NDA 2015 Paper 2 | Functions Question 5 | Mathematics

Consider the following statements :

Statement I The function f : R $$\to$$ R such that f(x) = x³ for all x$$\in$$R is one-one.

Statement II f(a) = f(b) $$\Rightarrow$$ a = b for all a, b $$\in$$R, if the function f is one-one.

Which one of the following is correct in respect of the above statements ?

Both the statements are true and Statement II is the correct explanation of Statement I

Both the statements are true and Statement II is not the correct explanation of Statement I

Statement I is true but Statement II is false

Statement I is false but Statement II is true

NDA 2016 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

If $$f({x_1}) - f({x_2}) = f\left( {{{{x_1} - {x_2}} \over {1 - {x_1}{x_2}}}} \right)$$ for x₁, x₂ $$\in$$($$-$$1, 1), then what is f(x) equal to ?

$$\ln \left( {{{1 - x} \over {1 + x}}} \right)$$

$$\ln \left( {{{2 + x} \over {1 - x}}} \right)$$

$${\tan ^{ - 1}}\left( {{{1 - x} \over {1 + x}}} \right)$$

$${\tan ^{ - 1}}\left( {{{1 + x} \over {1 - x}}} \right)$$

NDA 2016 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

What is the range of the function $$y = {{{x^2}} \over {1 + {x^2}}}$$ where x$$\in$$R ?

[0, 1)

[0, 1]

(0, 1)

(0, 1]

NDA 2016 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

Consider the function $$f(x) = {{27({x^{2/3}} - x)} \over 4}$$.

How many solutions does the function f(x) = 1 have ?

One

Two

Three

Four

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