Glucose and mannose are

If $x \sqrt{1+y}+y \sqrt{1+x}=0$, then $\frac{d y}{d x}$ is equal to

Work done to increase the temperature of one mole of an ideal gas by $30^{\circ} C$,if it is expanding under the condition $V \propto T^{2/3}$ is,$(R = 8.314 \ J/mol \cdot K)$ (in $J$)

$A$ plane passes through $(2,3,-1)$ and is perpendicular to the line having direction ratios $3,-4,7$. The perpendicular distance from the origin to this plane is

If the curves $y^2 = 6x$ and $9x^2 + by^2 = 16$ intersect each other at right angles,then the value of $b$ is:

$A$ ray of light passes through four transparent media with refractive indices $\mu_1$,$\mu_2$,$\mu_3$,and $\mu_4$ as shown in the figure. The surfaces of all media are parallel. If the emergent ray $CD$ is parallel to the incident ray $AB$,we must have