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A hollow spherical shell at outer radius R floats just submerged under the water surface.

A hollow spherical shell at outer radius R floats just submerged under the water surface. The inner radius of the shell is r. If the specific... View Article

The value of the acceleration due to gravity is g1 at a height h

The value of the acceleration due to gravity is g1 at a height h = R / 2 (R = radius of the earth) from the surface of the earth. It is again... View Article

Activities of three radioactive substances A, B and C are represented by the curves A, B and C, in the figure.

Activities of three radioactive substances A, B and C are represented by the curves A, B and C, in the figure. Then their half-lives T1/2 (A) :... View Article

An electrical power line, having a total resistance of 2Ω, delivers 1 kW at 220 V. The efficiency of the transmission line is approximately:

1) 72% 2) 91 % 3) 85% 4) 96% Answer: (4) = {[Pout] / [Pout + Ploss]} * 100 I = P / V = 100 / 220 = (5 / 11) A Ploss = I2R = (50 / 11)2... View Article

A balloon is moving up in air vertically above a point A on the ground

A balloon is moving up in air vertically above a point A on the ground. When it is at a height h1, a girl standing at a distance d(point B) from... View Article

A wheel is rotating freely with an angular speed on a shaft.

A wheel is rotating freely with an angular speed on a shaft. The moment of inertia of the wheel is I and the moment of inertia of the shaft is... View Article

A bullet of mass 5 g, travelling with a speed of 210 m/s, strikes a fixed wooden target.

A bullet of mass 5 g, travelling with a speed of 210 m/s, strikes a fixed wooden target. One half of its kinetic energy is converted into heat in... View Article

A helicopter rises from rest on the ground vertically upwards with a constant acceleration g.

A helicopter rises from rest on the ground vertically upwards with a constant acceleration g. A food packet is dropped from the helicopter when... View Article

Two capacitors of capacitances C and 2C are charged to potential differences V and 2V

Two capacitors of capacitances C and 2C are charged to potential differences V and 2V, respectively. These are then connected in parallel in such... View Article

Assume that the displacement (s) of air is proportional to the pressure difference

Assume that the displacement (s) of air is proportional to the pressure difference (Δp) created by a sound wave. Displacement(s) further... View Article

A square loop of side 2a, and carrying current I

A square loop of side 2a, and carrying current I, is kept in XZ plane with its centre at the origin. A long wire carrying the same current I is... View Article

With increasing biasing voltage of a photodiode, the photocurrent magnitude

1) increases initially and saturates finally 2) remains constant 3) increases linearly 4) increases initially and after attaining certain... View Article

Three different processes that can occur in an ideal monatomic gas are shown in the P vs V diagram

Three different processes that can occur in an ideal monatomic gas are shown in the P vs V diagram. The paths are labelled as A → B, A... View Article

Let tan α, tan β and tan γ; α, β, γ ≠ [2n – 1] π / 2, n ∈ N be the slopes of three-line segment

Let tan α, tan β and tan γ; α, β, γ ≠ [2n - 1] π / 2, n ∈ N be the slopes of three-line... View Article

Let P be an arbitrary point having the sum of the squares of the distances

Let P be an arbitrary point having the sum of the squares of the distances from the planes x + y + z = 0, lx – nz = 0 and x – 2y + z... View Article

If 1, log₁₀(4^x– 2) and log₁₀ [4^x + (18 / 5)] are in arithmetic progression for a real number x

If 1, log10 (4x – 2) and log10 [4x + (18 / 5)] are in arithmetic progression for a real number x, then the value of the determinant is... View Article

Consider a set of 3n numbers having variance 4.

Consider a set of 3n numbers having variance 4. In this set, the mean of the first 2n numbers is 6 and the mean of the remaining n numbers is 3.... View Article

Let x be a vector in the plane containing vectors

Let x be a vector in the plane containing vectors a = 2i - j + k and b = i + 2j - k. If the vector x is perpendicular to (3i + 2j - k) and its... View Article

Let f : [–3, 1]→ R be given as

Let f : [–3, 1]→ R be given as If the area bounded by y = f(x) and x-axis is A, then the value of 6A is equal to Answer: (41) Area... View Article

Let I_n = ∫₁^e x¹⁹ (log |x|)ⁿ dx, where n ∈ N.

Let In = ∫1e x19 (log |x|)n dx, where n ∈ N. If 20 (I10) = αI9 + βI8, for natural numbers α and β, then α... View Article

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