# Class 12 application of derivatives multiple choice

# 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)

**Answer (d)**

**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

**Answer (a)**

**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

**Answer (b)**

**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)

**Answer (c)**

**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)

**Answer (a)**

**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

**Answer (c)**

**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

**Answer (b)**

**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€

**Answer (b)**

**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

**Answer (d)**

**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

**Answer (c)**

**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)

**Answer (c)Â Â Â Â **

**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)

**Answer (c)**

**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

**Answer (c)**

**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

**Answer (b)**

**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

**Answer (c)**

**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

**Answer (b)**

**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.

**Answer (b)**

**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

**Answer (b)**

**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

**Answer(d)**

**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

**Answer (c)**

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