In the expansion of $(1+x)^n$,the coefficients of the $p^{th}$ and $(p+1)^{th}$ terms are respectively $p$ and $q$. Then $p+q$ is equal to:

The ratio of the longest wavelengths corresponding to the Lyman and Balmer series in the hydrogen spectrum is

$A$ mass $M$ attached to a horizontal spring executes $S.H.M.$ of amplitude $A_1$. When the mass $M$ passes through its mean position,a smaller mass $m$ is placed over it and both of them move together with amplitude $A_2$. The ratio $\left(\frac{A_1}{A_2}\right)$ is

How many organisms in the list given below show autotrophic nutrition method? Lactobacillus,Nostoc,Chara,Wolffia,Nitrosomonas,Nitrobacter,Porphyra,Streptococcus,Saccharomyces,Trypanosoma.

$A$ certain radioactive substance reduces to $25\%$ of its initial value in $16$ days. Its half-life is ........ $days$.

$A$ particle is moving along a circular path with constant speed and centripetal acceleration $a$. If the speed is doubled,the ratio of its acceleration after and before the change is