A storage battery of emf 8.0 V and internal resistance 0.5 \(\Omega\) is being charged by a 60 V dc supply using a series resistor of 12.5 \(\Omega\). The terminal potential difference between the terminals of the battery during charging is

Which of the following is the correct equation for the law of radioactive decay?
(Symbols have their usual meaning.)

Four identical bulbs are connected in series with a source. These together dissipate a power P. The power dissipated, if the four bulbs are connected in parallel with the same source, will be

A telescope has an objective of focal length \(3 0 ~ c m\) and an eyepiece of focal length \(3 . 0 ~ c m\). It is focused on a scale distant 2.0 m . For seeing with relaxed eye, the separation between the objective and eyepiece would be:

Choose the correct relation between drift velocity (\( v_d \)) and current density (\( J \)) from the following:

If a match box of size \( 5 \text{ cm} \times 4 \text{ cm} \times 1 \text{ cm} \) is filled with nuclear matter, what will be its expected mass? The density of nuclear matter is approximately \( 2.3 \times 10^{17} \text{ kg/m}^3 \).

If in a plano-convex lens, the radius of the convex surface is 10 cm and the focal length is 30 cm. Then the refractive index of the material will be :

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'?

Intermolecular hydrogen bonding is observed between chloroform and acetone.
Therefore, their binary solution will_
(A) Show positive deviation from Raoult's law
(B) Show negative deviation from Raoult's law
(C) Obey Raoult's law
(D) Show decrease in vapor pressure
Choose the correct answer from the options given below:

When a slab of insulating material 4 mm thick is introduced between the plates of a parallel plate capacitor of separation 4 mm , it is found that the distance between the plates has to be increased by 3.2 mm to restore the capacity to its original value. The dielectric constant of the material is

The dipole moment of a circular loop carrying a current I is m and the magnetic field at the centre of the loop is \( B_1 \). When the dipole moment is made three times by keeping the current I same, the magnetic field at the centre of the loop becomes \( B_2 \). The ratio of \( B_1 \) and \( B_2 \) is:

Transfer of genetic message from sequences of nitrogenous bases to
sequences of amino acids is called -

For the LPP, Min \(z=6 x+10 y\) subject to \(x \geq 6, y \geq 3,2 x+y \geq 10, x \geq 0, y \geq 0\), redundant constraint is: