Find here the NCERT chapter-wise Multiple Choice Questions from Class 12 Mathematics book Chapter 6 Application of Derivatives with Answers Pdf free download. This may assist you to understand and check your knowledge about the chapters. Students also can take a free test of the Multiple Choice Questions of Application of Derivatives. Each question has four options followed by the right answer. These MCQ Questions are selected supported by the newest exam pattern as announced by CBSE.
NCERT MCQ Chapters for Class 12 Mathematics
Q1. Find the maximum profit that a company can make, if the profit function is given by P(x) = 41 + 24x – 18x².
(i) 25
(ii) 43
(iii) 62
(iv) 49
(iv) 49
Q2. The curve y – x1/5 at (0, 0) has
(i) a vertical tangent (parallel to y-axis)
(ii) a horizontal tangent (parallel to x-axis)
(iii) an oblique tangent
(iv) no tangent
(ii) a horizontal tangent (parallel to x-axis)
Q3. The rate of change of the area of a circle with respect to its radius r at r = 6 cm is:
(i) 10π
(ii) 12π
(iii) 8π
(iv) 11π
(ii) 12π
Q4. The value of f’(x) is -1 at the point P on a continuous curve y = f(x). What is the angle which the tangent to the curve at P makes with the positive direction of x axis?
(i) π/2
(ii) π/4
(iii) 3π/4
(iv) 3π/2
(iii) 3π/4
Q5. It is given that at x = 1, the function x4 – 62×2 + ax + 9 attains its maximum value on the interval [0, 2]. Find the value of a.
(i) 100
(ii) 120
(iii) 140
(iv) 160
(ii) 120
Q6. If the curve ay + x² = 7 and x³ = y, cut orthogonally at (1, 1) then the value of a is
(i) 1
(ii) 0
(iii) -6
(iv) 6
(iv) 6
Q7. The interval in which y = x² e-x is increasing with respect to x is:
(i) (-∞, ∞)
(ii) (-2,0)
(iii) (2, ∞)
(iv) (0, 2).
(iv) (0, 2).
Q8. What will be the differential function of √(x² + 2)?
(i) x√(x² + 2) dx
(ii) x/√(x² + 2) dx
(iii) x/√(x² – 2) dx
(iv) -x/√(x² + 2) dx
(ii) x/√(x² + 2) dx
Q9. The area of a right-angled triangle of the given hypotenuse is maximum when the triangle is
(i) scalene
(ii) equilateral
(iii) isosceles
(iv) None of these
(iii) isosceles
Q10. The equation of tangent to the curve y (1 + x²) = 2 – x, w here it crosses x-axis is:
(i) x + 5y = 2
(ii) x – 5y = 2
(iii) 5x – y = 2
(iv) 5x + y = 2
(i) x + 5y = 2
Q11. The line y = x + 1 is a tangent to the curve y² = 4x at the point:
(i) (1, 2)
(ii) (2, 1)
(iii) (1, -2)
(iv) (-1, 2).
(i) (1, 2)
Q12. What will be the average rate of change of the function [y = 16 – x²] at x = 4?
(i) -8
(ii) 8
(iii) -9
(iv) Depends on the value of x
(i) -8
Q13. The equation of the normal to the curves y = sin x at (0, 0) is
(i) x = 0
(ii) x + y = 0
(iii) y = 0
(iv) x – y = 0
(ii) x + y = 0
Q14. Let the f: R → R be defined by f (x) = 2x + cos x, then f
(i) has a minimum at x = 3t
(ii) has a maximum, at x = 0
(iii) is a decreasing function
(iv) is an increasing function
(iv) is an increasing function
Q15. The approximate change in the volume of a cube of side x metres caused by increasing the side by 3% is:
(i) 0.06 x³ m³
(ii) 0.6 x³ m³
(iii) 0.09 x³m³
(iv) 0.9 x³ m³
(iii) 0.09 x³m³
Q16. The time rate of change of the radius of a sphere is 1/2π. When it’s radius is 5cm, what will be the rate of change of the surface of the sphere with time?
(i) 10 sq cm
(ii) 20 sq cm
(iii) 30 sq cm
(iv) 40 sq cm
(ii) 20 sq cm
Q17. The tangent to the curve y = 2x² -x + 1 is parallel to the line y = 3x + 9 at the point
(i) (2, 3)
(ii) (2, -1)
(iii) (2, 1)
(iv) (1, 2)
(iv) (1, 2)
Q18. The function f(x) = tan x – x
(i) always increases
(ii) always decreases
(iii) sometimes increases and sometimes decreases
(iv) never increases
(i) always increases
Q19. A cylindrical tank of radius 10 mis being filled with wheat at the rate of 314 cubic m per minute. Then the depth of the wheat is increasing at the rate of:
(i) 1 m/minute
(ii) 0 × 1 m/minute
(iii) 1 × 1 m/minute
(iv) 0 × 5 m/minute.
(i) 1 m/minute
I Think the given NCERT MCQ Questions for class 12 Maths book Chapter 6 Application of Derivatives with Answers Pdf free download will assist you. If you’ve got any queries regarding CBSE Class 12 Maths Application of Derivatives MCQs Multiple Choice Questions with Answers, drop a comment below and that we will come back to you soon.
MCQ Questions for Class 12 Mathematics Chapter wise with Answers
- Lesson 1. Relations and Functions MCQs
- Lesson 2. Inverse Trigonometric Functions MCQs
- Lesson 3. Matrices MCQs
- Lesson 4. Determinants MCQs
- Lesson 5. Continuity and Differentiability MCQs
- Lesson 6. Application of Derivatives MCQs
- Lesson 7. Integrals MCQs
- Lesson 8. Application of Integrals MCQs
- Lesson 9. Differential Equations MCQs
- Lesson 10. Vector Algebra MCQs
- Lesson 11. Three Dimensional Geometry MCQs
- Lesson 12. Linear Programming MCQs
- Lesson 13. Probability MCQs