Two solenoids of equal number of turns having their lengths and radii in the same ratio \(1: 3\). The ratio of their self inductances \(L _{ 1 }: L _{ 2 }\) will be :

The magnetic energy stored in an induction coil (choose the correct statement).

The power of a biconvex lens is 12 D and the radius of curvature of each surface is 10 cm. The refractive index of the material of the lens is

Identify the correct statements among the following.
(A) The number of electrons (\( n_e \)) is more than the number of holes (\( n_h \)) in intrinsic conductors.
(B) Semiconductors are elements (Si, Ge) type as well as compounds (GaAs, CdS).
(C) The number of charge carriers can be changed by 'doping' of a suitable impurity in pure semiconductors.
(D) Holes are essentially electron vacancies in a valence band.
Choose the correct answer from the options given below:

Four identical bulbs are connected in series with a source. These together dissipate a power P. The power dissipated, if the four bulbs are connected in parallel with the same source, will be

A monochromatic source emitting light of wavelength 600 nm has a power output of 66 W. The number of photons emitted by the source in 2 minutes is: (Given: \( h = 6.6 \times 10^{-34} \text{ Js} \))

The force between the plates of a parallel plate capacitor of capacitance C, distance between plates d and potential difference V is:

Let \(X\) and \(Y\) be any two invertible square matrices of order \(n\). Then which of the statements are true?
(A) \((A B)^{-1}=A^{-1} B^{-1}\)
(B) \((A B)^{-1}=B^{-1} A^{-1}\)
(C) \((A B)^T=A^T B^T\), where \(A^T\) denotes transpose of A
(D) \((A B)^T=B^T A^T\), where \(A^T\) denotes transpose of A
Choose the correct answer from the options given below :

The greatest integer function defined by \(f(x)=[2 x], 0 < x < 2\)

If \(\hat{i}, \hat{j}\) and \(\hat{k}\) are unit vectors along co-ordinates axes \(OX , OY\) and OZ respectively, then which of the following is/are true?
(A) \(\hat{i} \times \hat{i}=\overrightarrow{0}\)
(B) \(\hat{i} \times \hat{k}=\hat{j}\)
(C) \(i \cdot i=1\)
(D) \(\hat{ i } \cdot \hat{ j }=0\)
Choose the correct answer from the options given below:

Answer the question on basis of passage given below :
The noble gases have closed shell electronic configuration and are monatomic gases under normal conditions. The low boiling points of lighter noble gases are due to the weak dispersion forces between the atoms and the absence of other inter atomic interaction. The direct reaction of xenon with fluorine leads to a series of compounds with oxidation numbers \(+2, +4\) and \(+6\).
\(\text{XeF}_4\) reacts violently with water to give \(\text{XeO}_3\). The compound of Xenon exhibit stereoisomerism and their geometries can be deduced considering the total number of electrons in the valence shell.
\(X e F _4 \quad\) and \(X e F _6 \quad\) are expected to be :

The greatest biodiversity on the earth is seen in :

If \(A\) is square matrix of order \(3 \times 3\) and \(|\operatorname{adj} A|=64\), then the value of \(|5 A|\) is