1
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $f(x)=\left\{\begin{array}{ll}\frac{1-x^m}{1-x} & \text { if } x \neq 1 \\ 2 m-1 & \text { if } x=1\end{array}\right.$ and the function is discontinuous at $x=1$, then
A
$m=1$
B
$m \neq \frac{1}{2}$
C
$m=\frac{1}{2}$
D
$m \neq 1$
2
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
3
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
4
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 $$x=1$$
COMEDK Subjects
EXAM MAP