KENDRIYA VIDYALAYA SANGATHAN AHMEDABAD REGION
MATHS WORKSHEET I 2023-24
CLASS: XII
CHAPTER : APPLICATION OF DERIVATIVES
MCQS
Q1 The function f(x)= ax+b is strictly decreasing for all x∈R iff:
(a) a=0
(b) a<0
(c) a>0
(d) none of these)
Q2 The rate of change of the area of a circle with respect to its
radius r at r = 6 cm is
(a) 10π
(b) 12π
(c) 8π
(d) 11π
Q3 The function f(x)= cos x-sin x has maximum or minimum value at x=
𝜋
(a)
4
3𝜋
(b)
4
𝜋
(c)
2
𝜋
(d)
3
Q4 Which of the following functions is decreasing on (0, π/2)
(a)sin 2x
(b)tan x
(c)cos x
(d)cos 3x
Q5 A cylindrical vessel of radius 0.5 m is filled with oil at the rate of 0.25
π cu/min. The rate at which oil is rising is
(a)1m/min
(b)2m/min
(c)5m/min
(d)1.25 m/min
Note: For Q No 6 to 10 use separate sheet to solve and attach with
worksheet.
Q6 Sand is pouring from a pipe at the rate of 12 cm3/s. The falling sand
forms a cone on the ground in such a way that the height of the cone
MATHS WORKSHEET I 2023-24
CLASS: XII
CHAPTER : APPLICATION OF DERIVATIVES
MCQS
Q1 The function f(x)= ax+b is strictly decreasing for all x∈R iff:
(a) a=0
(b) a<0
(c) a>0
(d) none of these)
Q2 The rate of change of the area of a circle with respect to its
radius r at r = 6 cm is
(a) 10π
(b) 12π
(c) 8π
(d) 11π
Q3 The function f(x)= cos x-sin x has maximum or minimum value at x=
𝜋
(a)
4
3𝜋
(b)
4
𝜋
(c)
2
𝜋
(d)
3
Q4 Which of the following functions is decreasing on (0, π/2)
(a)sin 2x
(b)tan x
(c)cos x
(d)cos 3x
Q5 A cylindrical vessel of radius 0.5 m is filled with oil at the rate of 0.25
π cu/min. The rate at which oil is rising is
(a)1m/min
(b)2m/min
(c)5m/min
(d)1.25 m/min
Note: For Q No 6 to 10 use separate sheet to solve and attach with
worksheet.
Q6 Sand is pouring from a pipe at the rate of 12 cm3/s. The falling sand
forms a cone on the ground in such a way that the height of the cone
