1
NDA 2019 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the following statements in respect of the function $$f(x) = \sin \left( {{1 \over x}} \right)$$ for x $$\ne$$ 0 and f(0) = 0 :

1. $$\mathop {\lim }\limits_{x \to 0} f(x)$$ exits

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

hich of the above statement is/are correct?
A
Only 1
B
Only 2
C
Both 1 and 2
D
Neither 1 nor 2
2
NDA 2019 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
$$\mathop {\lim }\limits_{x \to 0} {{1 - {{\cos }^3}4x} \over {{x^2}}}$$ is equal to
A
0
B
12
C
24
D
36
3
NDA 2019 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
The value of k which makes $$f(x) = \left\{ {\matrix{ {\sin x,} & {x \ne 0} \cr {k,} & {x = 0} \cr } } \right.$$ continuous at x = 0, is
A
2
B
1
C
$$-$$1
D
0
4
NDA Mathematics 1st September 2024
MCQ (Single Correct Answer)
+2.5
-0.833
Change Language
Which one of the following is correct regarding $\rm \lim\limits_{x\rightarrow 3}\frac{|x-3|}{x-3}$?
1
Limit exists and is equal to 1 
2
Limit exists and is equal to 0 
3
Limit exists and is equal to -1 
4
Limit does not exist  
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