Visible light of wavelength 600 nm falls normally on a single slit and diffraction pattern is obtained on a screen. It is found that the second diffraction minima is at \( \frac{\pi}{3} \). If the first minimum is obtained at \( \theta_1 \), then \( \theta_1 \) is:
Given: \( \sin 25^\circ = \frac{\sqrt{3}}{4} \)

Match List-I with List-II

List-I (Physical quantity)	List-II (Unit)
(A) Threshold frequency	(I) J
(B) Planck's constant	(II) V
(C) Work function	(III) 1/s
(D) Stopping potential	(IV) J s

Choose the correct answer from the options given below:

A uniform metallic wire of resistance \(4 \Omega\) is bent to form a circle. What is the effective resistance between the end of its diameter?

The Mutual inductance \(M _{12}\) of coil 1 with respect to coil 2-

In a series L, C and R circuit with an ac source of frequency \( \omega \), the current leads the voltage by \( \pi/4 \). The value of capacitance C will be

A metal wire under constant potential difference, when heated, shows that the drift velocity of the electron :

For a medium with permittivity \( (\epsilon) \) and permeability \( (\mu) \), the speed of light \( (v) \) is given by :

The statement that is NOT true about induced emf is :

p-block elements are placed in groups 13 to 18 of the periodic table. Group 15 is nitrogen family.
Nitrogen makes various compounds like \(NH _3, HNO _3, N_2 O , NO _2\) etc. Phosphorus exists in the form of white and red phosphorus. White phosphorus glows in dark. \(PH _3\) gas is used as smoke screen. Group 16 is called oxygen family. Dry air contains \(21% O_2\) gas by volume. Combined sulphur exists as sulphates such as gypsum, epsome salt, baryte etc. The allotropic forms of sulphur are Rhombic and monoclinic sulphur. \(S_2\) is paramagnetic like \(O_2\) and it stable at high temperature. Group 17 is Halogen family. \(F _2\) is highly reactive, \(Cl _2\) is greenish yellow gas. Both \(SO _2\) and \(Cl _2\) are used for bleaching. Group 18 is Noble gas family but some noble gases also form compounds.
Complete hydrolysis of \(XeF _6\) gives HF and \(XeO _3\) as main products. The permanent bleaching effect is caused by :

A uniformly charged infinite plane sheet of charge density \( 2 \times 10^{-8} \text{ C m}^{-2} \) is held in air.
What will be the separation between two equipotential surfaces in the region of electric field produced by the sheet, if the potential difference between them is 10 V? (\( \varepsilon_0 = 8.85 \times 10^{-12} \text{ C}^2\text{N}^{-1}\text{m}^{-2} \))

Read the passage carefully and answer the questions
Many halogen containing organic compounds are present in nature and some of them are clinically useful. These classes of organic compounds find a wide range of applications in our daily life as well as in industries. Many of the polyhalogen compounds are useful too in agriculture. However, some of these compounds cannot be easily decomposed and are thus considered to be environmental hazards. These halo compounds are prepared via different synthetic routes where a variety of organic compounds can be used as substrates such as amines, hydrocarbons etc. They are used as solvents for relatively non-polar compounds. These compounds exhibit substitution and elimination reactions, in addition to their reactions with different metals, which leads to the formation of a versatile starting material for others organic compounds.
The reaction of aryl halide with sodium and dry ether is known as

A proton enters a uniform magnetic field of 0.2 T with speed v. It describes a semicircular path of radius 5 cm and comes out of the field. The final speed of the proton will be

An emf of \( 0.5 \text{ V} \) is developed in the secondary coil, when current in primary coil changes from \( 5.0 \text{ A} \) to \( 2.0 \text{ A} \) in \( 300 \text{ milliseconds} \). The mutual inductance of two coils would be :