$A$ wire of area of cross-section $10^{-6} \ m^2$ is increased in length by $0.1\%$. The tension produced is $1000 \ N$. The Young's modulus of the wire is:

$A$ massless string is wrapped around a disc of mass $M$ and radius $R$. Another end is tied to a mass $m$ which is initially at height $h$ from ground level as shown in the figure. If the mass is released,then its velocity while touching the ground level will be

If $\theta$ is the angle between vectors $\vec{a}$ and $\vec{b}$ and $|\vec{a} \times \vec{b}| = |\vec{a} \cdot \vec{b}|$,then $\theta$ is equal to

In which of the following complexes is the oxidation state of the metal zero?

Which of the following is the most toxic pesticide for vertebrates?

If $I_n = \int_0^{\pi / 4} \tan^n \theta \, d\theta$ for $n = 1, 2, 3, \ldots$,then $I_{n-1} + I_{n+1}$ is equal to