1
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
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 ?
A
Both the statements are true and Statement II is the correct explanation of Statement I
B
Both the statements are true and Statement II is not the correct explanation of Statement I
C
Statement I is true but Statement II is false
D
Statement I is false but Statement II is true
2
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 ?
A
$$\ln \left( {{{1 - x} \over {1 + x}}} \right)$$
B
$$\ln \left( {{{2 + x} \over {1 - x}}} \right)$$
C
$${\tan ^{ - 1}}\left( {{{1 - x} \over {1 + x}}} \right)$$
D
$${\tan ^{ - 1}}\left( {{{1 + x} \over {1 - x}}} \right)$$
3
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 ?
A
[0, 1)
B
[0, 1]
C
(0, 1)
D
(0, 1]
4
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 ?
A
One
B
Two
C
Three
D
Four
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