In This Post we are providing Chapter-6 Application of Derivatives NCERT MCQ for Class 12 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.
NCERT MCQ ON APPLICATION OF DERIVATIVES
Question 1.
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
Answer: (b) 12π
Question 2.
The total revenue 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) 126.
Question 3.
The interval in which y = x² e-x is increasing with respect to x is:
(a) (-∞, ∞)
(b) (-2,0)
(c) (2, ∞)
(d) (0, 2).
Answer: (d) (0, 2).
Question 4.
The slope of the normal to the curve y = 2x² + 3 sin x at x = 0 is
(a) 3
(b) 13
(c) -3
(d) –13
Answer: (d) –13
Question 5.
The line y = x + 1 is a tangent to the curve y² = 4x at the point:
(a) (1, 2)
(b) (2, 1)
(c) (1, -2)
(d) (-1, 2).
Answer: (a) (1, 2)
Question 6.
If f(x) = 3x² + 15x + 5, then the approximate value of f(3.02) is:
(a) 47.66
(b) 57.66
(c) 67.66
(d) 77.66.
Answer: (d) 77.66.
Question 7.
The approximate change in the volume of a cube of side x metres caused by increasing the side by 3% is:
(a) 0.06 x³ m³
(b) 0.6 x³ m³
(c) 0.09 x³m³
(d) 0.9 x³ m³
Answer: (c) 0.09 x³m³
Question 8.
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) (2 √2, 4)
Question 9.
For all real values of x, the minimum value of 1−x+x21+x+x2 is
(a) 0
(b) 1
(c) 3
(d) 13
Answer: (d) 13
Question 10.
The maximum value of [x (x – 1) + 1]1/3, 0 ≤ x ≤ 1 is
(a) (13)13
(b) 12
(c) 1
(d) 0
Answer: (c) 1
Question 11.
A cylindrical tank of radius 10 m 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:
(a) 1 m/minute
(b) 0 × 1 m/minute
(c) 1 × 1 m/minute
(d) 0 × 5 m/minute.
Answer: (a) 1 m/minute
Question 12.
The slope of the tangent to the curve x = t² + 3t – 8, y = 2 t² – 2t – 5 at the point (2, -1) is:
(a) 227
(b) 67
(c) 76
(d) −67
Answer: (b) 67
Question 13.
The line y = mx + 1 is a tangent to the curve y² = 4x if the value of m is:
(a) 1
(b) 2
(c) 3
(d) 12
Answer: (a) 1
Question 14.
The normal at the point (1, 1) on the curve 2y + x² = 3 is
(a) x + y = 0
(b) x – y = 0
(c) x + y + 1 = 0
(d) x – y + 1 = 0.
Answer: (b) x – y = 0
Question 15.
The normal to the curve x² = 4y passing through (2, 1) is:
(a) x + y = 3
(b) x – y = 3
(c) x + y = 1
(d) x – y = 1.
Answer: (a) x + y = 3
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