For an ac source rated at 220 V, 50 Hz, which of the following statements is correct?

What is the magnetic force acting on a proton (charge \( + 1.6 \times 10^{-19} \text{ C} \)) moving at an angle of \( 30^{\circ} \) across a magnetic field of \( 5.3 \times 10^{-3} \text{ T} \) at a speed of \( 3.0 \times 10^5 \text{ m s}^{-1} \)?

An iron ring of relative permeability \( \mu_r \) is introduced inside a toroidal solenoid having n turns per meter. If the current in the solenoid is I, then the magnetic field in the ring is :

A long straight wire of radius 'a' carries a steady current 'I'. The current is uniformly distributed across its area of cross-section. The ratio of magnitude of magnetic fields \( B_1 \) at a distance a/2 and \( B_2 \) at a distance 2a from the axis of the wire is :

Assume that an electric field \( (20\hat{i}) \text{ V m}^{-1} \) exists in the region of space. If \( V_0 \) is the potential at the origin and \( V_A \) is the potential at \( x = 1 \text{ m} \), then the potential difference \( V_A - V_0 \) is :

Two long coaxial solenoids of the same length L have inner and outer coils with diameters \( D_1 \) and \( D_2 \) and number of turns \( N_1 \) and \( N_2 \), respectively. What will be the ratio of the self-inductance of the inner solenoid to the mutual inductance of both the solenoids?

The resistivity of a wire depends on :
(A) its length
(B) its area of cross-section
(C) its temperature
(D) nature of material
(E) voltage applied across it
Choose the correct answer from the options given below :

What is the wavelength of light for the least energetic photon emitted in the Lyman series of the hydrogen atom spectrum lines ?
(Take \( h = 6.63 \times 10^{-34} \text{ Js} \); \( c = 3 \times 10^8 \text{ ms}^{-1} \); \( e = 1.6 \times 10^{-19} \text{ C} \))

The number of all onto functions from the set \(\{1,2, \ldots, n\}\) to itself is

Read the passage carefully and answer the questions
The coordination compounds are of great importance. These compounds are widely present in the mineral, plants and animal world and are known to play many important functions in the area of analytical chemistry, metallurgy, biological systems, industry and medicine. For example, coordination compounds find use in many qualitative and quantitative chemical analysis. Some important metal extraction and purification make use of complex formation. Hardness of water can be estimated by stable complex formation of Ca\(^{2+}\) and Mg\(^{2+}\)
Wilkinson catalyst used for hydrogenation of alkenes is a complex of ___________.

The energy of a Hydrogen atom in its first excited state is

The solution of \(\frac{7 x+12}{x-9}<4, x \neq 9\) is:

Why the Fusion reaction takes place at high temperature among the nuclei, though these experience repulsion between them: