1
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
If $$f(x) = {{\sin ({e^{x - 2}} - 1)} \over {\ln (x - 1)}}$$, then $$\mathop {\lim }\limits_{x \to 2} $$ f(x) is equal to
A
$$-$$2
B
$$-$$1
C
0
D
1
2
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the function

$$f(x) = \left\{ {\matrix{ { - 2\sin x,} & {if} & {x \le - {\pi \over 2}} \cr {A\sin x + B,} & {if} & { - {\pi \over 2} < x < {\pi \over 2}} \cr {\cos x,} & {if} & {x \ge {\pi \over 2}} \cr } } \right.$$

which is continuous everywhere.
The value of A is
A
1
B
0
C
$$-$$1
D
$$-$$2
3
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the function

$$f(x) = \left\{ {\matrix{ { - 2\sin x,} & {if} & {x \le - {\pi \over 2}} \cr {A\sin x + B,} & {if} & { - {\pi \over 2} < x < {\pi \over 2}} \cr {\cos x,} & {if} & {x \ge {\pi \over 2}} \cr } } \right.$$

which is continuous everywhere.
The value of B is
A
1
B
0
C
$$-$$1
D
$$-$$2
4
NDA 2016 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the following in respect of the function

$$f(x) = \left\{ \matrix{ 2 + x,x \ge 0 \hfill \cr 2 - x,x < 0 \hfill \cr} \right.$$.

I. $$\mathop {\lim }\limits_{x \to 1} f(x)$$ does not exist.

II. f(x) is differentiable at x = 0.

III. f(x) is continuous at x = 0.

Which of the above statements is/are correct?
A
I only
B
III only
C
II and III
D
I and III
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