Multiple Choice QuestionsA function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched?
| Interval | Function |
| (-∞, ∞) | x3 – 3x2 + 3x + 3 |
| Interval | Function |
| [2, ∞) | 2x3 – 3x2 – 12x + 6 |
| Interval | Function |
| (-∞, 1/3] | 3x2 – 2x + 1 |
| Interval | Function |
| (-∞, 1/3] | 3x2 – 2x + 1 |
Let f be differentiable for all x. If f(1) = - 2 and f′(x) ≥ 2 for x ∈ [1, 6] , then
f(6) ≥ 8
f(6) < 8
f(6) < 5
f(6) < 5
If cos-1 x - cos-1 y/2 = α, then 4x2 − 4xy cos α + y2 is equal to
2 sin 2α
4
4 sin2 α
4 sin2 α
A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thickness than melts at a rate of 50 cm3 /min. When the thickness of ice is 5 cm, then the rate at which the thickness of ice decreases, is
A particle is projected from a point O with velocity u at an angle of 60o with the horizontal. When it is moving in a direction at right angles to its direction at O, its velocity then is given by
u/3
u/2
2u/3
2u/3
A real valued function f(x) satisfies the functional equation f(x – y) = f(x) f(y) – f(a – x) f(a + y) where a is a given constant and f(0) = 1, f(2a – x) is equal to
–f(x)
f(x)
f(a) + f(a – x)
f(a) + f(a – x)
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then the solution of the equation is
