Calculate the number of atoms present in unit cell if an element having molar mass $$23 \mathrm{~g} \mathrm{~mol}^{-1}$$ and density $$0.96 \mathrm{~g} \mathrm{~cm}^{-3}$$.

$$[\mathrm{a}^3 \cdot \mathrm{N}_{\mathrm{A}}=48 \mathrm{~cm}^3 \mathrm{~mol}^{-1}]$$

If $$\mathrm{f}(x)=x^3+\mathrm{b} x^2+\mathrm{c} x+\mathrm{d}$$ and $$0<\mathrm{b}^2<\mathrm{c}$$, then in $$(-\infty, \infty)$$

Differentiation of $$\tan ^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right)$$ w.r.t. $$\cos ^{-1}\left(\sqrt{\frac{1+\sqrt{1+x^2}}{2 \sqrt{1+x^2}}}\right)$$ is

The function $$\mathrm{f}(\mathrm{t})=\frac{1}{\mathrm{t}^2+\mathrm{t}-2}$$ where $$\mathrm{t}=\frac{1}{x-1}$$ is discontinuous at