If the vectors $p\hat{i} + \hat{j} + \hat{k}$,$\hat{i} + q\hat{j} + \hat{k}$,and $\hat{i} + \hat{j} + r\hat{k}$ $(p \neq 1, q \neq 1, r \neq 1)$ are coplanar,then find the value of $pqr - (p + q + r)$.

Which element is responsible for the crimson red color in fireworks?

$A$ tension of $22 ~N$ is applied to a copper wire of cross-sectional area $0.02 ~cm^2$. The Young's modulus of copper is $1.1 \times 10^{11} ~N/m^2$ and the Poisson's ratio is $0.32$. The decrease in cross-sectional area will be:

In the circuit shown,the readings of the ammeter and voltmeter are $4\,A$ and $20\,V$ respectively. The meters are non-ideal. Then $R$ is:

$A$ tank with vertical walls is mounted so that its base is at a height $H$ above the horizontal ground. The tank is filled with water to a depth $h$. $A$ hole is punched in the side wall of the tank at a depth $x$ below the water surface. To have maximum range of the emerging stream, the value of $x$ is

The displacement of a particle from its mean position (in metre) is given by $y = 0.2 \sin(10\pi t + 1.5\pi) \cos(10\pi t + 1.5\pi)$. The motion of the particle is: