A cube of side \('a'\) has point charges \(+Q\) located at each of its vertices except at the origin where the charge is \(- Q\). The electric field at the centre of cube is

If the series limit frequency of the Lyman series is \(v_L\), then the series limit frequency of the \(P\)-fund series is

In Vander Waals equation \(\left[ P +\frac{ a }{ V ^{2}}\right][ V - b ]= RT\); \(P\) is pressure, \(V\) is volume, \(R\) is universal gas constant and \(T\) is temperature. The ratio of constants \(\frac{a}{b}\) is dimensionally equal to .................

A cube having a side of 10 cm with unknown mass and 200 gm mass were hung at two ends of an uniform rigid rod of 27 cm long. The rod along with masses was placed on a wedge keeping the distance between wedge point and 200 gm weight as 25 cm. Initially the masses were not at balance. A beaker is placed beneath the unknown mass and water is added slowly to it. At given point the masses were in balance and half volume of the unknown mass was inside the water.
(Take the density of unknown mass is more than that of the water, the mass did not absorb water and water density is \(1 \mathrm{gm} / \mathrm{cm}^3\).) The unknown mass is ________ kg.

A conducting circular loop made of a thin wire, has area \(3.5 \times 10^{-3}\, m^2\) and resistance \(10\,\Omega \). It is placed perpendicular to a time dependent magnetic field \(B(t) = (0.4\,T)\, sin\, (50\, \pi t)\). The field is uniform in space. Then the net charge flowing through the loop during \(t = 0\, s\) and \(t = 10\, ms\) is close to.......\(mC\)

If \(50\) Vernier divisions are equal to \(49\) main scale divisions of a travelling microscope and one smallest reading of main scale is \(0.5 \mathrm{~mm}\), the Vernier constant of travelling microscope is _______.

A force is applied to a steel wire ' \(A\) ', rigidly clamped at one end. As a result elongation in the wire is \(0.2\,mm\). If same force is applied to another steel wire ' \(B\) ' of double the length and a diameter \(2.4\) times that of the wire ' \(A\) ', the elongation in the wire ' \(B\) ' will be \(............\times 10^{-2}\,mm\) (wires having uniform circular cross sections)

The shortest distance between lines \(\mathrm{L}_1\) and \(\mathrm{L}_2\), where \(L_1: \frac{x-1}{2}=\frac{y+1}{-3}=\frac{z+4}{2}\) and \(L_2\) is the line passing through the points \(\mathrm{A}(-4,4,3) \cdot \mathrm{B}(-1,6,3)\) and perpendicular to the line \(\frac{x-3}{-2}=\frac{y}{3}=\frac{z-1}{1}\), is

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The binding energy per nucleon is found to be practically independent of the atomic number A, for nuclei with mass numbers between 30 and 170.
Reason (R): Nuclear force is long range.
In the light of the above statements, choose the correct answer from the options given below :

If \(\lim _{x \rightarrow 0} \frac{\cos (2 x)+a \cos (4 x)-b}{x^4}\) is finite, then \((a+b)\) is equal to :

The remainder when \(7^{2022}+3^{2022}\) is divided by 5 is.

Suppose \(\theta \in\left[0, \frac{\pi}{4}\right]\) is a solution of \(4 \cos \theta-3 \sin \theta=1\) Then \(\cos \theta\) is equal to :

If the refractive index of the material of a prism is \(\cot \left(\frac{A}{2}\right)\), where \(A\) is the angle of prism then the angle of minimum deviation will be