A wire of resistance \( 5\Omega \) is drawn out so that its length is increased by thrice its original length. The new resistance would be :

The ratio of the Nuclear density of the gold isotope \(^{197}_{79}\text{Au}\) and the silver isotope \(^{107}_{47}\text{Ag}\) is :

When a steady current flows in a metalic conductor of non-uniform cross section. Which of these quantities is constant along the conductor?
A. Current
B. Electric field
C. Drift speed
D. Current density
E. Potential gradient
Choose the correct answer from the options given below:

In Young's double slit experiment, the ratio of slit widths is 4 : 1. The intensity ratio in the interference pattern would be :

A change of current from 6.0 A to 3.0 A in 300 ms in a coil produces an induced emf of 0.5 V in the neighboring coil. The mutual inductance between the two coils would be

Diameter of the objective lens of a telescope is 250 cm. For light of wavelength 600 nm, coming from a distant object, the limit of resolution of the telescope is close to :

The de Broglie wavelength of an electron, a proton, and an alpha particle are represented by \(\lambda_e, \lambda_p, \lambda_\alpha\) respectively. If kinetic energy of electron, proton and alpha particle is same, then which of the following is correct.

If two substances A and B have \(P^o_A: P^o_B = 1 : 2\) and have mole fraction in the ratio \(1:2\), then mole fraction of A in vapours is:

If A is a skew-symmetric matrix of order n, then

Read the following passage carefully and answer the given questions
The earthworm is referred to as the farmer's friend. This is because they help in the breakdown of complex organic matter as well as in loosening of soil. Similarly, decomposers break down complex organic matter into inorganic substances like carbon dioxide, water and nutrients and the process is called decomposition. Dead plant remains such as leaves, bark, flowers and dead remains of animals, including fecal matter, constitute detritus, which is the raw material for decomposition. Some of the steps in the process of decomposition are fragmentation, catabolism, leaching, humification etc.
The degradation of detritus into simpler inorganic substances by the bacterial and fungal enzymes is called as-

The following have zero average value in a plane electromagnetic wave

Let \(A=\left[\begin{array}{ccc}1 & 2 & 1 \\ -1 & 3 & 2 \\ 2 & 4 & 1\end{array}\right]\) and \(M_{i j}, A_{i j}\) respectively denote the minor, co-factor of an element \(a_{i j}\) of matrix \(A\), then which of the following are true?
(A) \(M_{22}=-1\)
(B) \(A_{23}=0\)
(C) \(A_{32}=3\)
(D) \(M_{23}=1\)
(E) \(M_{32}=-3\)
Choose the correct answer from the options given below:

In Young's double slit experiment, the light has a frequency \( 12 \times 10^{14} \text{ Hz} \) and the distance between the centres of adjacent fringes is 0.8 mm. If the screen is 1.6 m away, what is the distance between the slits? (Take speed of light \( c = 3 \times 10^8 \text{ m s}^{-1} \))