When an \( \alpha \)-particle of mass M moving with velocity v bombards a heavy nucleus of charge Ze, its distance of closest approach from the nucleus depends on M as

A magnetic needle has magnetic moment of \( 5 \times 10^{-2} \, \text{Am}^2 \) and Moment of inertia \( 12 \times 10^{-6} \, \text{Kg m}^2 \). It performs 60 oscillations in 1 minute when suspended in a magnetic field. What is the magnitude of the magnetic field ?

The susceptibility of a paramagnetic material is \( \chi \) at \( 27^\circ \text{C} \). At what temperature will its susceptibility be \( \chi/3 \)?

A capacitor of capacitance C is first charged by a battery of V volts. It is disconnected from the battery and is filled with a dielectric of dielectric constant K. The ratio of energy stored in the two cases, respectively will be

Match List-I with List-II:

List-I (AC Circuit)	List-II (Phase Angle)
(A) Phase Difference between current and voltage in a pure inductive ac circuit	(I) zero
(B) Phase Difference between current and voltage in a pure resistive ac circuit	(II) \(\pi/2\), current lags voltage
(C) Phase Difference between current and voltage in a pure capacitive ac circuit	(III) \(\tan^{-1}(\frac{X_L - X_C}{R})\)
(D) Phase Difference between current and voltage in a series LCR circuit	(IV) \(\pi/2\), current leads voltage

Choose the correct answer from the options given below

Identify the correct statements among the following:
(A) The value of the electrostatic force constant, k depends on the medium between the two charges and on the choice of system of units.
(B) For two positively charged bodies, one more highly charged than the other, the force between them may be attractive.
(C) The charge on a body does change with its velocity.
(D) An electric dipole is a pair of two equal and similar charges placed at a very small distance.

If the magnetic flux through a coil of 1200 turns increases from zero to \(5.4 \times 10^{-5} \text{ Wb}\) in \(2.7 \text{ ms}\), what is the magnitude of the induced emf during this time?

The following system of equations has :
\(\begin{array}{l}x+2 y+3 z=1 \\x-y+4 z=0 \\2 x+y+7 z=1\end{array}\)

Match List-I with List-II

List-I (Evolutionary stages of human species)	List-II (Time of origin)
(A) Ramapithecus	(I) About 1.5 million years ago
(B) Neanderthal man	(II) About 2 million years ago
(C) Australopithecines	(III) 1,00,000-40,000 years ago
(D) Homo erectus	(IV) About 15 million years ago

Choose the correct answer from the options given below:

In order to link the alien DNA, the vector needs to have very few, preferably single, recognition sites for the commonly used restriction enzymes. Presence of more than one recognition sites within the vector will generate several fragments, which will complicate the gene cloning. In Biolistics or gene gun method cells are bombarded with high velocity micro particles of gold or tungsten coated with DNA. The ligation of alien DNA is carried out at a restriction site present in one of the two antibiotic resistance genes. For example, you can ligate a foreign DNA at the BamH I site of tetracycline resistance gene in the vector pBR322. Since the DNA is enclosed within the membranes, we have to break the cell open to release DNA along with other macromolecules such as RNA, proteins, polysaccharides and also lipids. The RNA can be removed by treatment with ribonuclease whereas proteins can be removed by treatment with protease. Other molecules can be removed by appropriate treatments and purified DNA ultimately precipitates out after the addition of chilled ethanol.
Which one of the following statements is correct with reference to biolistics?

One face of a prism of refractive index 1.5 and angle \(75^{\circ}\) is covered with a liquid of refractive index \(\frac{3 \sqrt{2}}{4}\).
What should be the angle of incidence of light on the clear face of prism for which light is just totally reflected at the liquid covered face?

The value of \(\int_1^2 \frac{\sqrt{x}}{\sqrt{3-x}+\sqrt{x}} d x\) is:

The far point of a myopic person is 80 cm. The power of corrective lens will be