The point in the interval [0, 2π], where f (x) = ex sin x has maximum slope, is
1) π / 4 2) π / 2 3) π 4) 3π / 2 Solution: (2) π / 2 f... View Article
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The displacement of a particle at time t is x, where x = t4 – kt3. If the velocity of the particle at time t = 2 is minimum, then
1) k = 4 2) k = – 4 3) k = 8 4) k = – 8 Solution: (1)... View Article
If f (x) = Integral from 0 to x e-x^2/2 (1 – t2) dt, minimum at x =
1) 1 2) –1 3) 2 4) –2 Solution: (2) –1 f (x) = ∫0x e-x^2/2 (1 – t2) dt... View Article
The minimum value of f (x) = |3 – x| + 7 is
1) 0 2) 6 3) 7 4) 8 5) 10 Solution: (3) 7 f (x) = |3 – x| +... View Article
The value of a for which the function f (x) = a sin x + (1 / 3) sin 3x has an extremum at x = π / 3 is
1) 1 2) –1 3) 0 4) 2 Solution: (4) 2 f (x) = a sin x + (1 /... View Article
Let f’’R → R be defined by f (x) = {k – 2x, if x ≤ – 1 and 2x + 3, if x > – 1. If f has a local minimum at x = – 1, then a possible value of k is
1) 1 2) 0 3) – 1 / 2 4) –1 Solution: (4) –1 f (x) = {k – 2x,... View Article
f (x) = x5 – 5x4 + 5x3 + 1 has
1) Two maximum and two minimum value 2) Two maximum and one minimum value 3) One maximum and one minimum... View Article
The minimum value of (x2 + (250 / x)), is
1) 75 2) 50 3) 25 4) 55 Solution: (1) 75 y = f (x) = (x2 + (250 /... View Article
The function y = a (1 – cos x) is maximum when x =
1) π 2) π / 2 3) – π / 2 4) – π / 6 Solution: (1) π y... View Article
If PQ and PR are the two sides of a triangle, then the angle between them which gives maximum area of the triangle is
1) π 2) π / 3 3) π / 4 4) π / 2 Solution: (4) π / 2 Assume... View Article
If ab = 2a + 3b, a > 0, b > 0 then the minimum value of ab is
1) 12 2) 24 3) 1 / 4 4) None of these Solution: (2) 24 ab = 2a + 3b... View Article
The maximum value of xy = 8 is
1) 20 2) 16 3) 24 4) 8 5) 4 Solution: (4) 8 x + 2y = 8 y =... View Article
On [1, e] the greatest value of x2 log x
1) e2 2) (1 / e) log (1 / √e) 3) e2 log √e 4) None of these Solution: (1)... View Article
In (- 4, 4), the function f (x) = Integral from -10 to x (t4 – 4) e-4t dt has
1) No extrema 2) One extremum 3) Two extrema 4) Four extrema Solution: (3) Two extrema f (x) = ∫-10x... View Article
If y = a log x + bx2 + x has its extremum value at x = – 1 and x = 2, then (a, b) =
1) (1, 1 / 2) 2) (1 / 2, 2) 3) (2, – 1 / 2) 4) (- 2 /... View Article
The perimeter of a sector is p. The area of the sector is maximum when its radius is
1) √p 2) 1 / √p 3) p / 2 4) p / 4 Solution: (4) p / 4 A... View Article
If f (x) = x + (1 / x), x > 0 then its greatest value is
1) –2 2) 0 3) 3 4) None of these Solution: (4) None of these f (x) = x +... View Article
If f (x) = 1 / [4x2 + 2x + 1], then its maximum value is
1) 4 / 3 2) 2 / 3 3) 1 4) 3 / 4 Solution: (1) 4 / 3 f... View Article
The function f (x) = 2x3 – 3x2 – 12x + 4 has
1) No maxima and minima 2) One maximum and one minimum 3) Two maxima 4) Two minima Solution: (2) One... View Article
Differential coefficient of √(sec√x) is
(1) (1/4√x)(sec√x)3/2sin √x (2) (1/2√x)(sec√x)3/2sin √x (3) (1/2√x)(sec√x)sin √x (4) none of these Solution: Let y = √(sec√x) Differentiate w.r.t.x... View Article
