Carbohydrates,the most abundant biomolecules on Earth,are produced by:

If $x$ is the specific conductance (in $S \ cm^{-1}$) of the electrolyte solution and $y$ is the molarity of the solution,then $\Lambda_m$ (in $S \ cm^2 \ mol^{-1}$) is given by:

Two soap bubbles of radii $r_1 = 4 \, cm$ and $r_2 = 5 \, cm$ are touching each other over a common surface $S_1S_2$ (as shown in the figure). The radius of curvature of this common surface will be ....... $cm$.

There is some change in length when a $33000 ~N$ tensile force is applied on a steel rod of area of cross-section $10^{-3} ~m^2$. The change of temperature required to produce the same elongation,if the steel rod is heated,is (The modulus of elasticity is $3 \times 10^{11} ~N/m^2$ and the coefficient of linear expansion of steel is $1.1 \times 10^{-5} /{ }^{\circ} C$). (in $^{\circ} C$)

$\int_0^{\pi / 2} \frac{d x}{1+\tan ^3 x}$ is equal to :

$A$ 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