JEE Questions for Maths Limits Continuity And Differentiability Quiz 22 - MCQExams.com

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3/2
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0
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1
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1/2

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If f : R → C is defined by f (x) = e^2ix for x R,then f is (where C denotes the set of all complex numbers)

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One-one
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Onto
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One-one and onto
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Neither one-one nor onto

Let [x] denote the greatest integer less than or equal to x.If x = (√3 + 1)⁵ , then [x] is equal to

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75
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50
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76
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51
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152

The range of the function f(x) = log_e(3x² +is equal to

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[loge 2, ∞]
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[loge 3, ∞)
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[2 loge 3, ∞]
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[0, ∞)
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[2loge 2, ∞]

If f(x) = sin x + cos x , x ∈ (–∞, ∞) and g(x) = x², x ∈ (–∞,∞) , then (fog) (x) is equal to

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1
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0
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sin2(x) + cos(x2)
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sin(x+ cos2(x)
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sin(x+ cos(x2)

The period of the function f(x) = |sin 2x| + |cos 8x| is

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2π
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π
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2π/3
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π/2
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π/4

If g(y) is inverse of function f : R → R given by f(x) = x + 3, then g(y) =

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y + 3
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y – 3
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y/3
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3y

If f is a real valued function such that f(x + y) = f(x) + f(y) and f(= 5, then the value of f(is

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200
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350
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400
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500

Let R be the set of real numbers and the mapping f : R → R and g : R → R be defined by f(x) = 5 – x² and g(x) = 3x – 4, then the value of (fog)(–is

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–44
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–54
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–32
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–64

A = {1,2,3,4}, B = {1,2,3,4,5,6} are two sets and function f : A → B is defined by f(x) = x + 2; ∀ x ∈ A, then the function f is

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Bijective
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Onto
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One-one
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Many-one

Maths-Limits Continuity and Differentiability-37739.png

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Odd
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Even
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Neither odd nor even
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Constant

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(–3,3)
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[–3,3]
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(–∞, –∪ (3, ∞)
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(–∞, –3] ∪ [3, ∞)

Let f = {1, 1), (2, 4), (0, –2), (0, –2), (–1, –} be a linear function from Z into Z. Then f(x) is

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f(x) = 3x – 2
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f(x) = 6x – 8
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f(x) = 5x – 2
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f(x) = 7x + 2

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f = g
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f = 2g
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g = 2f
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None of these

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The function f : [0,3] → [1, 29], defined by f(x) = 2x³ –15x² + 36x + 1 is

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One-one and onto
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Onto but not one-one
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One-one but not onto
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Neither one-one nor onto

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3
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f(x) is continuous at x = 0
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f(x) is discontinuous at x = 0
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none of these

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If f(x) is twice differentiable polynomial function such that f(= 1, f(= -4, f(= 9, then

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Which of the following is not true ?

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Every differentiable function is continuous
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If derivative of a function is zero at all points, then the function is constant
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If a function has maximum or minimum at a point, then the function is differentiable at that point and its derivative is zero
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If a function is constant, then its derivative is zero at all points

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Differentiable both at x = 0 and at x = 2
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Differentiable at x = 0 but not differentiable at x = 2
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Not differentiable at x = 0 but differentiable at x = 2
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Differentiable neither at x = 0 nor at x = 2

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Maths-Limits Continuity and Differentiability-37804.png

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A = 0, B = 1
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A = 1,B = 1
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A = –1, B = 1
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A = –1, B = 0

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0
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1/4
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–1/4
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None of these

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Maths-Limits Continuity and Differentiability-37813.png

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Continuous at the origin
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Discontinuous at the origin because |x| is discontinuous there
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Maths-Limits Continuity and Differentiability-37817.png

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a = 3, b = 2
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a = 2, b = 3
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a = 7,b = 9
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None of these

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1

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Is equal to -1
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Does not exist because f is bounded
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Is not attained even through f is bounded
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Is equal to +1

If for two functions g and f, gof is both injective and surjective, then which of the following is true?

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g and f should be injective and surjective
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g should be injective and surjective
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f should be injective and surjective
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None of them may be surjective and injective

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Even function
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Odd function

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Maths-Limits Continuity and Differentiability-37884.png

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One-one onto
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One-one not onto
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Not one-one but onto
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Not one-one not onto

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None of these

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