A bar magnet of magnetic moment 3 J/T lies aligned with the directions of a uniform magnetic field of 0.2 T. The amount of work, required so as to align its magnetic moment opposite to the field direction is :

The lateral shift produced by a glass slab during refraction through it, increases with -
(A) the increase in the thickness of the glass slab
(B) the increase in the value of the angle of incidence
(C) the increase in the value of the refractive index of the slab
(D) the increase in the length of the glass slab
Choose the correct answer from the options given below:

The frequency of revolution of an electron revolving in a circular path in a magnetic field of \( 7.8 \times 10^{-4} \, \text{T} \) will be (Take \( e = -1.6 \times 10^{-19} \, \text{C} \), \( m_e = 9.1 \times 10^{-31} \, \text{kg} \), \( \pi = 22/7 \))

Two coils have a mutual inductance 0.005 H . The current changes in the first coil according to the equation \(I=I_0 \sin \omega t\), where \(I_0=10 A\), and \(\omega=100 \pi rad / s\). The maximum value of emf in the second coil is (in V) :

The linear charge density of an infinite line charge producing a uniform electric field of \(9 \times 10^6 N / C\) at a distance of 2 cm is :
(Take permittivity of vacuum \(\epsilon_0=8.85 \times 10^{-12} C ^2 N^{-1} m^{-2}\) )

For a heavily doped n-type semiconductor, Fermi level lies:

The focal length of a thin lens in vacuum is f. If the material of the lens has refractive index \( \frac{3}{2} \), its focal length when immersed in water of refractive index \( \frac{4}{3} \) would be :

Match List I with List - II.

List - I	List - II
(A) A community that is in near equilibrium with the environment	(I) Ecological succession
(B) The entire sequence of communities that successively change in a given area	(II) Xerarch succession
(C) A gradual and fairly predictable change in species composition of an area	(III) Climax community
(D) Succession of plants in dry areas	(IV) Sere(s)

Choose the correct answer from the options given below :

If \(y=\log \left(x+\sqrt{x^2+a^2}\right)\) then \(\frac{d y}{d x}\) =

Read the following passage carefully and answer the given questions.
Bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus Trichoderma polysporum. Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by competitively inhibiting the enzyme responsible for synthesis of cholesterol. Baculoviruses are pathogens that attack insects and other arthropods. The majority of baculoviruses used as biological control agents are in the genus Nucleopolyhedrovirus. These viruses are excellent candidates for species-specific, narrow spectrum insecticidal applications. They have been shown to have no negative impacts on plants, mammals, birds, fish or even on non-target insects. BOD refers to the amount of the oxygen that would be consumed if all the organic matter in one liter of water were oxidised by bacteria. The sewage water is treated till the BOD is reduced. Cheese, is one of the oldest food items in which microbes were used. Different varieties of cheese are known by their characteristic texture, flavour and taste. For example, the large holes in ‘Swiss cheese’ are due to production of a large amount of CO₂ by a bacterium named Propionibacterium sharmanii.
Bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus

The correct order of increasing acidic strength is
(A) Ethanol
(B) Phenol
(C) Chloroacetic acid
(D) Acetic acid
Choose the correct answer from the options given below:

At room temperature (\(25.0^\circ C\)) the resistance of a heating element is \(100 \Omega\). The temperature of the element at which resistance becomes \(125.5 \Omega\) is : (Given that the temperature coefficient of the material of the resistor is \(1.70 \times 10^{-4} \text{ } ^\circ C^{-1}\))

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?