1
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
If f(x) = $\frac{x^2+x+|x|}{x}$, then what is $\displaystyle\lim_{x \rightarrow 0}$ f(x) equal to ?
A
0
B
1
C
2
D
$​\displaystyle\lim_{x \rightarrow 0}$ f(x) does not exist
2
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
What is $\displaystyle\lim_{h \rightarrow 0} \frac{\sin^2(x+h)−\sin^2x}{h}$ equal to ?
A
sin2 x
B
cos2 x
C
sin 2x
D
cos 2x
3
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Let f(x) be a function such that f'(x) = g(x) and f''(x) = −f(x). Let h(x) = {f(x)}2 + {g(x)}2. Then consider the following statements :

1. h'(3) = 0

2. h(1) = h(2)

Which of the statements given above is/are correct ?

A
1 only
B
2 only
C
Both 1 and 2
D
Neither 1 nor 2
4
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
If y = ln2$\left(\frac{x^2−x+1}{x^2+x+1}\right)$, then what is $\frac{\text{dy}}{\text{dx}}$ at x = 0 equal to ?
A
−2
B
0
C
1
D
2
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