1
COMEDK 2024 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { The number of points of discontinuity of the rational function } f(x)=\frac{x^2-3 x+2}{4 x-x^3} $$

A
3
B
2
C
5
D
1
2
COMEDK 2024 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { The value of } \lim _\limits{x \rightarrow 0} \frac{\sin (a+x)-\sin (a-x)}{x} \text { is } $$

A
1
B
0
C
$$ 2 \cos a $$
D
$$ 2 \sin a $$
3
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } f(x)=\left\{\begin{array}{cc} \frac{1-\sin x}{(\pi-2 x)^2} & , \quad \text { if } x \neq \frac{\pi}{2} \\ \lambda, & \text { if } x=\frac{\pi}{2} \end{array}\right. $$

Then $$f(x)$$ will be continues function at $$x=\frac{\pi}{2}$$, then $$\lambda=$$

A
$$-\frac{1}{8}$$
B
1
C
$$\frac{1}{4}$$
D
$$\frac{1}{8}$$
4
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$\lim _\limits{x \rightarrow 0} \frac{\sqrt{a+x}-\sqrt{a}}{x \sqrt{a(a+x)}}$$ equals to

A
$$a^{-\frac{3}{2}}$$
B
$$\frac{1}{2 a^{\frac{3}{2}}}$$
C
$$\frac{1}{2}$$
D
$$2 a^{-\frac{3}{2}}$$
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