The work done on a wire of volume of \(2 \mathrm{~cm}^3\) is \(16 \times 10^2 \mathrm{~J}\). If the young's modulus of the material of the wire is \(4 \times 10^{12} \mathrm{Nm}^{-2}\). Then the strain produced in the wire is

In an experiment, four quantities \(a, b, c, d\) are measured with percentage errors 2\%, \(1 \%, 3 \%\) and 5\%, respectively. Quantity \(P\) is measured as \(P=\frac{a^2 b^2}{c d}\). Find the percentage error in measuring \(P\).

If the angles of dip at two places are \(30^{\circ}\) and \(45^{\circ}\) respectively, then the ratio of horizontal components of earth's magnetic field at the two places will be

The maximum amplitude of an AM wave is found to be \(20 \mathrm{~V}\) while its minimum amplitude is \(4 \mathrm{~V}\). The modulation index is

The ends of an element of zinc wire are kept at a small temperature difference \(\Delta T\) and a small current \((I)\) is passed through the wire. Then, the heat developed per unit time

Among the following, the unit of permeability is NOT represented by

During phase change, entropy

The ratio of de Broglie wave lengths of two particles, having mass ratio $1: 3$ and kinetic energy ratio $2: 1$ is

Which of the following is true about \(f(x)=3\) \(\sinh (x)-2 \cosh (x), \forall x \in \mathbf{R}\)

If the number of diagonals of a regular polygon of \(n\) sides is 104 , then \(\mathrm{n}=\)

If the radius of a sphere is mentioned as \(7 \mathrm{~m}\) with an error of \(0.02 \mathrm{~m}\), then the approximate error in calculating its volume is

If the function \(f(x)=a \sin (x)+\frac{1}{3} \sin (3 x)\) attains maximum value at \(x=\frac{\pi}{3}\), then \(a\) equals

Let \(\overrightarrow{\mathbf{a}}=a_1 \hat{\mathbf{i}}+a_2 \hat{\mathbf{j}}+a_3 \hat{\mathbf{k}}\)
Assertion (A) : The identity
\(|\overrightarrow{\mathbf{a}} \times \hat{\mathbf{i}}|^2+|\overrightarrow{\mathbf{a}} \times \hat{\mathbf{j}}|^2+|\overrightarrow{\mathbf{a}} \times \hat{\mathbf{k}}|^2=2|\overrightarrow{\mathbf{a}}|^2\) holds for
\(\vec{a}\).
Reason (R) : \(\overrightarrow{\mathbf{a}} \times \hat{\mathbf{i}}=a_3 \hat{\mathbf{j}}-a_2 \hat{\mathbf{k}}\),
\(\overrightarrow{\mathbf{a}} \times \hat{\mathbf{j}}=a_1 \hat{\mathbf{k}}-a_3 \hat{\mathbf{i}}, \overrightarrow{\mathbf{a}} \times \hat{\mathbf{k}}=a_2 \hat{\mathbf{i}}-a_1 \hat{\mathbf{j}}\)
Which of the following is correct?