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Let a computer program generate only the digits 0 and 1

Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with a probability of occurrence of 0 at even places... View Article

Let the tangent to the circle x² + y² = 25 at the point R (3, 4)

Let the tangent to the circle x2 + y2 = 25 at the point R (3, 4) meet the x-axis and y-axis at points P and Q, respectively. If r is the radius... View Article

A transmitting station releases waves of wavelength 960 m. A capacitor of 256 μF is used in the resonant circuit. The self inductance of coil necessary for resonance is _____ × 10^–8H.

Answer: 10 At resonance ωr = 1/√(Lc) ∴ 2πf = 1/√(Lc) ∴ 4π2c2/λ2 = 1/Lc... View Article

A coil of inductance 2 H having negligible resistance is connected to a source of supply whose voltage is given by V = 3t volt. (where t is in second). If the voltage is applied when t = 0, then the energy stored in the coil after 4 s is _______ J.

Answer: 144 L di/dt = ε = 3t L ∫di = 3 ∫t dt Li = 3t2/2 i = 3t2/2L Energy stored in the coil, E = ½ Li2 = ½ L (3t2/2L)2 = ½ × 9t4/4L =... View Article

A monoatomic gas of mass 4.0 u is kept in an insulated container. Container is moving with a velocity 30 m/s. If container is suddenly stopped then change in temperature of the gas (R=gas constant) is x/3R. Value of x is ______.

Answer: 3600 ΔKE = ΔU ΔU = nCVΔT ½ mv2 = (3/2) nRΔT mv2/3nR = ΔT 4×(30)2/3×1×R... View Article

Circuit of potentiometer

In the given circuit of potentiometer, the potential difference E across AB (10 m length) is larger than E1 and E2 as well. For key K1 (closed),... View Article

In a certain thermodynamic process, the pressure of a gas depends on its volume as kV³. The work done when the temperature changes from 100⁰C to 300⁰C will be ____ nR, where n denotes number of moles of a gas.

Answer: 50 P = kv3 pv–3 = k x = –3 w = nR(T1 - T2)/(x - 1) = nR(100-300)/(-3 -1) = nR(-200)/-4 = 50nR... View Article

A small bob tied at one end of a thin string of length 1m is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio 5 : 1. The velocity of the bob at the highest position is ______ m/s. (take g = 10 m/s²)

Answer: 5 By conservation of energy, v2min = V2 – 4gl ....(1) Tmax = mg + mv2/l ....(2) Tmin = mv2min/l - mg ....(3) from equation (1) and... View Article

The potential energy (U) of a diatomic molecule is a function dependent on r (interatomic distance) as U= α/r¹⁰– β/r⁵– 3. Where, a and b are positive constants. The equilibrium distance between two atoms will (2α/β)^a/b. Where a =_______

Answer: 1 F = -dU/dr F = -[-10α/r11 + 5β/r6] for equilibrium, F = 0 10α/r11 = 5β/r6 2α/β = r5 r =... View Article

512 identical drops of mercury are charged to a potential of 2 V each. The drops are joined to form a single drop. The potential of this drop is ____ V.

Answer: 128 Let charge on each drop = q Radius = r V = kq/r 2 = kq/r Radius of bigger 4πR3/3 = 512 × (4/3) πr3 R = 8r V =... View Article

The electric field in a region is given by [latex]left ( frac{3}{5}E_{o}hat{i}+ frac{4}{5}E_{o}hat{j}right )frac{N}{C}[/latex]. The ratio of flux of reported field through the rectangular surface of area 0.2 m2 (parallel to y-z plane) to that of the surface of area 0.3 m2(parallel to x-z plane) is a : 2, where a = ________

[Here i, j and k are unit vectors along x, y and z-axes respectively] Answer: 1 Therefore, a = 1 ... View Article

The same size images are formed by a convex lens when the object is placed at 20 cm or at 10 cm from the lens. The focal length of a convex lens is ______ cm.

Answer: 15 1/v – 1/u = 1/f ...(1) m = v/u ....(2) from (1) and (2) we get m = f/(f + u) Given conditions m1 = -m2 f/(f - 10) = -f/(f... View Article

Magnetic fields at two points on the axis of a circular coil at a distance of 0.05 m and 0.2 m from the centre are in the ratio 8 : 1. The radius of coil is ______

a. 0.15 m b. 0.2 m c. 0.1 m d. 1.0 m Answer: (c) B = μ0NiR2/2(R2 + x2)3/2 at x1 = 0.05m, B1 = μ0NiR2/2(R2 + (0.05)2)3/2 at x2 =... View Article

Two coherent light sources having intensities in the ratio 2x produce an interference pattern. The ratio (I_max – I_min)/(I_max + I_min) will be:
a. 2√(2x)/(x + 1)b. √(2x)/(2x + 1)c. 2√(2x)/(2x + 1)d. √(2x)/(x + 1)

a. 2√(2x)/(x + 1) b. √(2x)/(2x + 1) c. 2√(2x)/(2x + 1) d. √(2x)/(x + 1) Answer: (c) Let I1 = 2x I2 = 1 Imax = (√I1... View Article

The angular frequency of alternating current in a L-C-R circuit is 100 rad/s. The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.

The angular frequency of alternating current in a L-C-R circuit is 100 rad/s. The components connected are shown in the figure. Find the value of... View Article

Given below are two statements: one is labelled as Assertion A and the other is labelled as reason R

Assertion A: The escape velocities of planet A and B are same. But A and B are of unequal masses. Reason R: The product of their masses and radii... View Article

An α particle and a proton are accelerated from rest by a potential difference of 200 V. After this, their de Broglie wavelengths are λ_α and λ_p respectively. The ratio λ_p/λ_α is:

a. 8 b. 2.8 c. 3.8 d. 7.8 Answer: (b) λ = h/p = h/√(2mqV) λp/λα = √(mαqα/mpqp) =... View Article

If the time period of a two meter long simple pendulum is 2 s, the acceleration due to gravity at the place where pendulum is executing S.H.M. is:

a. 2π2 ms–2 b. 16 m/s2 c. 9.8 ms–2 d. π2 ms–2 Answer: (a) T = 2π√(l/g) T2 = 4π2l/g g = 4π2l/T2 =... View Article

The pitch of the screw gauge is 1 mm and there are 100 divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lines 8 divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while 72^nd division on circular scale coincides with the reference line. The radius of the wire is

a. 1.64 mm b. 1.80 mm c. 0.82 mm d. 0.90 mm Answer: (c) Least count. = pitch/no. of div. = 1 mm/100 = 0.01 mm +ve zero error = 8 × L.C. =... View Article

Match List-I with List-II:

Match List-I with List-II: List-I List-II (a)h (Planck’s constant) (i) [MLT–1] (b)E... View Article

M	T	W	T	F	S	S
	1	2	3	4	5	6
7	8	9	10	11	12	13
14	15	16	17	18	19	20
21	22	23	24	25	26	27
28	29	30