1
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
2
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
3
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following for the next two (02) items that follow:

Let $f(x) = \frac{x}{\ln x}; (x > 1)$

Consider the following statements :
1. $f(x)$ is increasing in the interval $(e, \infty)$
2. $f(x)$ is decreasing in the interval $(1, e)$
3. $9 \ln 7 > 7 \ln 9$
Which of the statements given above are correct ?

A

1 and 2 only

B

2 and 3 only

C

1 and 3 only

D

1, 2 and 3

4
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following for the next two (02) items that follow:

Let $f(x) = |x| + 1$ and $g(x) = [x] - 1$, where [.] is the greatest integer function.

Let $h(x) = \frac{f(x)}{g(x)}$.

What is $\lim\limits_{x \to 0-} h(x) + \lim\limits_{x \to 0+} h(x)$ equal to?

A

$-\frac{3}{2}$

B

$-\frac{1}{2}$

C

$\frac{1}{2}$

D

$\frac{3}{2}$

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