The length of an elastic string is $a \, m$ when the longitudinal tension is $4 \, N$ and $b \, m$ when the longitudinal tension is $5 \, N$. The length of the string in metres when the longitudinal tension is $9 \, N$ is

The locus of the point $z=x+iy$ satisfying $\left|\frac{z-2i}{z+2i}\right|=1$ is

$A$ projectile is fired at a speed of $100 \, m/s$ at an angle of $37^\circ$ above the horizontal. At the highest point,the projectile breaks into two parts of mass ratio $1:3$,the smaller coming to rest. Then the distance of the heavier part from the launching point is ............... $m$.

One mole of an ideal diatomic gas undergoes a transition from $A$ to $B$ along a path $AB$ as shown in the figure. The change in internal energy of the gas during the transition is:

The symmetric equation of the line formed by the intersection of the planes $3x + 2y + z - 5 = 0$ and $x + y - 2z - 3 = 0$ is:

Platinum crystallizes in a face-centered cubic $(FCC)$ crystal with a unit cell edge length $a$. The distance between nearest neighbours is