1
NDA 2015 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
$${1 \over 5}$$
B
$${1 \over {\sqrt {24} }}$$
C
$$\sqrt {24} $$
D
$$ - {1 \over {\sqrt {24} }}$$
2
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the function

$$f(x) = \left\{ {\matrix{ {ax - 2,} & {for} & { - 2 < x < - 1} \cr { - 1,} & {for} & { - 1 \le x \le 1} \cr {a + 2{{(x - 1)}^2},} & {for} & {1 < x < 2} \cr } } \right.$$

What is the value of a for which f(x) is continuous at x = $$-$$1 and x = 1?
A
$$-$$1
B
1
C
0
D
2
3
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
The function $$f(x) = {{1 - \sin x + \cos x} \over {1 + \sin x + \cos x}}$$ is not defined at x = $$\pi$$. The value of f($$\pi$$), so that f(x) is continuous at x = $$\pi$$, is
A
$$ - {1 \over 2}$$
B
$${1 \over 2}$$
C
$$-$$1
D
1
4
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the following functions

1. $$f(x) = \left\{ \matrix{ {1 \over x},\,if\,x \ne 0 \hfill \cr 0,\,if\,x = 0 \hfill \cr} \right.$$

$$f(x) = \left\{ {\matrix{ {2x + 5,} & {if\,x > 0} \cr {{x^2} + 2x + 5,} & {if\,x \le 0} \cr } } \right.$$

Which of the above functions is/are derivable at x = 0 ?
A
Only 1
B
Only 2
C
Both 1 and 2
D
Neither 1 nor 2
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