Which of the following statements are correct?
(A) Kirchhoff's loop rule represents energy conservation.
(B) Resistivity is a property of the material and depends on temperature.
(C) The electrical conductivity of the material does not depend on the material of the conductor and its temperature.
(D) The emf of a battery equals the potential difference between its terminals when the terminals are connected externally.
Choose the correct answer from the options given below:

A rectangular coil of sides 2 cm and 5 cm having 2000 turns and carrying a current of 200 mA is placed in a uniform magnetic field of 5.0 T directed along positive X-axis. The maximum torque experienced by the coil is

On an optical bench of 150 cm, a student used a concave mirror of focal length 20 cm to observe object distance (u) and image distance (v) respectively as :
(A) (40 cm, 10 cm)
(B) (60 cm, 15 cm)
(C) (80 cm, 38 cm)
(D) (60 cm, 30 cm)
(E) (40 cm, 40 cm)

If \( \vec{M} \) is magnetic moment and \( \vec{B} \) is magnetic field, then the torque (\( \vec{\tau} \)) is given by

\( (1/16) \)th of the initial amount of a certain radio-active isotope remains undecayed after two hours. The half life of the isotope would be :

A uniform electric field of 16 N/C exists in the vertically downward direction. The increase in electric potential as one goes up through a height of 75 cm.

Match List-I with List-II

List-I (Motion of a charge particle)	List-II (Path)
(A) Initial velocity of charge particle parallel to B	(I) Circular Path
(B) Initial velocity of charge particle perpendicular to B	(II) Helical Path
(C) Initial velocity of charge particle inclined to B	(III) Straight Path
(D) Initial velocity of charge particle perpendicular to E	(IV) Parabolic Path

Choose the correct answer from the options given below :

Read the given paragraph and answer the question:
Humans have 23 pairs of chromosomes. 22 pairs are exactly same in both males and females; these are the autosomes. A pair of X-chromosome are present in the female, whereas the presence of an X and Y chromosome are determinant of the male characteristic.
A number of disorders in human beings have been found to be associated with the inheritance of changed or altered genes or chromosomes. Broadly, genetic disorder may be grouped into two categories-Mendelian disorders and Chromosomal disorders
A colour blind man marries a carrier woman. Choose the possible progeny outcome.

The value of the determinant \(\left|\begin{array}{ccc}\cos ^2 \theta & \cos \theta \sin \theta & 0 \\ -\sin \theta & \cos \theta & 0 \\ 0 & 0 & 1\end{array}\right|\) is equal to

The least non-negative remainder when \(2^{75}\) is divided by 5 will be:-

Chemically, which of the following hormones is a polypeptide?

If \(x \cos (a+y)+\cos a \sin (a+y)=0\), then \(\frac{d y}{d x}\) is equal to

\(\int \frac{d x}{\sqrt{5-4 x-x^2}}\) is equal to :