The magnetic field in a plane electromagnetic wave is given by \( B_y = 2 \times 10^{-7} \sin(0.5 \times 10^3 x + 1.57 \times 10^{11} t) \text{ T} \). The frequency of the wave is

If \( \mu_0 \) is the permeability and \( \epsilon_0 \) is the permittivity of free space, then the velocity of light (c) is:

The angle of minimum deviation of an equilateral prism is equal to its refracting angle. The refractive index of the material of the prism is :

What will be the time taken by light to travel 2 cm thickness of glass of refractive index 1.5?

At any instant t the values of voltage applied and the current through a series LCR circuit are given as : \( V = \frac{1}{\sqrt{2}} \sin(100\pi t) \text{ V}, I = \frac{1}{\sqrt{2}} \sin(100\pi t + \frac{\pi}{3}) \text{ A} \). The average power consumed in the circuit is given by :

The flux of the electric field \( \vec{E} = 2 \times 10^3 \hat{i} \text{ N/C} \) through a square of 10 cm, on a side whose plane is parallel to the \( xy \) plane is:

What is the magnification of simple microscope having focal length 5 mm?

"Answer the question on basis of passage given below :
Carboxylic acids are weaker than mineral acids, but they are stronger acids than alcohols and many simple phenols (\(\text{pKa}\) is ~ 16 for ethanol and 10 for phenol). The higher acidity of carboxylic acids as compared to phenols can be understood similarly. The conjugate base of carboxylic acid, a carboxylate ion, is stabilised by two equivalent resonance structures in which the negative charge is at the more electronegative oxygen atom. The conjugate base of phenol, a phenoxide ion, has non-equivalent resonance structures in which the negative charge is at the less electronegative carbon atom. Further, the negative charge is delocalised over two electronegative oxygen atoms in carboxylate ion whereas it is less effectively delocalised over one oxygen atom and less electronegative carbon atoms in phenoxide ion. Thus, the carboxylate ion is more estabilised than phenoxide ion, so carboxylic acids are more acidic than phenols.
Effect of substituents on the acidity of carboxylic acids: substituents may affect the stabliity of the conjugate base and thus, also affect the acidity of the carboxylic acids. Electron withdrawing group increase the acidity of carboxylic acids by stabilising the conjugate base through delocalisation of the negative charge by inductive and/or resonance effects. Conversely, electron donating groups decrease the acidity by destabilising the conjugate base.
The weakest among the following acid is :"

When two independent small samples of sizes \(n_1\) and \(n_2\) with means \(\bar{x}_1\) and \(\bar{x}_2\) respectively are drawn from populations with identical population variances, the test-statistic is computed as :

What is the increasing order of the oxidation state of the metal ion in following compounds?
(A). \(ScBr_{3}\)
(B). \(V_{2}O_{5}\)
(C). \(CrF_{6}\)
(D). \(Tc_{2}O_{7}\)
Choose the correct answer from the options given below:

The matrix \(A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 3 \end{bmatrix}\) then \(A^{-1}\) is equal to:

In a large building, there are 20 bulbs of 40 W each, 5 bulbs of 100 W each, 5 fans of 80 W each, and 1 heater of 1 kW. The voltage supply is 220 V. The minimum capacity of the main fuse of the building should be

The maximum value of the determinant of the matrix \(\left[\begin{array}{ccc}1 & 1 & 1 \\ 1 & 1+\sin x & 1 \\ 1+\cos x & 1 & 1\end{array}\right]\)
(where \(x\) is real) is :