Question Paper (Section wise)
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1) 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:
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0.9 N
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0.6 N
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0.1 N
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3 ×10-2N
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2) 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:
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3) 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 )
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R
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4) Taking the wavelength of first Balmer line in hydrogen spectrum ( n = 3 to n = 2 ) as 660 nm, the wavelength of the 2nd Balmer line ( n = 4 to n = 2 ) will be
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889.2 nm
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642.7 nm
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448.9 nm
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388.9 nm
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5) 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?
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3.75 × 10-6 J
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2.55 × 10-6 J
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6.25 × 10-6 J
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2.16 × 10-6 J
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6) 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?
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1.5 kg
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1.2 kg
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1.8 kg
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1.0 kg
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7) 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:
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Repulsive and equal to
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Attractive and equal to
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Zero
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Repulsive and equal to
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8) A string is clamed at both the ends and it is vibrating in its 4th harmonic. The equation of the stationary wave is Y =0.3 sin ( 0.157x ) cos ( 200Ï€t ). The length of the string is: ( all quantities are in SI units )
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80 m
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60 m
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40 m
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20 m
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9) 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:
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10) 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:
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12°C
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11°C
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15°C
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4°C
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1) Among the following, the molecule expected to be stabilized by anion formation is:
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F2
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C2
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O2
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NO
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2) The degenerate orbitals of [ Cr(H2O)6 ]3+Â Â are:
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dxz and dyz
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dx2-y2 and dxy
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dyz and dz2
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dz2 and dxz
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3) 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:
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4) The major product of the following reaction is:
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CH3CD(I)CHD(CI)
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CH3C(I)(CI)CHD2
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CH3CD2CH(CI)(I)
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CH3CD(CI)CHD(I)
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5) The standard Gibbs energy for the given cell reaction in kJ mol-1 at 298 K is:
[Faraday’s constant F = 96000 C/mol
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-192
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384
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-384
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192
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6) Which of the following statements is not true about sucrose?
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The glycosidic linkage is present between C1 of α-glucose and C1 of β-fructose
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It is a non-reducing sugar
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It is also named as invert sugar
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On hydrolysis it produces glucose and fructose
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7) Match the catalysis (Column – I ) with products ( Column –II )
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(a)-(iii); (b)-(iv); (c)-(i); (d)-(ii)
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(a)-(iv); (b)-(iii); (c)-(ii); (d)-(i)
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(a)-(ii); (b)-(iii); (c)-(i); (d)-(iv)
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(a)-(iii); (b)-(i); (c)-(ii); (d)-(iv)
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8) The major product of the following reaction is:
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9) C60, an allotrope of carbon contains:
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20 hexagons and 12 pentagons.
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12 hexagons and 20 pentagons.
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18 hexagons and 14 pentagons.
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16 hexagons and 16 pentagons.
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10) 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:
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HCOONa
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CH3COONa
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Na2C2O4
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C6H5COONa
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1) The solution of the differential equation
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2) 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:
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( A, 50 + 46A )
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( A, 50 + 45A )
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( 50, 50 + 45A )
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( 50, 50 + 46A )
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3) is continuous, then k is equal to:
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1
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2
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4) 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:
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5) Â
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6) The area ( in sq. units ) of the region A = { ( x, y ): x2 ≤ y ≤ x + 2 } is:
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7) 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:
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8) Let S = { θ ϵ [ -2π, 2π ]: 2 cos2θ + 3 sin θ = 0 }. Then the sum of the elements of S is:
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2Ï€
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Ï€
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4
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16
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2
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3
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10) -
y (y2 – 3)
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y3 – 1
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y3
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y (y2 – 1)
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