The smallest unit of life is...

$\int \frac{1+x+\sqrt{x+x^2}}{\sqrt{x}+\sqrt{1+x}} d x$ is equal to

When an object is placed at a distance of $25 \, cm$ from a concave mirror,the magnification is $m_1$. The object is moved $15 \, cm$ farther away with respect to the earlier position,and the magnification becomes $m_2$. If $m_1/m_2 = 4$,the focal length of the mirror is $..... \, cm$ (Assume image is real,$m_1$ and $m_2$ are numerical values).

Which of the following is responsible for mechanical support, enzyme transport and protein synthesis?

If one of the lines in the pair of straight lines given by $4x^2+6xy+ky^2=0$ bisects the angle between the coordinate axes,then $k \in$

If $\cos (\alpha+\beta)=\frac{4}{5}$,$\sin (\alpha-\beta)=\frac{5}{13}$ and $\alpha, \beta$ are between $0$ and $\frac{\pi}{4}$,then $\tan 2\alpha$ is equal to