NCERT Class 12 Math Application of Derivatives Chapter 6 MCQ Question Answer for Preparation of Exams. Here we Provide Class 12 Math Question Answer, Important Questions, MCQ for Various State Boards Students like CBSE, Haryana, uttar pradesh, mp and other state students.

**Also Read : – Class 12 Math NCERT Solution**

NCERT Class 12 Math Chapter 6 Application of Derivatives MCQ Question Answer Solution.

**Application of Derivatives Class 12 Math Chapter 6 MCQ Question Answer**

**Multiple Choice Questions and Answer for Easy to Understand the Chapter.**

**1. The rate of change of the area of a circle per second with respect to its radius r when r = 5cm is**

(A) 8π cm^{2}/s

(B) 10π cm^{2}/s

(C) 16π cm^{2}/s

(D) 3π cm^{2}/s

**Answer**

**Ans. (B) 10π cm ^{2}/s**

**2. The interval in which y = x ^{2}e^{-x }is increasing in**

(A) ( -∞, ∞)

(B) (-2, 0)

(C) (2, ∞)

(D) (0, 2)

**Answer**

**Ans. (D) (0, 2)**

**3. The slope of the tangent to the curve y = x ^{3 }– x at x = 2 is**

(A) 9

(B) 10

(C) 11

(D) 12

**Answer**

**Ans. (C) 11**

**4. The slope of the normal to the curve y = 2x ^{2 }+ 3sinx at x = 0 is**

(A) 3

(B) 1/3

(C) -3

(D) -1/3

**Answer**

**Ans. (D) -1/3**

**5. The line y = x + 1 is a tangent to the curve y ^{2} = 4x at the point**

(A) (1, 2)

(B) (2, 1)

(C) (1, -2)

(D) (-1, 2)

**Answer**

**Ans. (A) (1, 2)**

**6. The approximate change in the volume of a cube of side x metres caused by increasing the side by 3% is**

(A) 0.06 x^{3} m^{3}

(B) 0.6 x^{3} m^{3}

(C) 0.09 x^{3} m^{3}

(D) 0.9 x^{3} m^{3}

**Answer**

**Ans. (C) 0.09 x ^{3} m^{3}**

**7. f(x) = x ^{3} − 3x + 4 has a maxima at x is equal to : **

(A) -1

(B) 1

(C) 0

(D) None of the above

**Answer**

**Ans. (A) -1**

**8. f (x) = log(sinx) is strictly decreasing in interval : **

(A) ( 0, π/2 )

(B) ( π/2, π )

(C) ( 0, π )

(D) None of the above

**Answer**

**Ans. (B) ( π/2, π )**

**9. f (x) = sin x + cos x has a local maxima at x is equal to :**

(A) 0

(B) π/6

(C) π/4

(D) π/2

**Answer**

**Ans. (C) π/4**

**10. f (x) = log(sinx) is strictly increasing in the interval : **

(A) ( 0, π/2 )

(B) ( π/2, π )

(C) ( 0, π )

(D) None of the above

**Answer**

**Ans. (A) ( 0, π/2 )**

**11. The function f (x) = sin x − cos x, 0 < x < 2π has a local maxima at x is equal to : **

(A) π/4

(B) 3π/4

(C) 5π/4

(D) None of the above

**Answer**

**Ans. (B) 3π/4**

**12. f (x) = log(cos x) is strictly increasing in the interval :**

(A) ( 0, π/2 )

(B) ( -π/2, π/2 )

(C) ( 0, π )

(D) None of the above

**Answer**

**Ans. (D) None of the above**

**13. f (x) = cos x − sin x has a local maxima at x is equal to :**

(A) π/4

(B) 3π/4

(C) 5π/4

(D) 7π/4

**Answer**

**Ans. (D) 7π/4**