How many even numbers of $3$ different digits can be formed from the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ (repetition is not allowed)?

Which of the following statements is correct for any thermodynamic system?

The solution of the differential equation $\frac{dy}{dx} = \sin(x+y) \tan(x+y) - 1$ is

In $YDSE$ setup,light of wavelength $640 \, nm$ is used with $d = 0.8 \, mm$ and $D = 1 \, m$. If intensity at central maximum is $I_0$ and its position is $y = 0$,then:

If the length of a stretched string is shortened by $x \%$ and the tension is increased by $44 \%$,then the ratio of the final and initial fundamental frequencies is $2:1$. The value of $x$ is:

If $b+c=3a$,then $\cot \frac{B}{2} \cot \frac{C}{2}$ is equal to :