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The value of ∫₀^∞ dx / [(a² + x²)] is

1) π/2 2) π/2a 3) π/a 4) 1/2a Solution: (2) π/2a... View Article

3a ∫₀¹ [(ax – 1) / (a – 1)]² dx =

1) a - 1 + (a - 1)-2 2) a + a-2 3) a - a-2 4) a2 + 1/a2 Solution: (1) a - 1 + (a - 1)-2... View Article

∫₀^λ y / [√y + λ] dy =

1) (2 / 3) [2 - √2] λ √λ 2) (2 / 3) [2 + √2] λ √λ 3) (1 / 3) [2 - √2] λ √λ 4) (1 / 3) [2 + √2] λ √λ Solution: (1) (2 / 3) [2 - √2] λ... View Article

∫₂^k (2x + 1) dx = 6, then k =

1) 4 2) -2 3) -3 4) 3 Solution: (4) 3... View Article

If ∫₀^p dx / [(1 + 4x²)] = π / 8, then the value of p is

1) 1/4 2) - (1/2) 3) 3/2 4) 1/2 Solution: (4) ½... View Article

If b > a, then ∫_a^b dx / [√(x – a) (b – x)] =

1) π / 2 2) π 3) (π / 2) (b - a) 4) (π / 4) (b - a) Solution: (2) π... View Article

The value of integral ∫_-1¹ [|x + 2| / (x + 2)] dx =

1) 1 2) 2 3) 0 4) -1 Solution: (2) 2... View Article

Which of the following is correct?

1) ∫01 ex dx = e 2) ∫01 2x dx = log 2 3) ∫01 √x dx = 2 / 3 4) ∫01 √x dx = 2 / 4 5) ∫01 x dx = 1 / 3 Solution: (3) ∫01 √x dx = 2 / 3... View Article

The value (s) of ∫₀¹ [x⁴ (1 – x)⁴ / (1 + x²)] dx is (are)

1) [(22 / 7) - π] 2) 2 / 105 3) 0 4) [(71 / 15) - (3π / 2)] Solution: (1) [(22 / 7) - π]... View Article

If (d / dx) (ɸ (x)) = f (x), then ∫₁² f (x) dx =

1) f (1) - f (2) 2) ∅ (1) - ∅ (2) 3) f (2) - f (1) 4) ∅ (2) - ∅ (1) Solution: (4) ∅ (2) - ∅ (1)... View Article

The value of ∫_π/6^π/2 {[1 + sin 2x + cos 2x] / (sin x + cos x)} dx =

1) 16 2) 8 3) 4 4) 1 Solution: (4) 1... View Article

∫₀^π/2 |cos (x / 2)| dx =

1) 1 2) -2 3) √2 4) 0 Solution: (3) √2... View Article

∫₀¹ dx / (1 + x + x²) =

1) π / √3 2) π / 2√3 3) 2π / 3√3 4) π / 3√3 Solution: (4) π / 3√3... View Article

If [latex]\triangle (x)= \begin{vmatrix} 1 &cosx &1-cosx \\ 1+sinx &cosx &1+sinx-cosx \\ sinx&sinx &1 \end{vmatrix}[/latex], then ∫₀ ^π/4 Δ (x) dx =

1) 1/4 2) 1/2 3) 0 4) - (1/4) Solution: (4) - (1/4)... View Article

If P x Q = Q x P the angle between P and Q is theta(0o

If is θ(0o<θ< 360o). The value of 'θ' will be ____. Answer: 180... View Article

Two particles having masses 4g and 16g respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is n:2. The value of n will be_____.

Answer: 1 Relation b/w kinetic energy & momentum is p = √(2mKE) (∵KE = same) p1/p2 = √(m1/m2) n/2 = √(4/16) n = 1... View Article

A reversible heat engine converts one- fourth of the heat input into work. When the temperature of the sink is reduced by 52 K, its efficiency is doubled. The temperature in Kelvin of the source will be_______.

Answer: 208 ∵ n = W/Qin = 1/4 ¼ = 1 - T2/T1 [for reversible heat engine] T2/T1 = 3/4 When the temperature of the sink is reduced by 52k... View Article

The wavelength of an X-ray beam is 10 Å. The mass of a fictitious particle having the same energy as that of the X-ray photons is (x/3) h kg. The value of x is _______.

Answer: 10 Given wavelength of an X-ray beam = 10 Å ∵E = hc/λ = mc2 m = hc/λ will be the mass of a particle having the same... View Article

A current of 6A enters one corner P of an equilateral triangle PQR having 3 wires of resistance

A current of 6A enters one corner P of an equilateral triangle PQR having 3 wires of resistance 21Ω each and leaves by the corner R. The... View Article

The initial velocity v₁ required to project a body vertically upward from the surface of the earth to just reach a height of 10R

The initial velocity v1 required to project a body vertically upward from the surface of the earth to just reach a height of 10R, where R is the... View Article

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