According to the Biot- Savart law, the magnetic field due to a current element is
(A) inversely proportional to the square of the distance from the current element to the point of interest.
(B) produced by a vector source.
(C) perpendicular to the plane containing the displacement vector and the current element.
(D) non-zero at any point in the direction of the current element.
Choose the correct answer from the options given below:

Time period of oscillation of a bar magnet in a uniform magnetic field is \( T_o \). The magnet is cut into 3 equal parts transverse to its length. The new time period of oscillation of one part will be :

Which of the following statements is correct?

Which of the following statement(s) is/are incorrect?
(A) A current carrying loop may act as a magnetic dipole whose magnetic moment may depend on its area and the number of turns.
(B) A linear solenoid carrying current, may act as a bar magnet.
(C) The magnetic lines of forces due to the current carrying solenoid makes closed curves like in a bar magnet.
(D) The magnetic field inside a solenoid is perpendicular to its axis.
Choose the correct answer from the given options:

The experimental circuit arrangements for studying V-I characteristics of a p-n junction diode are given below:

Identify the circuit for forward bias and for reverse bias.

The energy required to excite an electron in hydrogen atom to its first excited state is

The radius of a wire having resistance R is made half and its length reduced to one - fourth of its original length. The new resistance of the wire will be

Read the passage carefully and answer the given questions.
DNA Fingerprinting
Polymorphism in DNA sequence is the basis of genetic mapping of the human genome as well as of DNA fingerprinting. DNA fingerprinting involves identification of differences in some specific regions in the DNA sequence called repetitive DNA. It works on the principle of polymorphisms in DNA sequences. The repetitive DNA are separated from bulk genomic DNA. The bulk DNA forms a major peak and the other small peaks are referred to as satellite DNA. These repetitive/satellite DNA sequences show a high degree of polymorphisms and form the basis of DNA fingerprinting.
DNA polymorphism forms the basis of

At what rate of interest will the present value of a perpetuity of ₹ 500 payable at the end of every 6 months be ₹ 20,000 ?

Minimum value of the function \(f(x) = \sin(3x) + 5\) is equal to :

Match List-I with List-II

List-I (Reaction Name)	List-II (Reaction)
(A) Rosenmund Reaction	(I)
(B) Stephen Reaction	(II)
(C) Gattermann Koch Reaction	(III)
(D) Etard Reaction	(IV)

Choose the correct answer from the options given below:

If \(|\vec{a}|=3\) and \(|\vec{b}|=4\), then a value of \(\lambda\) for which \(\vec{a}+\lambda \vec{b}\) and \(\vec{a}-\lambda \vec{b}\) are perpendicular is :

The limiting molar conductivities for \(NaCl\), \(HCl\) and \(CH_3COONa\) are \(126.4\), \(425.9\) and \(91.0\ S\ cm^2\ mol^{-1}\), respectively. Calculate the limiting molar conductivity for acetic acid.