If $f(x) = \frac{1}{x^2} \int_3^x (2t - 3f'(t)) dt$,then $f'(3)$ is equal to

An eight-digit number divisible by $9$ is to be formed using digits from $0$ to $9$ without repeating the digits. The number of ways in which this can be done is: (in $(7!)$)

$A$ bomb moving with velocity $(40 \hat{i} + 50 \hat{j} - 25 \hat{k}) \text{ m/s}$ explodes into two pieces of mass ratio $1:4$. After the explosion,the smaller piece moves away with velocity $(200 \hat{i} + 70 \hat{j} + 15 \hat{k}) \text{ m/s}$. The velocity of the larger piece after the explosion is:

Which zone of the blast furnace has the highest temperature?

$A$ train moving at a speed of $220\, ms^{-1}$ towards a stationary object,emits a sound of frequency $1000\, Hz$. Some of the sound reaching the object gets reflected back to the train as echo. The frequency of the echo as detected by the driver of the train is .... $Hz$ (speed of sound in air is $330\, ms^{-1}$)

The joint equation of the lines passing through the origin and trisecting the first quadrant is . . . . . .