**MCQs Questions for Class 12 Maths Chapter 6 Application of Derivatives**

In this 21^{st} century, Multiple Choice Questions (MCQs) play a vital role to prepare for a competitive examination. CBSE board has also brought a major change in its board exam patterns.

In most of the competitive examinations, only MCQ questions are asked. So, for getting ready for the competitive examinations, we have to practice for MCQ questions to solve. It strengthens the critical thinking and problem solving skills.

In future, if you want to prepare for competitive examination and to crack it, then you should more focus on the MCQ questions. Thus, from the board examinations point of view and competitive examinations point of view, you should practice more on multiple choice questions.

Thus, let’s solve these MCQs Questions to make our foundation very strong.

**MCQs Questions for Class 12 Maths Chapter 6 Application of
Derivatives**

**1.** If f(x) = (x – 1)^{3 }(x + 1)^{2}, then the points of local maxima and local minima of the
function are

(a) 1, -1,
-1/5

(b) 1, -1

(c) 1, -1/5

(d) -1,
-1/5

**Answer: a**

**2.** The slope of the
tangent to the curve y = 2x/(x^{2} + 1) at (0,
0) is

(a) 1

(b) 0

(c) 3

(d) 2

**Answer:**** d**

**3. **The sides of an equilateral triangle are increasing at the
rate of 2 cm/sec. The rate at which the area increases, when side is 10 cm, is:

(a) 10
cm²/s

(b) √3
cm²/s

(c) 10√3
cm²/s

(d) 10/3 cm²/s

**Answer:**** c**

**4. **The maximum profit that a company can make, if the profit
function is given by P(x) = 41 + 24x – 18x^{2} is

(a) 25

(b) 49

(c) 62

(d) 43

**Answer: b**

**5. **The value of f’(x) is -1
at the point P on a continuous curve y = f(x). Find the angle between the
tangent and the curve at P with the positive direction of x-axis.

(a) Ï€/2

(b) 3Ï€/4

(c) Ï€/4

(d) 3Ï€/2

**Answer:**** b**

**6. **The curve y = x^{1/5} at (0, 0) has

(a) a vertical
tangent (parallel to y-axis)

(b) a
horizontal tangent (parallel to x-axis)

(c) an
oblique tangent

(d) no
tangent

**Answer:**** b**

**7. **If y = x^{3} + x^{2} + x + 1, then y

(a) has a
local minimum

(b) has a
local maximum

(c) neither
has a local minimum nor local maximum

(d) None of
these

**Answer: c**

**8. **The differential
function of log (x^{2} + 4) is

(a) 2x/(x^{2} + 4) dx

(b) 2x/(x^{2} – 4) dx

(c) -2x/(x^{2} + 4) dx

(d) -2x/(x^{2} – 4) dx

**Answer:**** a**

**9. **The equation of normal to the curve 3x² – y² = 8, which is
parallel to the line x + 3y = 8, is

(a) 3x – y
= 8

(b) 3x + y
+ 8 = 0

(c) x + 3y
± 8 = 0

(d) x + 3y
= 0

**Answer:**** c**

**10. **The maximum and minimum values of 3x^{4} – 8x^{3} + 12x^{2} – 48x + 1 on the interval [1, 4] are

(a) -63 and
257

(b) 257 and
-40

(c) 257 and
-63

(d) 63 and
-257

**Answer: c**

**11. **The rate of change of
the radius of a sphere is 1/2Ï€. If its radius is 5 cm, what will be the rate of
change of the surface area of sphere with time?

(a) 10 sq
cm

(b) 20 sq
cm

(c) 30 sq
cm

(d) 40 sq
cm

**Answer:**** b**

**12. **The equation of tangent to the curve y (1 + x²) = 2 – x, where
it crosses x-axis, is

(a) x + 5y
= 2

(b) x – 5y
= 2

(c) 5x – y
= 2

(d) 5x + y
= 2

**Answer:**** a**

**13. **The equation of the normal to the curve y = sin x at (0, 0)
is

(a) x = 0

(b) x + y =
0

(c) y = 0

(d) x – y =
0

**Answer: b**

**14. **The nature of the function
f(x) = x^{3} – 3x^{2} + 4x on R
is

(a)
Increasing

(b)
Decreasing

(c)
Constant

(d)
Increasing and Decreasing

**Answer:**** a**

**15. **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]

**Answer:**** b**

**16. **The tangent to the curve y = 2x^{2} -x + 1 is
parallel to the line y = 3x + 9 at the point

(a) (2, 3)

(b) (2, -1)

(c) (2, 1)

(d) (1, 2)

**Answer: d**

**17. **The interval in which
the function f(x) = sin x + cos x is increasing, is

(a) (5Ï€/4,
2Ï€)

(b) [0,
Ï€/4) and (5Ï€/4, 2Ï€]

(c) (Ï€/4,
-5Ï€/4)

(d) (-Ï€/4,
Ï€/4)

**Answer:**** b**

**18. **Which of the following functions is decreasing on (0, Ï€/2)?

(a) cos 2x

(b) tan x

(c) sin x

(d) cos 3x

**Answer:**** a**

**19. **If there is an error of 2% in measuring the length of a
simple pendulum, then the percentage error in its period is

(a) 4%

(b) 3%

(c) 2%

(d) 1%

**Answer: d**

**20. **The value of b for which
the function f (x) = sin x – bx + c is decreasing for x ∈ R is given by

(a) b <
1

(b) b ≥ 1

(c) b >
1

(d) b ≤ 1

**Answer:**** c**