A cylindrical coil of radius \(r\), having \(n\) turns per unit length and carrying a current \(I\) has a magnetic field near its end equal to:

Light of frequency \( \nu \) falls on a metal whose work function is \( h\nu_0 \). Choose the most appropriate condition from the following under which the photoelectric effect will take place.

Which of the following statements are correct?
A. Number of photoelectrons emitted per second is directly proportional to the intensity of incident radiation
B. Cut off potential is the minimum negative potential given to the plate for which photocurrent becomes maximum
C. For a given frequency of the incident radiation, the stopping potential is independent of its intensity
D. Even for the exceedingly dim incident radiation apparent time lag is \( \sim 10^{-9} \) s or less
E. Photons are electrically neutral and are not deflected by electric and magnetic fields
Choose the correct answer from the options given below:

Three concentric metallic spherical shells of radii \( R, 2R \), and \( 3R \) are given charges \( Q_1, Q_2 \) and \( Q_3 \), respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells \( Q_1 : Q_2 : Q_3 \) is:

The half life of a radioactive nuclide is 20 hours. What fraction of original activity will remain after 80 hours ?

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 similar magnetic poles having pole strengths in the ratio 1 : 4 are placed 6 cm apart. The distance from a smaller pole in strength where net magnetic field is zero will be :

Which of the complexes give white precipitate when treated with aqueous solution of \(BaCl_2\)?
\(\left[ Co \left( NH _3\right)_5 SO _4\right] Cl\)
\(\left[ Co \left( NH _3\right)_5 Cl \right] SO _4\)
\(\left[ Co \left( NH _3\right)_5\left( NO _2\right)\right]\left( NO _2\right)_2\)
\(\left[ Co \left( NH _3\right)_5 CN \right] SO _4\)
Choose the correct answer from the options given below :

A 10 pF capacitor is connected to a 24 V battery. The electrostatic energy stored in the capacitor is:

The conversions which are represented correctly are
(A)

(B)

(C)

(D)

Choose the correct answer from the options given below:

What will be the product of the following reaction :
\(C_6H_5ONa + C_2H_5Cl \rightarrow ?\)

Identify the correct statements.
(A) A concave mirror is preferred over a plane mirror for the purpose of shaving.
(B) The absolute refractive index of a medium can be less than unity.
(C) Snell's law gives the relative refractive index of a medium.
(D) When a convex lens is placed inside a transparent medium of refractive index greater than that of its own material, it behaves as a diverging lens.
Choose the correct answer from the options given below:

Two parallel beams of monochromatic light pass through a long slit of width 0.2 mm one by one. The angular divergence in which most of the light is diffracted for both the beams are \( 2.25 \times 10^{-3} \text{ rad} \) and \( 4.50 \times 10^{-3} \text{ rad} \) respectively. If the wavelength of the first beam is \( \lambda_1 = 3000 \text{ Å} \), then the wavelength of the second beam is: