Question Paper (Section wise)

The magnetic field of a plane electromagnetic wave is given by:

 Where B₀ = 3 × 10^-5 T and B₁ = 2 ×10^-6 T. The rms value of the force experienced by a stationary charge Q = 10^-4 = C at z = 0 is closet to:

A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of θ, where θ is the angle by which it has rotated, is given as kθ². If its moment of inertia is I then the angular acceleration of the disc is:

A wire of resistance R is bent to form a square ABCD as shown in the figure. The effective resistance between E and C is: ( E is mid-point of arm CD )

Taking the wavelength of first Balmer line in hydrogen spectrum ( n = 3 to n = 2 ) as 660 nm, the wavelength of the 2^nd Balmer line ( n = 4 to n = 2 ) will be

A capacitor with capacitance 5 μF is charged to 5 μC. If the plates are pulled apart to reduce the capacitance to 2 μF, how much work is done?

A body of mass 2 kg makes an elastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass of the second body?

A rigid square loop of side ‘a’ and carrying current I₂ is laying on a horizontal surface near a long current I₁ wire in the same plane as shown in figure. The net force on the loop due to the wire will be:

A string is clamed at both the ends and it is vibrating in its 4^th harmonic. The equation of the stationary wave is Y =0.3 sin ( 0.157x ) cos ( 200πt ). The length of the string is: ( all quantities are in SI units )

A solid sphere of mass ‘M’ and radius ‘a’ is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at distance ‘3a’ from the centre will be:

The pressure wave, P = 0.01 sin [ 1000t – 3x ] NM^–2, corresponds to the sound produced by a vibrating blade on a day when atmospheric temperature is 0°C. On some other day when temperature is T, the speed of sound produced by the same blade and at the same frequency is found to be 336 ms^–1. Approximate value of T is:

Among the following, the molecule expected to be stabilized by anion formation is:

The degenerate orbitals of [ Cr(H₂O)₆ ]³⁺   are:

Aniline dissolved in dilute HCl is reacted with sodium nitrite at 0^° C. This solution was added drop wise to a solution containing equimolar mixture of aniline and phenol in dil. HCl. The structure of the major products is:

The major product of the following reaction is:

The standard Gibbs energy for the given cell reaction in kJ mol^-1 at 298 K is:

[Faraday’s constant F = 96000 C/mol

Which of the following statements is not true about sucrose?

Match the catalysis (Column – I ) with products ( Column –II )

The major product of the following reaction is:

C₆₀, an allotrope of carbon contains:

Sodium salt of an organic acid ‘X’ produces effervescence with conc. H₂SO₄. ‘X’ reacts with the acidified aqueous CaCl₂ solution to give a white precipitate which decolourises acidic solution of KMnO₄. ‘X’ is:

The solution of the differential equation

Let the sum of the first n terms of a non-constant A.P., a₁, a₂, a₃, ……… be, where A is a constant. If d is the common difference of this A.P., then the ordered pair ( d, a₅₀ ) is equal to:

is continuous, then k is equal to:

Slope of a line passing through P( 2, 3 ) and interesting the line, x + y = 7 at a distance of 4 units from P, is:

The area ( in sq. units ) of the region A = { ( x, y ): x² ≤ y ≤ x + 2 } is:

Let S be the set of all values of x for which the tangent to the curve y = f ( x ) = x³ – x² – 2x at ( x, y ) is parallel to the line segment joining the points ( 1, f ( 1 ) ) and ( -1, f ( -1 ) ), then S is equal to:

Let S = { θ ϵ [ -2π, 2π ]: 2 cos²θ + 3 sin θ = 0 }. Then the sum of the elements of S is: