JEE Questions for Maths Applications Of Derivatives Quiz 11 - MCQExams.com

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Which one is the correct statement about the function f(x) = sin 2x

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The statements (a), (b) and (c) are all correct

The function f defined by f(x) = (x + 2)e^–x is

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Decreasing for all x
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Decreasing in (–∞, –and increasing (–1, ∞)
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Increasing for all x
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Decreasing in (–1, ∞) and increasing in (–∞, –1)

If f(x) = x³ – 10x² + 200x – 10 then

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f(x) is decreasing in [ – ∞, 10] and increasing in [10, ∞]
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f(x) is increasing in [–∞, 10] and decreasing in [10, ∞]
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f(x) is increasing through real line
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f(x) is decreasing through real line

Maths-Applications of Derivatives-10148.png

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Both f(x) and g (x) are increasing functions
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Both f(x) and g(x) are decreasing functions
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f(x) is an increasing function
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g(x) is an increasing function

Select the correct statement from (a), (b), (c), (d). The function f(x) = x e^1–x

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If f(x) = x² + ax + 5 is increasing function in (2,then the minimum value of a is…; a ϵ R

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2
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–4
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–2
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4

Maths-Applications of Derivatives-10156.png

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ad – bc > 0
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ad – bc < 0
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ab – ad > 0
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ab – cd < 0

Maths-Applications of Derivatives-10158.png

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Increasing when x ≥ 0
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Strictly increasing when x > 0
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Strictly increasing at x = 0
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Not continuous at x = 0 and so it is not increasing when x > 0

Maths-Applications of Derivatives-10160.png

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cosec x
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tan x
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x2
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|x – 1|

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λ > 1
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λ < 1
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λ < 4
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λ>4

Maths-Applications of Derivatives-10164.png

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Strictly decreasing
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Strictly increasing
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Decreasing in (2,only
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Neither increasing nor decreasing

Maths-Applications of Derivatives-10166.png

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None of these

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(1,2e)
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(0, e)
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(2, 2e)
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Maths-Applications of Derivatives-10186.png

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An increasing function
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A decreasing function
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Both increasing and decreasing function
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None of the above

The function f(x) = x + cos x is

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Always increasing
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Always decreasing
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Increasing for certain range of x
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None of the above

The function f(x) = x^1/x is

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Increasing in (1, ∞)
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Decreasing in (1, ∞)
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Increasing in (1, e) decreasing in (e, ∞)
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Decreasing in (1, e), increasing in (e, ∞)

The function x^x is increasing, when

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For all real x

A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched?

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The length of the longest interval, in which the function 3 sin x – 4 sin3x increasing is

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Let f(x) = x³ + bx + cx + d, 0 < b² < c. Then f

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Is bounded
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Has a local maxima
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Has a local minima
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Is strictly increasing

Maths-Applications of Derivatives-10205.png

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Increasing
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Decreasing
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Stationary
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Discontinous

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Maths-Applications of Derivatives-10213.png

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The function f(x) = tan^–1 (sinx + cos x), x > 0 is always an increasing function on the interval

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2)
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Maths-Applications of Derivatives-10225.png

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Increasing
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Decreasing
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Even
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None of these

The function f(x) = ax + b is strictly increasing for all real x if

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a > 0
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a < 0
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a = 0
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a ≤ 0

Maths-Applications of Derivatives-10228.png

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[1.5, 3]
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For no interval
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[0, 3]
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[–3, 0]

Rolle’s theorem is not applicable to the function f(x) = |x| defined on [–1, 1] because

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f is not continuous on [–1, 1]
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f is not differentiable on (–1, 1)
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f(– ≠ f(1)
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f(–= f(≠ 0

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1
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2
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None of these

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None of these

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None of these

A function f is defined by f(x) = e^x sin x in [0, π]. Which of the following is not correct

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f is continuous in [0, π]
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f is differentiable in [0, π]
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f(= f(π)
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Rolle’s theorem is not true in [0, π]

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0
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None of these

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3
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0
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1
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2

Maths-Applications of Derivatives-10275.png

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a = – 11
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a = – 6
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a = 6
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a = 11

Maths-Applications of Derivatives-10277.png

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The abscissa of the points of the curve y = x³ in the interval [–2,2], where the slope of the tangents can be obtained by mean value theorem for the interval [–2, 2], are

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0

The function f(x) = (x – 3)² satisfies all the conditions of mean value theorem in [3, 4]. A point on y = (x – 3)², where the tangent is parallel to the chord joining (3,and (4,is

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(1, 4)
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(4, 1)

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In which of the following functions, Rolle’s theorem is applicable

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0:0:1

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