CBSE Class 12 Maths Application of Derivatives Quiz 2

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CBSE › Class 12 › Maths › Application of Derivatives

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1. The two curves; x³ – 3xy² + 2 = 0 and 3x²y – y³ – 2 = 0 intersect at an angle of

A \(\frac{π}{4}\) B \(\frac{π}{3}\) C \(\frac{π}{2}\) D \(\frac{π}{6}\)

2. The interval on which the function f (x) = 2x³ + 9x² + 12x – 1 is decreasing is

A [-1, ∞] B [-2, -1] C [-∞, -2] D [-1, 1]

3. Let the f: R → R be defined by f (x) = 2x + cos x, then f

A has a minimum at x = 3t B has a maximum, at x = 0 C is a decreasing function D is an increasing function

4. y = x (x – 3)² decreases for the values of x given by

A 1 < x < 3 B x < 0 C x > 0 D 0 < x <\(\frac{3}{2}\)

5. The function f(x) = 4 sin³ x – 6 sin²x + 12 sin x + 100 is strictly

A increasing in (π, \(\frac{3π}{2}\)) B decreasing in (\(\frac{π}{2}\), π) C decreasing in [\(\frac{-π}{2}\),\(\frac{π}{2}\)] D decreasing in [0, \(\frac{π}{2}\)]

6. Which of the following functions is decreasing on(0, \(\frac{π}{2}\))?

A sin 2x B tan x C cos x D cos 3x

7. The function f(x) = tan x – x

A always increases B always decreases C sometimes increases and sometimes decreases D never increases

8. If x is real, the minimum value of x² – 8x + 17 is

A -1 B 0 C 1 D 2

9. The smallest value of the polynomial x³ – 18x² + 96x in [0, 9] is

A 126 B 0 C 135 D 160

10. The function f(x) = 2x³ – 3x² – 12x + 4 has

A two points of local maximum B two points of local minimum C one maxima and one minima D no maxima or minima

Practice more on Application of Derivatives

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