An atom has a positively charged point nucleus of charge Ze surrounded by a uniform density of negative charge up to a radius R. The atom is taken as neutral. The electric field at a distance r < R from the nucleus is given by:

A radioactive nucleus decays as given below:
\( {}_Z^A P \rightarrow {}_{Z+1}^A Q \rightarrow {}_{Z-1}^{A-4} R^* \rightarrow {}_{Z-1}^{A-4} R \)
Which particles are emitted in the sequence?

A solenoid of length 0.4 m having 500 turns of wire carries a current of 3 A.
A coil of 10 turns and radius 0.01 m carries a current of 0.4 A.
What will be the torque required to hold the coil in the middle of the solenoid with its axis perpendicular to the axis of the solenoid?

In the depletion layer of a reverse biased p-n junction, the :

What is the distance that a beam of light of wavelength 500 nm can travel without significant broadening, if the diffracting aperture is 3 mm wide ?

A light of wavelength 500 nm falls on a metal surface, whose work function is 2.14 eV. The kinetic energy of the emitted electrons is

The least distance of distinct vision of a person is 50 cm. He wants to read a book placed at 25 cm. The focal length of the spectacles would be :

Value of \(\int_2^3 \frac{\sqrt{x}}{\sqrt{x}+\sqrt{5-x}} d x\) is

For \(y \neq 0\), the particular solution of the differential equation \(2 y e^{x / y} d x+\left(y-2 x e^{x / y}\right) d y=0\) at the point \((1,1)\) is

It is known that \(3\%\) of plastic bags manufactured in a factory are defective. Using the Poisson distribution on a sample of 100 bags, the probability of at most one defective bag is :

A circuit containing a \( 80 \text{ mH} \) inductor and a \( 60 \mu\text{F} \) capacitor in series is connected to a \( 200 \text{ V, 50 Hz} \) supply. The resistance of the circuit is negligible. The average power (average over one cycle) transferred to capacitor is:

Read the passage carefully and answer the questions
Alcohols and phenols are formed when a hydrogen atom in a hydrocarbon, aliphatic and aromatic respectively is replaced by -OH group. These are further classified on the basis of number of hydroxy groups and according to the hybridization of the carbon atom \(sp ^2\) or \(sp ^3\) to which the -OH group is attached. They find applications in industry as well as in day-to-day life. One of the most commercially obtained alcohol also known as wood spirit is obtained by destructive distillation of wood. Both alcohols and phenols are acidic in nature. The acidity of alcohols and phenols vary according to the nature of substituent(s) attached to them. Alcohols and phenols react with carboxylic acids, acid chlorides and acid anhydrides to form esters. Introduction of acetyl group in alcohols and phenols is called acetylation. Phenol undergo electrophilic aromatic substitution reaction because the -OH activates the benzene ring. It undergoes nitration, halogenation and sulphonation reactions.
Which compound is also known as 'wood spirit'?

A flask contains Argon and Chlorine in the ratio of 2:1 by mass. The temperature of the mixture is \( 27^{\circ}\text{C} \). The ratio of root mean square speed of molecules of two gases will be : (atomic mass of Argon = 40 u and molecular mass of Chlorine = 71 u)