A long solenoid has 500 turns. When a current of 2 A is passed through it, the resulting magnetic flux linked with each turn of the solenoid is \(4 \times 10^{-3} Wb\). The self-inductance of the solenoid is

A symmetrical double convex lens is cut into two equal parts by a plane containing the principal axis. The power of the divided lens is :

A sample of radioactive nuclei has a half life of 5.5 years. The fraction of sample remaining undecayed after 22 years is

Identify the basic features of the photon picture of electromagnetic radiation from the following:
(A) Each photon has energy \(E = h\nu\) in vacuum.
(B) Photons are electrically neutral and are not deflected by electric and magnetic fields.
(C) All photons of light of a particular frequency \(\nu\) or wavelength \(\lambda\) have the same energy and momentum.
(D) If the intensity of light of a given wavelength is increased, there is an increase in the number of photons incident on a given area in a given time.
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A 50 cm long air core solenoid has a 2 cm radius and 500 turns. The self-inductance of the solenoid would be (given \(\mu_0=4 \pi \times 10^{-7} \operatorname{Tm} * A^{-1}\) and \(\pi^2=10\) )

A wire of length 4 m carrying current I A is bent in the form of a circle. Its magnetic moment will be :

What are the respective numbers of \( \alpha \) and \( \beta \) particles emitted respectively in the following radioactive decay?
\( {}^{200}_{90}X \rightarrow {}^{168}_{80}Y \)

The unit of Boiling point Elevation Constant (\(K_b\)) is

Match List-I with List-II

List-I  (Geological periods)	List-II (Plant forms)
(A) Cretaceous	(I) Seed ferns
(B) Jurassic	(II) Progymnosperms
(C) Carboniferous	(III) Sphenopsids
(D) Devonian	(IV) Conifers

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Which of the following is true ?
(A) The equilibrium of a charged particle under the action of coulomb force alone can never be stable.
(B) A hollow metal sphere placed on an insulating stand is charged positively. The electric potential inside is same as on surface
(C) A free electron and a free proton are placed in a uniform field, both will experience same magnitude of the force
(D) A free electron and a free proton are placed in a uniform field, both will experience same acceleration
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Maximum value of the objective function Z = 4x + 3y subject to the constraints \(x+y \geq 4, x \geq 4, y \geq 0\) exists at

Which one of the following cause of biodiversity loss is reflected in the phrase "need turns to greed"?

Answer the question on the basis of passage given below :
Nitrogen differs from rest of the members of group 15 due to its small size, high electronegativity, high ionization enthalpy and non-availability of d orbitals. Nitrogen has unique ability to form pa - pa multiple bonds with itself and with other elements having small size and high electronegativity. Heavier elements of this group do not form pa - pr bonds as their atomic orbitals are so large and diffuse that they cannot have effective overlapping.
Planar structures with \(N - N\) single bond are shown by
A. \(N _2 O _3\)
B. \(N _2 O _4\)
C. \(N _2 O _5\)
D. \(N _2 O\)
E. \(NO\)
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