1
NDA 2016 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
If $$\mathop {\lim }\limits_{x \to 0} \phi (x) = {a^2}$$, where a $$\ne$$ 0, then what is $$\mathop {\lim }\limits_{x \to 0} \phi \left( {{x \over a}} \right)$$ equal to ?
A
a2
B
a$$-$$2
C
$$-$$a2
D
$$-$$a
2
NDA 2016 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
What is $$\mathop {\lim }\limits_{x \to 0} {e^{ - {1 \over {{x^2}}}}}$$ equal to ?
A
0
B
1
C
$$-$$1
D
Limit does not exist
3
NDA 2016 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the function $$f(x) = \left| {x - 1} \right| + {x^2}$$ where x $$\in$$ R, then which one of the following statements is correct?
A
f(x) is continuous but not differentiable at x = 0
B
f(x) is continuous but not differentiable at x = 1
C
f(x) is differentiable at x = 1
D
f(x) is not differentiable at x = 0 and x = 1
4
NDA 2017 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
A function is defined as follows

$$f(x) = \left\{ {\matrix{ { - {x \over {\sqrt {{x^2}} }},} & {x \ne 0} \cr {0,} & {x = 0} \cr } } \right.$$

Which one of the following is correct in respect of the above function?
A
f(x) is continuous at x = 0 but not differentiable at x = 0
B
f(x) is continuous as well as differentiable at x = 0
C
f(x) is discontinuous at x = 0
D
None of the above
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