A \(10\, \mu F\) capacitor is fully charged to a potential difference of \(50\, V\). After removing the source voltage it is connected to an uncharged capacitor in parallel. Now the potential difference across them becomes \(20\, V\). The capacitance of the second capacitor is......\(\mu F\)

The stopping potential in the context of photoelectric effect depends on the following property of incident electromagnetic radiation

Two separate wires \(A\) and \(B\) are stretched by \(2 \,mm\) and \(4\, mm\) respectively, when they are subjected to a force of \(2\, N\). Assume that both the wires are made up of same material and the radius of wire \(B\) is 4 times that of the radius of wire \(A\). The length of the wires \(A\) and \(B\) are in the ratio of \(a : b\). Then \(a / b\) can be expressed as \(1 / x\) where \(x\) is

The truth of the given circuit diagram is _______.

A constant Power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time \('t'\) is proportional to

A bat moving at \(10\,ms^{-1}\) towards a wall sends a sound signal of \(8000\,Hz\) towards it. On reflection it hears a sound of frequency \(f\). The value of \(f\) in \(Hz\) is close to (speed of sound \(= 320\,ms^{-1}\) )

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R .
Assertion A : If oxygen ion \(\left(\mathrm{O}^{-2}\right)\) and Hydrogen ion \(\left(\mathrm{H}^{+}\right)\)enter normal to the magnetic field with equal momentum, then the path of \(\mathrm{O}^{-2}\) ion has a smaller curvature than that of \(\mathrm{H}^{+}\).
Reason R : A proton with same linear momentum as an electron will form a path of smaller radius of curvature on entering a uniform magnetic field perpendicularly.
In the light of the above statements, choose the correct answer from the options given below :

If \( x^{2}+x+1=0 \) then the value of \( (x+\frac{1}{x})^{4}+(x^{2}+\frac{1}{x^{2}})^{4}+(x^{3}+\frac{1}{x^{3}})^{4}+...+(x^{25}+\frac{1}{x^{25}})^{4} \) is:

A cube has side length \(5\) cm and modulus of rigidity \(10^5\) N/m\(^2\). The displacement produced by a force of \(10\) N in the upper face of cube is _____ mm.

Let \(\alpha, \beta\) be the roots of the equation \(x^2-\sqrt{2} x+2=0\). Then \(\alpha^{14}+\beta^{14}\) is equal to

For a positive integer \(n,\left(1+\frac{1}{x}\right)^{n}\) is expanded in increasing powers of \(x\). If three consecutive coefficients in this expansion are in the ratio, \(2: 5: 12,\) then \(n\) is equal to

Let \(\vec{a}=\hat{i}+\alpha \hat{j}+3 \hat{k}\) and \(\vec{b}=3 \hat{i}-\alpha \hat{j}+\hat{k} \cdot\) If the area of the parallelogram whose adjacent sides are represented by the vectors \(\vec{a}\) and \(\vec{b}\) is \(8 \sqrt{3}\) square units, then \(\overrightarrow{ a } \cdot \overrightarrow{ b }\) is equal to ....... .

Number of solutions of \( \sqrt{3}\cos 2\theta+8\cos \theta+3\sqrt{3}=0 \), \( \theta \in [-3\pi, 2\pi] \) is: