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NCERT Class 12 Mathematics Chapters
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1.
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An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?
(a) 100 cm3/s (b) 300 cm3/s (c) 900 cm3/s (d) 600 cm3/s
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2.
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The point on the curve y2 = 8x for which the abscissa and ordinate change at the same rate is :
(a) (2, 4) (b) (4, 2) (c) (0, 2) (d) (2, 0)
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3.
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The rate of change in area of a triangle having sides 10 cm and 12 cm when the variable angle between them is θ = 60°, is :
(a) 30 cm2/radian (b) 120 cm2/radian (c)
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4.
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The rate of change of the area of an equilateral triangle with respect to its side when its side = 2 is:
(a)
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5.
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An insect moves along the ellipse
A. I or II B. III or IV C. II or III D. II or IV
Choose the correct answer from the options given below:
(a) D only (b) C only (c) A only (d) B only
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1.
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A particle moves along the curve 3y = ax3 + 1 such that at a point with x-coordinate = 1, y-coordinate is changing twice as fast as x-coordinate. Find the value of a.
(CBSE 2023, 2M)
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2.
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If the circumference of circle is increasing at the constant rate, prove that rate of change of area of circle is directly proportional to its radius.
(CBSE 2023, 2M)
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3.
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If equal sides of an isosceles triangle with fixed base 10 cm are increasing at the rate of 4 cm/sec, how fast is the area of triangle increasing at an instant when all sides become equal?
(CBSE 2023, 2M)
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4.
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Find the points on the curve 6y = x3 + 2 at which ordinate is changing 8 times as fast as abscissa.
(CBSE 2023, 2M)
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5.
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Find the point on the curve y2 = 8x for which the abscissa and ordinate change at the same rate.
(CBSE 2023, 2M)
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Chapter Name
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Sub Topic Name
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Chapter 6: Application of Derivatives
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6.1 Introduction
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6.2 Rate of Change
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6.3 Tangents and Normals
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6.4 Maxima and Minima
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6.5 Increasing and Decreasing Functions
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6.6 Applications in Physics and Engineering
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