∫0∞ dx / [(x + √x2 + 1)3] = 1) 3/8 2) 1/8 3) -3/8 4) None of these Solution: (1) ⅜... View Article
The value of ∫-π/4π/4 sin-4 x dx is 1) - (8/3) 2) 3/2 3) 8/3 4) None of these Solution: (1) - (8/3)... View Article
If k ∫01 x . f (3x) dx = ∫03 t . f (t) dt, then the value of k is 1) 9 2) 3 3) 1/9 4) 1/3 Solution: (1) 9... View Article
The value of ∫12 dx / [(x + 1) (√x2 – 1)] is 1) 1 2) √3 3) 2/√3 4) -2/√3 Solution: (2) √3... View Article
The value of ∫π/4π/2 ex (log sin x + cot x) dx = 1) eπ/4 log 2 2) - eπ/4 log 2 3) (1 / 2) eπ/4 log 2 4) (- 1 / 2) eπ/4 log 2 Solution: (3) (1 / 2) eπ/4 log 2... View Article
The value of ∫0a [√(a – x) / x] dx is 1) a/2 2) a/4 3) Ï€a/2 4) Ï€a/4 Solution: (3) Ï€a/2... View Article
The value of ∫0∞ dx / [(x2 + 4) (x2 + 9)] is 1) π/60 2) π/20 3) π/40 4) π/80 Solution: (1) π/60... View Article
∫510 1 / [(x – 1) (x – 2)] dx = 1) log (27 / 32) 2) log (32 / 27) 3) log (8 / 9) 4) log (3 / 4) Solution: (2) log (32 / 27)... View Article
∫ab √(x – a) (b – x) dx (b > a) = 1) [Ï€ (b - a)2 / 8] 2) [Ï€ (b + a)2] / 8 3) (b - a)2 4) (b + a)2 Solution: (1) [Ï€ (b - a)2 / 8]... View Article
Find the value of ∫02 f’ (x2) 2x dx 1) f(4) - f(0) 2) f(4) + f(0) 3) f(0) - f(4) 4) None of these Solution: (1) f(4) - f(0)... View Article
∫01 x tan-1 x dx = 1) π/4 2) [(π / 4) + (1 / 2)] 3) [(π /4) - (1 / 2)] 4) 1/2 Solution: (3) [(π /4) - (1 / 2)]... View Article
If ∫0π/3 [cos x / (3 + 4 sin x)] dx = k log [(3 + 2√3) / 3], then k = 1) 1/2 2) 1/3 3) 1/4 4) 1/8 Solution: (3) ¼... View Article
If p(x) be a polynomial of degree three that has a local maximum value 8 at x = 1 and a local minimum value 4 at x = 2; then p(0) is equal to a) 12 b) -12 c) -24 d) 6 Solution: p’(1) = 0 and p’(2) = 0 p’(x) = a(x-1)(x-2) p(x) = a[(x3/3)-(3x2/2)+2x]+b p(1) = 8... View Article
Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random and a card is drawn from it.... View Article
Let A be a 2×2 real matrix with enries from {0,1} and A ≠ 0. Consider the following two statements: Let A be a 2×2 real matrix with enries from {0,1} and A ≠ 0. Consider the following two statements: (P) If A ≠I2 , then A = -1 (Q)... View Article
Let P(h,k) be a point on the curve y = x2+7x+2, nearest to the line, y = 3x-3. Then the equation of the normal to the curve at P is a) x+3y-62 = 0 b) x-3y-11 = 0 c) x-3y+22 = 0 d) x+3y+26 = 0 Solution: C: y = x2+7x+2 Let P : (h, k) lies on Curve k = h2+7h+2 ...(1)... View Article
The value of (1+sin (2π/9)+i cos(2π/9)/(1+sin (2π/9)-i cos(2π/9))3 is a) (-1/2)(1-i√3) b) (1/2)(1-i√3) c) (-1/2)(√3-i) d) (1/2)(√3-i) Solution: = (ei(5π/36)+i(5π/36))3 =... View Article
