Two coherent sources whose intensity ratio is $64: 1$ produce interference fringes. The ratio of intensities of maxima and minima is

If $x y \neq 0, x+y \neq 0$ and $x^m y^n=(x+y)^{m+n}$, where $m, n \notin N$, then $\frac{d y}{d x}$ is equal to

$\frac{d}{d x}\left[a \tan ^{-1} x+b \log \left(\frac{x-1}{x+1}\right)\right]=\frac{1}{x^4-1}$
$\Rightarrow a-2 b$ is equal to

An insect crawls up a hemispherical surface very slowly (see figure). The coefficient of friction between the insect and the surface is $\mu = 1/3$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical,the maximum possible value of $\alpha$ is given by

$A$ particle is performing simple harmonic motion along the $x$-axis with an amplitude of $4\, cm$ and a time period of $1.2\, s$. The minimum time taken by the particle to move from $x = 2\, cm$ to $x = +4\, cm$ and back again is given by .... $s$.

Which of the following is responsible for the conversion of milk into curd?