CUET Mathematics MCQs Applications of Derivatives

Question : If the rate of change of volume of a sphere is equal to the rate of change of its radius then the surface area of sphere is

a) 1

b) 3

c) 1/3

d) 0

Answer : 1

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

a) 12π

b) 11π

c) 8π

d) 10π

Answer : 12π

Question : The rate of change of volume of a sphere is equal to the rate of change of the radius then its radius equal to

a)

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b)

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c) π units

d)

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Answer :

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Question :  Let h(x) = f(x) – [f (x)]² + [f (x)]³ for every real number x. Then

a) h is increasing whenever f is increasing

b) h is increasing whenever f is decreasing

c) h is decreasing whenever f is increasing

d) Nothing can be said in general

Answer : h is increasing whenever f is increasing

Question :  Total revenue in rupees 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) Rs 126

b) Rs 36

c) Rs 96

d) Rs 116

Answer : Rs 126

Question : The function f(x) = Sinx (1 + Cosx) is maximum in the interval [0, π] at x is equal to

a) π/3

b) π/4

c) π/6

d) π/2

Answer : π/3

Question :  Let f (x) = 1 + 2x² + 2²x⁴ + …… + 2¹⁰x²⁰. Then f (x) has

a) Exactly one minima

b) Ablest one maximum

c) None of these

d) More than one minima

Answer : Exactly one minima

Question : If the rate of change of area of the circle is equal to the rate of change of its diameter then its radius is equal to

a)

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b)

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c) π units

d)

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Answer :

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Question :  The number of roots of x³– 3x + 1 = 0 in [1, 2] is

a) One

b) Two

c) Three

d) None of these

Answer :  One

Question : The maximum value of sin x . cos x is

a) 1/2

b) 1/4

c) √2

d) None of these

Answer : 1/2