The component of vector $\overrightarrow{A} = a_x \hat{i} + a_y \hat{j} + a_z \hat{k}$ along the direction of $\hat{i} - \hat{j}$ is

$A$ particle of mass $4 m$ explodes into three pieces of masses $m, m$ and $2 m$. The equal masses move along $X$-axis and $Y$-axis with velocities $4 ms^{-1}$ and $6 ms^{-1}$ respectively. The magnitude of the velocity of the heavier mass is

Which of the following statements is $NOT$ correct?

Which one of the following halogens liberates oxygen,when passed through hot concentrated $KOH$ solution?

If $x$ is numerically so small that $x^2$ and higher powers of $x$ can be neglected,then $\left(1+\frac{2 x}{3}\right)^{3 / 2} \cdot(32+5 x)^{-1 / 5}$ is approximately equal to

$A$ telescope has an objective lens of focal length $150 \ cm$ and an eyepiece of focal length $5 \ cm$. If a $50 \ m$ tall tower at a distance of $1 \ km$ is observed through this telescope in normal setting,the angle formed by the image of the tower is $\theta$ (in degrees),then $\theta$ is close to..... (in $^{\circ}$)