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) (-∞, ∞) (b) (-∞, 0)
(c) (2, ∞) (d) (0, 2)
Answer (d)
2.) 
decreasing for the values of x given by
(a) 1 < x < 3 (b) x < 0
(c) x > 0 (d) 0 < x < 3/2
Answer (a)
3.) 
has a stationary point at
(a) x = e (b) x = 1/e
(c) x = 1 (d) x = √e
Answer (b)
4.) the maximum value of 
is
(a) e (b) 
(c) 
(d) 
Answer (c)
5.) the point on the curve x² = 2y which is nearest to the point (0, 5) is
(a) (2√2, 4) (b) (2√2, 0)
(c) (0, 0) (d) (2, 2)
Answer (a)
6.) The maximum value of ![[x(x-1)+1]^{1/3}, 0 \leq x\leq 1](https://gmath.in/wp-content/ql-cache/quicklatex.com-d136fa5f360eab0b5c42d638ccd3221f_l3.png "Rendered by QuickLaTeX.com")
is
(a) 
(b) 1/2
(c) 1 (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 decreasing when lower end of ladder is 2 metres from the wall is
(a) 1/10 radyan/sec (b) 1/20 radian/sec
(c) 20 radian/sec (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 π (b) 12 π
(c) 8 π (d) 11 π
Answer (b)
9.) The total revenue in rupees received from the sale of x units of a product is given by R(x) =3x² + 36x + 5. The marginal revenue, when x = 15 is
(a) 116 (b) 96
(c) 90 (d) 126
Answer (d)
10.) If x is real, the minimum value of x² – 8x + 17 is
(a) -1 (b) 0
(c) 1 (d) 2
Answer (c)
11.) The function f(x) = 2x³ – 15x² + 36x + 6 is increasing in the interval
(a) (-∞, 2)∪(3, ∞) (b) (-∞, 2)
(c) (-∞, 2]∪[3, ∞) (d) [3, ∞)
Answer (c)
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 is
(a) 2πr²rh(2rh + h²) (b) π²rh(2rh + h²)
(c)2π²r(2rh² – h²) (d) 2π²r²(2rh – h²)
Answer (c)
13.) If 
and 
, where 0< x ≤ 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) 0 (b) 1
(c) 2 (d) infinite
Answer (b)
15.) If xy = a² and S = b² x + c²y where a, b, and c are positive constants then the minimum value of S is
(a) abc (b) bc√a
(c) 2abc (d) None of these
Answer (c)
16.) The least value of the function 
is
(a) a/b (b) 2√ab
(c) 0 (d) None of these
Answer (b)
17.) If 
, then its maximum value is
(a) 0 (b) 4/3
(c) ±5 (d) Maximum value does not exist.
Answer (b)
18.) Let 
. then f(x) is
(a) Decreasing in [0, π/2]
(b) Increasing in [0, π/2]
(c) increasing in [0, π/4] and decreasing in [π/4, π/2]
(d) None of these
Answer (b)
19.) Let f(x) be a function such that f'(a) ≠ 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) 6 (b) 8
(c) 4 (d) Does not exist
Answer (c)
21.) The rate change in volume of sphere wrt r when radius is (1/2) is
(a) π (b) 2π
(c) 4π (d) None of these
22.) The maximum value of slope of the curve 
is
(a) 15 (b) 12
(c) 9 (d) 0
