New Quiz from Text

Q1: The number of non-empty equivalence relations on the set {1,2,3} is :

• 6
• 7
• 5
• 4

Q2: Let ƒ : R→R be a twice differentiable function such that ƒ(x + y) = ƒ(x)ƒ(y) for all x, y ∈ R. If ƒ'(0) = 4a and ƒ satisfies ƒ''(x) – 3aƒ'(x) – ƒ(x) = 0, a > 0, then the area of the region R = {(x,y) | 0 ≤ y ≤ ƒ(ax), 0 ≤ x ≤ 2} is :

• e² – 1
• e⁴ + 1
• e⁴ – 1
• e² + 1

Q3: Let the triangle PQR be the image of the triangle with vertices (1,3), (3,1) and (2,4) in the line x + 2y = 2. If the centroid of ΔPQR is the point (α, β), then 15(α – β) is equal to :

• 24
• 19
• 21
• 22

Q4: Let z₁, z₂ and z₃ be three complex numbers on the circle |z| = 1 with arg(z₁) = –π/4, arg(z₂) = 0 and arg(z₃) = 3π/4. If z₁z₂ + z₂z₃ + z₃z₁ = α + β√2, α, β ∈ Z, then the value of α² + β² is :

• 24
• 41
• 31
• 29

Q5: Using the principal values of the inverse trigonometric functions the sum of the maximum and the minimum values of 16((sec⁻¹x)² + (cosec⁻¹x)²) is :

• 24π²
• 18π²
• 31π²
• 22π²

Q6: A coin is tossed three times. Let X denote the number of times a tail follows a head. If μ and σ² denote the mean and variance of X, then the value of 64(μ + σ²) is :

• 51
• 48
• 32
• 64

Q7: Let a₁, a₂, a₃ ... be a G.P. of increasing positive terms. If a₁a₅ = 28 and a₂ + a₄ = 29, then a₆ is equal to :

• 628
• 526
• 784
• 812

Q8: Let L₁ : (x–1)/2 = (y–2)/3 = (z–3)/4 and L₂ : (x–2)/3 = (y–4)/4 = (z–5)/5 be two lines. Then which of the following points lies on the line of the shortest distance between L₁ and L₂ ?

• (–5/3, 7, 1)
• (2/3, 3, 3)
• (–8/3, 1, 1/3)
• (–14/3, 22/3, 3)

Q9: The product of all solutions of the equation e^(5 log x) + 3 = 8e^x, x > 0, is :

• e^(8/5)
• e^(6/5)
• e²
• e

Q10: If Tₙ = [(2n–1)(2n+1)(2n+3)] / 8, then lim (n→∞) Σ (r=1 to n) 1/Tᵣ is equal to :

• 1
• 0
• 2/3
• 1/3