# Multiple choice(Application of derivatives)

Choose and write the correct option in the following question:(application of derivatives multiple choice)

1.) The interval in which the function f given by is strictly increasing, is

(a) (-âˆž, âˆž)Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (b) (-âˆž, 0)

(c) (2, âˆž)Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (d) (0, 2)

2.) decreasing for the values of x given by

(a) 1 < x < 3Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (b)Â  x < 0

(c) x > 0Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (d) 0 < x < 3/2

3.) has a stationary point at

(a) x = eÂ  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (b) x = 1/e

(c) x = 1Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (d) x = âˆše

4.) the maximum value of is

(a) eÂ  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (b)

(c) Â  Â  Â  Â  Â  Â  Â  Â  Â  (d)

5.) the point on the curve xÂ² = 2y which is nearest to the point (0, 5) is

(a) (2âˆš2, 4)Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (b) (2âˆš2, 0)

(c) (0, 0)Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (d) (2, 2)

6.) The maximum value of is

(a) Â  Â  Â  Â  Â  Â  (b) 1/2

(c) 1Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (d) 0

7.) A ladder, 5 meter long, dtanding on a horizontal floor, leans against a vertical wall. If the top of the ladder slides downwards at the rate of 10 cm/sec, then the rate at which the angle between the floor and the ladder is decreasingÂ  when lower end of ladder is 2 metres from the wall is

(a) 1/10 radyan/secÂ  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (b) 1/20 radian/sec

(c) 20 radian/secÂ  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (d) 10 radian/sec

8.) The rate of change of the area of a circle with respect to its radius r at r = 6 cm is

(a) 10 Ï€Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (b) 12 Ï€

(c) 8 Ï€Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (d) 11 Ï€

9.) The total revenue in rupees received from the sale of x units of a product is given by R(x) =3xÂ² + 36x + 5. The marginal revenue, when x = 15 is

(a) 116Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (b) 96

(c) 90Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (d) 126

10.) If x is real, the minimum value of xÂ² – 8x + 17 is

(a) -1Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (b) 0

(c) 1Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (d) 2

11.) The function f(x) = 2xÂ³ – 15xÂ² + 36x + 6 is increasing in the interval

(a) (-âˆž, 2)âˆª(3, âˆž)Â  Â  Â  Â  Â  Â  Â  Â (b) (-âˆž, 2)

(c)Â  (-âˆž, 2]âˆª[3, âˆž)Â  Â  Â  Â  Â  Â  Â  Â (d) [3, âˆž)

Â 12.) In a sphere of radius r, a right circular cone of height h having maximum curved surface area is inscribed. The expression for the square of curved surface of cone isÂ  Â

(a) 2Ï€rÂ²rh(2rh + hÂ²)Â  Â  Â  Â  Â  Â (b) Ï€Â²rh(2rh + hÂ²)

(c)2Ï€Â²r(2rhÂ² – hÂ²)Â  Â  Â  Â  Â  Â  Â  Â  (d) 2Ï€Â²rÂ²(2rh – hÂ²)

13.) If and , where 0< x â‰¤ 1, then in the interval

(a) Both f(x) and g(x) are increasing functions

(b) Both f(x) and g(x) are decreasing functions

(c) f(x) is an increasing function.

(d) g(x) is an increasing function

14.) The number of values of x where th function attains its maximum is

(a) 0Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (b) 1

(c) 2Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (d) infinite

15.) If xy = aÂ² and S = bÂ² x + cÂ²y where a, b, and c are positive constants then the minimum value of S is

(a) abcÂ  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (b) bcâˆša

(c) 2abcÂ  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (d) None of these

16.) The least value of the function is

(a) a/bÂ  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (b) 2âˆšab

(c) 0Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (d) None of these

17.) If , then its maximum value is

(a) 0Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (b) 4/3

(c) Â±5Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (d) Maximum value does not exist.

18.) Let . then f(x) is

(a) Decreasing in [0, Ï€/2]

(b) Increasing in [0, Ï€/2]

(c) increasing in [0, Ï€/4] and decreasing in [Ï€/4, Ï€/2]

(d) None of these

19.) Let f(x) be a function such that f'(a) â‰  0. Then at x = a,f(x)

(a) Cannot have a maximum

(b) Cannot have a minimum

(c) Must have neither a maximum nor a minimum

(d) None of these

20.) The global minimum value of

(a) 6Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (b) 8

(c) 4Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (d) Does not exist

21.) The rate change in volume of sphere wrt r when radius is (1/2) is

(a) Ï€Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (b) 2Ï€

(c) 4Ï€Â  Â  Â  Â  Â  Â  Â  Â  Â  (d) None of these

22.) The maximum value of slope of the curve is

(a) 15Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (b) 12

(c) 9Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (d) 0