Light from a point source in air falls on a spherical glass surface. If \(\mu = 1.5\) and radius of curvature \(= 20\) cm. The distance of light source from the glass surface is 100 cm, at what position will the image be formed?

You are given three magnetic needles \( N_F, N_P \) and \( N_D \) made up of ferromagnetic, paramagnetic and diamagnetic materials respectively. If a magnet is brought close to each of the needle one by one, then the magnet will :

In a potentiometer, a cell is balanced at 240 cm. On shunting the cell with 2 \(\Omega\) resistance, the balancing comes at 120 cm. What is the internal resistance of the cell ?

A metal cube of side 0.1 m is uniformly charged by 18 \( \mu C \). Its surface charge density will be

A freshly prepared radioactive sample of half life 1 hour emits radiations that are 128 times as intense as the permissible safe limit. What is the minimum time after which the sample can be safely used?

Match List-I with List-II for a cyclotron

LIST I	LIST II
(A) Frequency of revolution of charged particle	(I) Bqv
(B) Velocity of charged particle	(II) \(\frac{q^2 B^2 R^2}{2m}\)
(C) Kinetic energy of charged particle	(III) \(\frac{qBR}{m}\)
(D) Force on charged particle when it is inside	(IV) \(\frac{B q}{2 \pi m}\)

Identify the correct statement(s).
(A) In any lens, the optical centre is always at the centre of the lens.
(B) In a lens, if the curvature of its two surfaces is equal, the optical centre is at the centre of the lens.
(C) A light ray passing through the optical centre of a lens never shifts from the direction of the incident ray.
(D) A ray of light incident perpendicularly on a lens passes through its focus after refraction.
Choose the correct answer from the following given options.

When a magnet is being brought towards a coil, the emf induced in the coil does not depend on:

Magnetic susceptibility \(X\) of a given material is \(- 0 . 5\). Identify the magnetic material.

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.
When phenol is treated with concentrated sulphuric acid, then it gets converted into phenol-2,4-disulphonic acid \(( X )\). On further treatment of X with conc. nitric acid, product Y is formed. Identify Y .

A resistor develops 800 J of thermal energy in 20 s on applying a potential difference of 20 V. Its resistance is

Identify the free living nitrogen fixing bacteria
A. Rhizobium
B. Mycorrhiza
C. Azospirillum
D. Azotobacter
Choose the correct answer from the options given below:

The general solution of the differential equation \(\left(1+e^x\right) d y+y e^x d x=0\), where \(y>0\), is