Two strings $A$ and $B$ of lengths $L_A = 80 \ cm$ and $L_B = x \ cm$ respectively are used separately in a sonometer. The ratio of their densities $(d_A / d_B)$ is $0.81$. The diameter of $B$ is one-half that of $A$. If the strings have the same tension and fundamental frequency,the value of $x$ is:

$\lim _{x \rightarrow 0} \frac{4^x-9^x}{x(4^x+9^x)}$ is equal to

An object of mass $2m$ is projected with a speed of $100 \ m/s$ at an angle $\theta = \sin^{-1}(3/5)$ to the horizontal. At the highest point,the object breaks into two pieces of same mass $m$ and the first one comes to rest. The distance between the point of projection and the point of landing of the bigger piece (in metre) is (Given,$g = 10 \ m/s^2$)

Choose the correct option from the following:
$I$. Dehydration and dormancy of mature seed are crucial for seed storage.
$II$. Seed of $Lupinus \; arcticus$ is the oldest one which germinated after $2,000 \; years$.
$III$. Orchid seed is one of the largest seeds in the plant kingdom.
$IV$. Seeds of parasitic plants $Orobanche$ and $Striga$ are tiny seeds.

Which of the following does not decolourise iodine?

Which of the following acts as an antagonist to gibberellic acid?