The order of the differential equation whose solution is $y = a \cos x + b \sin x + c e^{-x}$ is:

$A$ committee of $12$ members is to be formed from $9$ women and $8$ men. The number of committees in which the women are in majority is

$A$ radioactive material decays by simultaneous emission of two particles with respective half-lives $1620 \, years$ and $810 \, years$. The time, in years, after which one-fourth of the material remains is

The sound waves of wavelengths $5 ~m$ and $6 ~m$ produce $30$ beats in $3 ~s$. The velocity of sound is: (in $~m/s$)

The adjacent graph shows the extension $(\Delta l)$ of a wire of length $1 \ m$ suspended from the top of a roof at one end with a load $W$ connected to the other end. If the cross-sectional area of the wire is $10^{-6} \ m^2$,calculate the Young's modulus of the material of the wire.

Leaves that produce microspores and megaspores are called: