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

Let $$\alpha$$ and $$\beta$$ be the distinct roots of $$a x^2+b x+c=0$$, then $$\lim _\limits{x \rightarrow \alpha} \frac{1-\cos \left(a x^2+b x+c\right)}{(x-\alpha)^2}$$ is equal to

A
$$ \frac{a^2(\alpha-\beta)^2}{2} $$
B
$$ \frac{(\alpha-\beta)^2}{2} $$
C
$$ \frac{-a^2(\alpha-\beta)^2}{2} $$
D
0
2
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { The value of } \lim _\limits{x \rightarrow 1} \frac{x^{15}-1}{x^{10}-1}= $$

A
$$\frac{2}{3}$$
B
1
C
$$\frac{3}{2}$$
D
Does not exist
3
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } f(x)=\left\{\begin{array}{cc} x & , \quad 0 \leq x \leq 1 \\ 2 x-1 & , \quad x>1 \end{array}\right. \text { then } $$

A
$$f$$ is not continuous but differentiable at $$x=1$$
B
$$f$$ is differentiable at $$x=1$$
C
$$f$$ is continuous but not differentiable at $$x=1$$
D
$$f$$ is discontinuous at $$x=1$$
4
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
$$\frac{1}{8}$$
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