Gametophyte is the dominant phase in the life cycle of

$A$ body of mass $m_1 = 4 \ kg$ moves at $5 \hat{i} \ m/s$ and another body of mass $m_2 = 2 \ kg$ moves at $10 \hat{i} \ m/s$. The kinetic energy of the centre of mass is

For a binomial variate $X$ with $n=6$, if $P(X=2)=9 P(X=4)$, then its variance is

$A$ three-digit number $n$ is such that the last two digits are equal and differ from the first digit. The number of such $n$'s is:

The magnetic flux near the axis and inside the air-core solenoid of length $60 \ cm$ carrying current $I$ is $1.57 \times 10^{-6} \ Wb$. Its magnetic moment will be (cross-sectional area of a solenoid is very small as compared to its length,$\mu_0 = 4\pi \times 10^{-7} \ SI \ units$). (in $A \ m^2$)

If $\cos ^{-1}\left(\frac{x^2-y^2}{x^2+y^2}\right)=k$ (a constant),then $\frac{d y}{d x}$ is equal to