In a series LCR circuit, \( C = 80 \, \mu\text{F} \), \( L = 5.0 \, \text{H} \) and \( R = 40 \, \Omega \) are connected to a variable frequency source of 240 V. The angular frequency of the source which drives the circuit at resonance will be:

A coil of 500 turns is threaded by a magnetic flux of \( 7 \times 10^{-5} \text{ Wb} \). If the flux changes to \( 3 \times 10^{-5} \text{ Wb} \) in 0.01 s, what average induced emf is developed in the coil? If resistance offered by the coil is \( 10 \, \Omega \), then the flow of average induced current will be :

If the A.C. main supply is given to be 220 V in a circuit. The average emf during a positive half cycle is

A particle moves three times as fast as an electron. The ratio of the de Broglie wavelength of the particle to that of the electron is \( 1.813 \times 10^{-4} \). The mass of the particle is :

Resolving power of a telescope can be increased by increasing :

An electric dipole is placed at an angle of \(30^\circ\) with an electric field of intensity \(3 \times 10^5 \text{ N/C}\). It experiences a torque equal to \(6 \text{ N m}\). If the dipole length is 2 cm, the value of charge will be

If the two ends of a p-n junction are joined by a wire:

The peak value of the electric field associated with an electromagnetic wave traveling through vacuum is \( 8.1 \, \text{N}\cdot\text{C}^{-1} \). The peak value of the associated magnetic field will be:

Answer the question on the basis of passage given below :
One of the notable features of the transition element is the great variety of oxidation states it may show in its compounds. The elements which give the greatest number of oxidation states occur in or near the middle of the series. Manganese, for example exhibits all the oxidation states from +2 to +7. The lesser number of oxidation states at the extreme ends is either due to losing or sharing of few electrons (Sc, Ti) or too many d electrons of higher valence. Early in the first series scandium (II) is virtually unknown and titanium (IV) which is more stable than Ti (III) or Ti (II). On the other end, the only oxidation state of zinc is \(+ 2\).
For balancing the given reaction, value of \(x\) will be.
\(4 FeCr_2 O_4+Na_2 CO_3+7 O_2 \longrightarrow x Na_2 CrO_4+2 Fe_2 O_3+8 CO_2\)

If x is real, the minimum value of \(x^2-8 x+17\) is:

The mean of the number of heads in a simultaneous toss of three coins is

Hybridization of carbon atoms attached with halogens in haloalkanes \\& haloarenes are

What is the distance that a beam of light of wavelength 500 nm can travel without significant broadening, if the diffracting aperture is 3 mm wide ?