1
NDA 2016 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the equation $$f(x) = {{{a^{[x] + x}} - 1} \over {[x] + x}}$$ where [ . ] denotes the greatest integer function.
What is $$\mathop {\lim }\limits_{x \to {0^ + }} f(x)$$ equal to
A
1
B
ln a
C
1 $$-$$ a$$-$$1
D
Limit does not exist
2
NDA 2016 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the equation $$f(x) = {{{a^{[x] + x}} - 1} \over {[x] + x}}$$ where [ . ] denotes the greatest integer function.
What is $$\mathop {\lim }\limits_{x \to {0^ - }} f(x)$$ equal to?
A
0
B
ln a
C
1 $$-$$ a$$-$$1
D
Limit does not exist
3
NDA 2016 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
A function f(x) is defined as follows

$$f(x) = \left\{ {\matrix{ {x + \pi ,} & {for\,x \in [ - \pi ,0)} \cr {\pi \cos x,} & {for\,x \in \left[ {0,{\pi \over 2}} \right]} \cr {{{\left( {x - {\pi \over 2}} \right)}^2},} & {for\,x \in \left( {{\pi \over 2},\pi } \right]} \cr } } \right.$$
Consider the following statements

1. The function f(x) is continuous at x = 0.

2. The function f(x) is continuous at $$x = {\pi \over 2}$$

Which of the above statements is/are correct?
A
Only 1
B
Only 2
C
Both 1 and 2
D
Neither 1 nor 2
4
NDA 2016 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
A function f(x) is defined as follows

$$f(x) = \left\{ {\matrix{ {x + \pi ,} & {for\,x \in [ - \pi ,0)} \cr {\pi \cos x,} & {for\,x \in \left[ {0,{\pi \over 2}} \right]} \cr {{{\left( {x - {\pi \over 2}} \right)}^2},} & {for\,x \in \left( {{\pi \over 2},\pi } \right]} \cr } } \right.$$
Consider the following statements

1. The function f(x) is differentiable at x = 0.

2. The function f(x) is differentiable at x = $${\pi \over 2}$$.

Which of the above statements is/are correct?
A
Only 1
B
Only 2
C
Both 1 and 2
D
Neither 1 nor 2
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