1
NDA 2017 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the following statements
1. If $$\mathop {\lim }\limits_{x \to a} f(x)$$ and $$\mathop {\lim }\limits_{x \to a} g(x)$$ both exist, then $$\mathop {\lim }\limits_{x \to a} \{ f(x)g(x)\} $$ exists.
2. If $$\mathop {\lim }\limits_{x \to a} \{ f(x)g(x)\} $$ exists, then both $$\mathop {\lim }\limits_{x \to a} f(x)$$ and $$\mathop {\lim }\limits_{x \to a} g(x)$$ must exist.
Which of the above statement is/are correct?
1. If $$\mathop {\lim }\limits_{x \to a} f(x)$$ and $$\mathop {\lim }\limits_{x \to a} g(x)$$ both exist, then $$\mathop {\lim }\limits_{x \to a} \{ f(x)g(x)\} $$ exists.
2. If $$\mathop {\lim }\limits_{x \to a} \{ f(x)g(x)\} $$ exists, then both $$\mathop {\lim }\limits_{x \to a} f(x)$$ and $$\mathop {\lim }\limits_{x \to a} g(x)$$ must exist.
Which of the above statement is/are correct?
2
NDA 2018 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the function $$f(x) = \left\{ {\matrix{
{{{\sin 2x} \over {5x}},} & {if\,x \ne 0} \cr
{{2 \over {15}},} & {if\,x = 0} \cr
} } \right.$$
Which one of the following is correct in respect of the function?
Which one of the following is correct in respect of the function?
3
NDA 2018 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
For the function f(x) = | x $$-$$ 3 |, which one of the following is not correct?
4
NDA 2018 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
If the function $$f(x) = {{2x - {{\sin }^{ - 1}}x} \over {2x + {{\tan }^{ - 1}}x}}$$ is continuous at each point in its domain then what is the value of f(0) ?
Questions Asked from Limit, Continuity and Differentiability (Marks 2.5)
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Trigonometric Angles and Equations Inverse Trigonometric Function Height and Distance Properties of Triangles
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