In a series LCR circuit an ac voltage source is connected. When inductor is removed from the circuit, the phase difference between the voltage and the current in the circuit is \( \frac{\pi}{3} \). If capacitor is removed from the circuit instead of inductor, the phase difference is again \( \frac{\pi}{3} \). What is the power factor of the circuit?

For a long wire carrying a current of \( 10 \text{ A} \), the magnitude of magnetic field at a point \( 4 \text{ cm} \) away from it will be :

Electrical potential V and electric flux \( \phi \) are :

When a dielectric slab is introduced in between the plates of a charged capacitor with battery connected across the plates, following are the observations. Choose which observation is incorrect?

A double convex lens of refractive index 1.5 has a radius of curvature R each. The focal length of the lens is

A resistor of resistance R, an inductor of \((20/\pi) \text{ H}\) and a capacitor of \((5/\pi) \mu F\) are connected in series to a voltage source of 220 V, 50 Hz. The value of current in the circuit is 4 A. The impedance of the circuit is

Rainbow is a phenomenon due to the combined effect of
(A) Interference
(B) Dispersion
(C) Reflection
(D) Refraction
(E) Scattering
Choose the correct answer from the options given below:

On the basis of the information available from the reaction:
\(\frac{4}{3}Al+O_2\rightarrow \frac{2}{3}Al_2O_3, \Delta G = -827 kJ/mol\)
The minimum e.m.f required to carry the electrolysis of \(Al_2O_3\) is (\(F = 96500 C\ mol^{-1}\)):

A ray of light passes through an equilateral glass prism such that the angle of incidence (i) = angle of emergence (e). If the angle of emergence is 0.75 times the angle of the prism, the refractive index of the prism will be

An electric dipole of dipole moment \(5 \times 10^{-6} \mathrm{Cm}\) is placed in a uniform electric field of \(10^{-2} \mathrm{~N} / \mathrm{C}\) making an angle of \(30^{\circ}\) with the direction of the field. The torque exerted by the electric field on the dipole is:

Salicylaldehyde is formed as a main product from phenol by :

Which of the following is related to DNA Replication?
(A) DNA ligase
(B) DNA-dependent RNA polymerase
(C) Rho factor
(D) Replication fork
Choose the correct answer from the options given below:

Read the given paragraph and answer the question:
Humans have 23 pairs of chromosomes. 22 pairs are exactly same in both males and females; these are the autosomes. A pair of X-chromosome are present in the female, whereas the presence of an X and Y chromosome are determinant of the male characteristic.
A number of disorders in human beings have been found to be associated with the inheritance of changed or altered genes or chromosomes. Broadly, genetic disorder may be grouped into two categories-Mendelian disorders and Chromosomal disorders.
A haemophilic man marries a normal woman. What is the possibility that their child have haemophilia?