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The equivalent resistance of a series combination of two resistors is ‘s’. When they are connected in parallel, the equivalent resistance is ‘p’. If s = np, then the maximum value for n is ______. (Round off to the nearest integer)

Answer: (4) s = np R12+ R22+ 2R1R2 = nR1R2 R12+(2–n)R1R2 +R12 = 0 (Considering this quadratic equation, for real roots) b2 –... View Article

The radius in kilometre to which the present radius of the earth (R = 6400 km) to be compressed so that the escape velocity is increased 10 times is ______.

Answer: (64) Ves√R= constant Ves√R = 10Ves√R' R’ = R/100 = 64 KM... View Article

Two blocks (m = 0.5 kg and M = 4.5 kg) are arranged on a horizontal frictionless table as shown in figure

Two blocks (m = 0.5 kg and M = 4.5 kg) are arranged on a horizontal frictionless table as shown in figure. The coefficient of static friction... View Article

Consider two identical springs each of spring constant k and negligible mass compared to the mass M as shown

Consider two identical springs each of spring constant k and negligible mass compared to the mass M as shown. Fig.1 shows one of them and Fig. 2... View Article

For VHF signal broadcasting,_______ km² of the maximum service area will be covered by an antenna tower of height 30 m, if the receiving antenna is placed on the ground. Let the radius of the earth be 6400 km. (Round off to the nearest integer) (Take as 3.14)

Answer: (1206) r = √2hR Area = πr2(consider ‘r’ to be the maximum line of sight distance) Area = π(2hR) =... View Article

The following bodies a. a ring b. a disc c. a solid cylinder d. a solid sphere of same mass ‘m’ and radius ‘R’ are allowed to roll down without slipping simultaneously from the top of the inclined plane. The body which will reach first at the bottom of the inclined plane is________.

[Mark the body as per their respective numbering given in the question] Answer: (4) Acceleration of a body rolling down an inclined plane is,... View Article

If 2.5 × 10^-6 N average force is exerted by a light wave on a non-reflecting surface of 30 cm² area during 40 minutes of time span, the energy flux of light just before it falls on the surface is _______ W/cm². (Round off to the nearest integer) (Assume complete absorption and normal incidence conditions are there)

Answer: (25) Radiation pressure =Intensity/C (for absorbing surface) I = P × C I = 25 W/cm2... View Article

A parallel plate capacitor whose capacitance C is 14pF is charged by a battery to a potential difference V = 12 V between its plates. The charging battery is now disconnected and a porcelin plate with k = 7 is inserted between the plates, then the plate would oscillate back and forth between the plates, with a constant mechanical energy of ____ pJ. (Assume no friction)

Answer: (864) Initial energy stored in capacitor is, Ui =(½) cv2 = (½) × 14 × (12)2 pJ = 1008 pJ Final energy stored in... View Article

Which level of the single ionized carbon has the same energy as the ground state energy of hydrogen atom?

a. 8 b. 1 c. 6 d. 4 Answer: (c) En = –13.6(Z2/n2)(energy in nth state for hydrogen-like atom) Enth of Carbon = E1st of Hydrogen... View Article

When two soap bubbles of radii a and b (b > a) coalesce, the radius of curvature of common surface is

a. (b-a/ab) b. ab/(b-a) c. ab/(a+b) d. (a+b)/ab Answer: (b) P1– P0 = 4S/b P2– P0 = 4S/a P2– P1 = 4S/R→excess pressure at... View Article

A solenoid of 1000 turns per metre has a core with a relative permeability of 500. Insulated windings of the solenoid carry an electric current of 5 A. The magnetic flux density produced by the solenoid is: (Permeability of free space = 4 × 10^-7 H/m)

a. 2 × 10-3 πT b. π/5 c. 10-4πT d. πT Answer: (d) Magnetic flux density (B) will be, B = μn i B = μrμ0 ni B =... View Article

A current of 10 A exists in a wire of cross-sectional area of 5 mm²with a drift velocity of 2 × 10^-3 ms^-1. The number of free electrons in each cubic meter of the wire is ________

a. 1 × 1023 b. 2 × 106/ c. 2 × 1025 d. 625 × 1025 Answer: (d) Current through a wire is given by, I = neAVd n... View Article

A polyatomic ideal gas has 24 vibrational modes. What is the value of γ?

a. 1.03 b. 1.30 c. 10.3 d. 1.37 Answer: (a) f = 3T + 3R + 24×2V = 54 γ = 1+ (2/f) f = number of degrees of freedom due to... View Article

A boy releases a 0.5 kg ball on the frictionless floor with the speed of 20 ms^-1. The ball gets deflected by an obstacle on the way. After deflection it moves with 5% of its initial kinetic energy. What is the speed of the ball now ?

a. 14.41 ms–1 b. 1.00 ms–1 c. 19.0 ms–1 d. 4.47 ms–1 Answer: (d) K.E.f = 5% KEi (since it is a frictionless floor,... View Article

Two identical metal wires of thermal conductivities K1 and K2 respectively are connected in series. The effective thermal conductivity of the combination is

a. b. c. d. Answer: (a) Req = R1+R2 , , ,... View Article

An AC current is given by I=I₁ sinωt + I₂ cosωt. A hot wire ammeter will give a reading :

a. b. c. d. Answer: (b)... View Article

If an electron is moving in the n^th orbit of the hydrogen atom, then its velocity (v_n) for the n^thorbit is given as :

a. vn ∝ n b. vn ∝ (1/n) c. vn ∝ n2 d. vn ∝ 1/n2 Answer: (d) Velocity of electron of the hydrogen atom in nth orbit is,... View Article

The thickness at the centre of a plano-convex lens is 3 mm and the diameter is 6 cm. If the speed of light in the material of the lens is 2 × 10⁸ mm^-1. The focal length of the lens kept in the air is ____.

a. 0.30 cm b. 1.5 cm c. 15 cm d. 30 cm Answer: (d) R2 = 32 + (R – 0.3)2 R2 = 9 + R2 + 0.09 – 2 × 0.3R 2 × 0.3 R = 9.09 R... View Article

A modern grand-prix racing car of mass m

A modern grand-prix racing car of mass m is travelling on a flat track in a circular arc of radius R with a speed v.If the coefficient of static... View Article

A triangular plate is as shown.

A triangular plate is as shown. A force is applied at point P. The torque at point P with respect to point 'O' and 'Q' are : a. 15 –... View Article