1
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?
A
It is not continuous at x = 0
B
It is continuous at every x
C
It is not continuous at x = $$\pi$$
D
It is continuous at x = 0
2
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?
A
The function is not continuous at x = $$-$$3
B
The function is continuous at x = 3
C
The function is differentiable ta x = 0
D
The function is differentiable at x = $$-$$3
3
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) ?
A
$$ - {1 \over 3}$$
B
$${1 \over 3}$$
C
$${2 \over 3}$$
D
2
4
NDA 2018 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
If $$f(x) = \sqrt {25 - {x^2}} $$, then what is $$\mathop {\lim }\limits_{x \to 1} {{f(x) - f(1)} \over {x - 1}}$$ equal to ?
A
$$ - {1 \over {\sqrt {24} }}$$
B
$${1 \over {\sqrt {24} }}$$
C
$$ - {1 \over {4\sqrt 3 }}$$
D
$${1 \over {\sqrt{4\sqrt 3} }}$$
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