Cellular respiration is carried out by

If the tangent at point $(1, 2)$ on the curve $y = ax^2 + bx + \frac{7}{2}$ is parallel to the normal at point $(-2, 2)$ on the curve $y = x^2 + 6x + 10$,then:

The velocities of three particles of masses $20 \ g$,$30 \ g$,and $50 \ g$ are $10 \hat{i}$,$10 \hat{j}$,and $10 \hat{k}$ respectively. The velocity of the centre of mass of the three particles is:

In an optical fibre,the core and cladding are made with materials of refractive indices $1.5$ and $1.414$ respectively. To observe total internal reflection,what will be the range of the incident angle with the axis of the optical fibre?

Two polaroids are placed in the path of an unpolarized beam of intensity $I_0$ such that no light is emitted from the second polaroid. If a third polaroid,whose polarization axis makes an angle $\theta$ with the polarization axis of the first polaroid,is placed between these polaroids,then the intensity of light emerging from the last polaroid will be

If $\cos ^{-1}\left(\frac{x}{2}\right)+\cos ^{-1}\left(\frac{y}{3}\right)=\theta$,then $9x^2-12xy\cos \theta+4y^2=$