Two parallel beams of monochromatic light pass through a long slit of width 0.2 mm one by one. The angular divergence in which most of the light is diffracted for both the beams are \( 2.25 \times 10^{-3} \text{ rad} \) and \( 4.50 \times 10^{-3} \text{ rad} \) respectively. If the wavelength of the first beam is \( \lambda_1 = 3000 \text{ Å} \), then the wavelength of the second beam is:

Choose the correct statements from following:
A. Resistivity of a conductor increases with increase in its length.
B. When a small resistor is connected in parallel across a galvanometer, it is converted into ammeter.
C. Current density is a vector quantity.
D. Potentiometer is used to measure the electric current.
E. Kirchoff's junction rule is based on the conservation of charge.
Choose the correct answer from the options given below:

In a double slit experiment, if the distance between the slits be reduced to half, then the new fringe width will be

In a compound microscope the focal length of objective lens and eye lens are 4 em and 10 cm respectively. An object is placed at 6 cm from the objective lens. If the final image is formed at the near point of eye, then the magnifying power of microscope is:

A potentiometer wire has a uniform potential gradient. The specific resistance of the material of the wire is \(10^{-7} \text{ ohm-m}\), the current passing through it is 0.1 A and its cross-sectional area is \(10^{-6} \text{ m}^2\). What is the value of the potential gradient?

The term 'mobility' is:

Identify the incorrect statements from the following.
(A) A charged particle of charge e is moving through a magnetic field, work will be done by the magnetic field on the charge.
(B) A conductor with free electrons is placed in a magnetic field. No current is flowing through the conductor. No magnetic force acts on the conductor.
(C) A charged particle is moving perpendicular to the magnetic field. The magnetic force does not change the speed of the particle but changes its direction.
(D) A charged particle is moving in a straight direction without any change of direction. It shows that no magnetic field is there.
Choose the correct answer from the options given below:

Match List-l with List-II

List-l	List-II
A. Methyl alcohol	I. Highly poisonous
B. Ethyl alcohol	II. Carbolic acid
C. Phenol	III. Highly soluble in water
D. Picric acid	IV. Turns blue litmus red

Choose the correct answer from the options given below :

Two point charges \(+3 \mu C\) and \(-8 \mu C\) attracts each other with a force of 40 N , when separated by finite distance d . If a charge of \(+5 \mu C\) is added to each of them, then the force between them will become:

Read the following passage carefully.
Restriction enzyme
Restriction enzymes cut the strand of DNA a little away from the center of the palindrome sites, but between the same two bases on the opposite strands. This leaves single stranded portions at the ends. There are overhanging stretches called sticky ends on each strand. These are named so because they form hydrogen bonds with their complementary cut counterparts. This stickiness of the ends facilitates the action of the enzyme DNA ligase. The word palindromes refer to group of letters that forms the same words when read both forward and backward. Restriction endonucleases are used in genetic engineering as molecular scissors.
Which bond forms on sticky end of each strand?

Which one represents the correct reduction reaction for the \(Cu^{2+}/Cu\) half-cell?

Grignard reagent should be prepared under anhydrous condition because

The number of arbitrary constants in the particular solution of a differential equation of order 4 and degree 3 is