The displacements of four light waves are given below. If the amplitudes \( a_1 \) and \( a_2 \) are nearly equal, then the interference fringes may be observed due to superposition of:
(A) \( y = a_1 \sin \omega t \)
(B) \( y = a_2 \sin (\omega t + \phi) \)
(C) \( y = a_1 \sin 2\omega t \)
(D) \( y = a_2 \sin 3(\omega t + \phi) \)

The current through a 4/3 \(\Omega\) external resistance connected to a parallel combination of two cells with emfs of 2 V and 1 V, internal resistances 1 \(\Omega\) and 2 \(\Omega\) respectively, is :

A light of wavelength of \( \lambda = 6 \times 10^{-7} \text{ m} \) illuminates a single slit of width \( a = 1.2 \text{ mm} \). The screen is at a distance of \( D = 2.4 \text{ m} \) away from the slit. The width of central maximum (\( \beta_0 \)) is

When a slab of insulating material 4 mm thick is introduced between the plates of a parallel plate capacitor of separation 4 mm, it is found that the distance between the plates has to be increased by 3.2 mm to restore the capacity to its original value. The dielectric constant of the material is :

A point charge – 5 µC is at a distance 5 cm directly above the centre of a square of side 10 cm.
The magnitude of electric flux through this square is:

A charged particle moving with a certain velocity enters a uniform electric field perpendicular to its direction. In this context, which of the following statements are correct?
(A) Force acting on the particle is constant
(B) Acceleration of the particle is constant
(C) Velocity of the particle is constant
(D) Displacement of the particle follows a parabolic path
Choose the correct answer from the options given below:

Arrange the following nuclei in the ascending order of their stability.
(A) Oxygen (\( {}^{16}\text{O} \)) with binding energy 127.5 MeV
(B) Uranium (\( {}^{238}\text{U} \)) with binding energy 1808.8 MeV
(C) Helium (\( {}^{4}\text{He} \)) with binding energy 28.3 MeV
(D) Iron (\( {}^{56}\text{Fe} \)) with binding energy 490 MeV
Choose the correct answer from the options given below:

A current change of 6 A in one coil causes the flux in the second coil of 2000 turns to change by \(12 \times 10^{-4} \text{ Wb}\) per turn. The mutual inductance of the pair of coils would be:

Match the complex given in List-I with type of hybridisation given in List-II.

List-I (Complex)	List-II (Hybridisation)
(A) \([Ni(CO)_4]\)	(I) \(sp^3d^2\)
(B) \([Ni(CN)_4]^{2-}\)	(II) \(dsp^2\)
(C) \([Co(NH_3)_6]^{3+}\)	(III) \(d^2sp^3\)
(D) \([CoF_6]^{3-}\)	(IV) \(sp^3\)

Choose the correct answer from the options given below:

Three pipes \(A, B\) and \(C\) can fill a tank in \(12\) hours, \(15\) hours and \(20\) hours respectively. If A is open all the time and \(B\) and \(C\) are open for one hour each alternately, in how many hours will the tank be full?

The magnetic flux passing perpendicular to the plane of a coil is changing according to the equation \( \Phi = 6t^2 + 7t + 1 \) where \( \Phi \) is in mWb and t is in seconds. The magnitude of induced emf at t = 2 s is:

Read the following paragraph and answer the given questions.
Cancer detection is based on biopsy and histopathological studies. Techniques like radiography (use of X-rays), CT (computed tomography) and MRI (magnetic resonance imaging) are very useful to detect cancers of the internal organs. Do you know why mother's milk is considered very essential for the new-born infant? The yellowish fluid colostrum secreted by mother during the initial days of lactation has abundant antibodies (IgA) to protect the infant. Different species of Plasmodium (P. vivax, P. malaria and P. falciparum) are responsible for different types of malaria. Of these, malignant malaria caused by Plasmodium falciparum is the most serious one and can even be fatal. The exaggerated response of the immune system to certain antigens present in the environment is called allergy. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Drugs like barbiturates, amphetamines, benzodiazepines, and other similar drugs, that are normally used as medicines to help patients cope with mental illnesses like depression and insomnia, are often abused. Morphine is a very effective sedative and painkiller, and is very useful in patients who have undergone surgery.
A pregnant female is advised not to discard the yellowish fluid called colostrum, secreted during the initial days of lactation, because it is rich in:

Match List - I with List - II.

List - I (Process)	List - II (Metal)
A. Electrolytic reduction	I. Iron
B. Bessemerization	II. Zinc
C. Smelting	III. Aluminium
D. Reduction from oxide	IV. Copper

Choose the correct answer from the options given below: