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Class 12 Mathematics - Chapter 6: Application of Derivatives MCQ Questions

25 Questions 50 Minutes
Answered: 0 / 25Unanswered: 25

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Question 1

The interval in which y = x² e-x is increasing with respect to x is:

Question 2

The abscissa of the point on the curve 3y = 6x – 5x³, the normal at which passes through origin is:

Question 3

The rate of change of the area of a circle with respect to its radius r at r = 6 cm is:

Question 4

The slope of the tangent to the curve x = t² + 3t – 8, y = 2 t² – 2t – 5 at the point (2, -1) is:

Question 5

The two curves x³ – 3xy² + 2 = 0 and 3x²y – y³ = 2

Question 6

The normal at the point (1, 1) on the curve 2y + x² = 3 is

Question 7

The point on the curve y² = x, where the tangent makes an angle of (frac { π }{4}) with x-axis is:

Question 8

The normal to the curve x² = 4y passing through (2, 1) is:

Question 9

( lim _{x rightarrow infty}) (frac { f(3x) }{f(x)}) = 1. Then ( lim _{x rightarrow infty}) (frac { f(2x) }{f(x)}) =

Question 10

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

Question 11

For all real values of x, the minimum value of (frac { 1-x+x^2 }{1+x+x^2}) is

Question 12

x = et cos t, y = et sm t at t = (frac { π }{4}) makes with x-axis an angle:

Question 13

The slope of the normal to the curve y = 2x² + 3 sin x at x = 0 is

Question 14

The points on the curve 9y² = x³, where the normal to the curve makes equal intercepts with the axes are

Question 15

The point on the curve x² = 2y, which is nearest to the point (0, 5), is:

Question 16

The line y = mx + 1 is a tangent to the curve y² = 4x if the value of m is:

Question 17

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:

Question 18

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:

Question 19

The maximum value of [x (x – 1) + 1]1/3, 0 ≤ x ≤ 1 is

Question 20

The line y = x + 1 is a tangent to the curve y² = 4x at the point:

Question 21

Let f (x) = x² – (frac { 1 }{x^2}) and g(x) = x – (frac { 1 }{x}), x ∈ R – {-1, 0, 1}. If h(x) = (frac { f(x) }{g(x)}), then the local minimum value of h(x) is:

Question 22

If f(x) = 3x² + 15x + 5, then the approximate value of f(3.02) is:

Question 23

Twenty metres of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower bed is:

Question 24

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

Question 25

The real number k for which the equation 2x³ + 3x + k = 0 has two distinct real roots in [0,1]:

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