callipers, one vernier scale division is always smaller than one main scale division.
Statement II : The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions.
In the light of the above statements, choose the correct answer from the options given below.

Consider the following statements : \(A.\) Atoms of each element emit characterstics spectrum. \(B.\) According to Bohr's Postulate, an electron in a hydrogen atom, revolves in a certain stationary orbit. \(C.\) The density of nuclear matter depends on the size of the nucleus. \(D.\) A free neutron is stable but a free proton decay is possible. \(E.\) Radioactivity is an indication of the instability of nuclei. Choose the correct answer from the options given below 

The total length of a sonometer wire between fixed ends is \(110\, cm\). Two bridges are placed to divide the length of wire in ratio \(6 : 3 : 2\). The tension in the wire is \(400\, N\) and the mass per unit length is \(0.01\, kg/m\) . What is the minimum common frequency with Which three parts can vibrate ........... \(Hz\) ?

The current flowing through a conductor connected across a source is \(2\,A\) and \(1.2\,A\) at \(0^{\circ}\,C\) and \(100^{\circ}\,C\) respectively. The current flowing through the conductor at \(50^{\circ}\,C\) will be \(......\times 10^2\,mA\).