1
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following for the next items that follow:

Let $f(x)=\left\{\begin{array}{cc} a x(x+1)+b, & x<1 \\ x-1, & 1 \leq x \leq 2 \end{array}\right.$

If the function f(x) is differentiable at x = 1, then what is the value of (a + b)?
A
$-\frac{1}{3}$
B
-1
C
0
D
1
2
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following for the next items that follow:

Let $f(x)=\left\{\begin{array}{cc} a x(x+1)+b, & x<1 \\ x-1, & 1 \leq x \leq 2 \end{array}\right.$

What is $\displaystyle \lim _{x \rightarrow 0} $ f(x) equal to ?
A
$- \frac{1}{3} $
B
$-\frac{2}{3}$
C
0
D
1
3
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
If f(x) = |ln|x|| where 0 < x < 1, then what is f'(0.5) equal to ?
A
-2
B
-1
C
0
D
2
4
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
If f'(x) = cos (In x) and $y=f\left(\frac{2 x-3}{x}\right)$, then what is $\frac{d y}{d x}$ equal to ?
A
$ \cos \left(\ln \left(\frac{2 \mathrm{x}-3}{\mathrm{x}}\right)\right)$
B
$-\frac{3}{\mathrm{x}^2} \sin \left(\ln \left(\frac{2 \mathrm{x}-3}{\mathrm{x}}\right)\right)$
C
$\frac{3}{\mathrm{x}^2} \cos \left(\ln \left(\frac{2 \mathrm{x}-3}{\mathrm{x}}\right)\right)$
D
$-\frac{3}{\mathrm{x}^2} \cos \left(\ln \left(\frac{2 \mathrm{x}-3}{\mathrm{x}}\right)\right)$
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