A slit is illuminated by light of wavelength \( 6500 \text{ \AA} \).
The first minimum is observed at \( \theta = 30^\circ \). The width of the slit is:

A small piece of metal wire is dragged in the region of magnetic flux \( 8 \times 10^{-4} \, \text{Wb} \) in 0.5 s. The length of the wire is perpendicular to the magnetic field. The emf induced in the wire would be:

A system consists of two protons and one electron. They are separated by a distance of 1 \(\text{\AA}\) from each other. If the potential energy at infinity is taken to be zero, the potential energy of the system is

Keeping the voltage of the charging source constant, the separation between the plates of the capacitor is decreased by 10%. The percentage change in the energy stored in the capacitor will be:

A transmitting station transmits radio waves of wavelength 300 m. The inductance of the coil required with a capacitor of capacity 1.0 \( \mu F \) in a resonant circuit will be

An a.c. voltage is applied to a resistor of resistance \(5 \Omega\) and an inductor having inductive reactance \(5 \Omega\) connected in series. The phase difference between the applied voltage and the current in the circuit is:

Electrons in an experiment are accelerated by a voltage of 36 kV. If the voltage is increased to 144 kV, then the de-broglie wavelength associated with the electron would

Read the passage carefully and answer the questions
The carbonyl group of aldehydes and ketones is highly polar. The positively charged carbon is readily attacked by electron-rich nucleophile and the negatively charged oxygen atom is attacked by an electro-deficient electrophile. Aldehydes and ketones undergo nucleophilic addition reactions in the presence of acid or a base. The mechanism involves attack of a nucleophile on the electron deficient carbonyl carbon to form a tetrahedral intermediate. A new bond is formed between the carbon and oxygen. Protonation of the anion furnished by the reaction medium yields a neutral addition product. The addition product is same whether the reaction is catalyzed by acid or a base. For example in the presence of base aldehydes and ketones react with hydrogen cyanide to form cyanohydrin.
The source of nucleophile in the base catalyzed cyanohydrin formation is:

If \(A=\left[\begin{array}{cc}2 & 1 \\ 1 & 4 \\ -1 & 6 \\ 0 & 7\end{array}\right]\) and \(B=\left[\begin{array}{cccc}1 & 2 & 3 & 0 \\ 2 & -1 & 6 & 7\end{array}\right]\), then

\(\int_0^{\frac{\pi}{2}} \sin 2 x \log (\tan x) d x=\)

Particular solution of the differential equation \(\log \left(\frac{d y}{d x}\right)=x+y\) given that when x = 0 y = 0 is:

The sweet smelling compound \(\text{[D]}\) is:
(1) Acid anhydride
(2) Acyl halide
(3) Aldehyde
(4) Ester
Explanation: The reaction between a carboxylic acid and an alcohol in the presence of acid
is Esterification. The product \(\text{[D]}\) is Methyl Acetate, which is an \textbf{Ester}.
Answer: (4)

Which of the following reagents can bring about the given conversion?
3-Nitrobromobenzene to 3-Nitrobenzoic acid