question_answer

A biconvex lens of focal length / forms a circular image of sun of radius r in focal plane. Then,

A) \[\pi {{r}^{2}}=f\]                                            

B) \[\pi {{r}^{2}}-f\]

C)  if bower hall part is covered by black sheet, then area of the image is equal to \[f(x)=\left\{ \begin{align}   & |{{x}^{3}}+{{x}^{2}}+3x+\sin x|.\left( 3+\sin \frac{1}{x} \right),\,x\ne 0 \\  & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=3 \\ \end{align} \right.\]

D)  if f is doubled, intensity will increase

Correct Answer: B

Solution :

\[C{{H}_{3}}CHO+{{H}_{2}}NOH\xrightarrow[{}]{Na,{{C}_{2}}{{H}_{5}}OH}\] Hence,\[C{{H}_{3}}CHO+{{N}_{2}}C{{H}_{2}}\xrightarrow[{}]{NaB{{H}_{4}}}\]