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1
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
Find the value of $\lim\limits_{h \rightarrow 0} \frac{(a+h)^2 \sin (a+h)-a^2 \sin a}{h}$
A
$-a^2 \sin a$
B
0
C
1
D
$a^2 \cos a+2 a \sin a$
2
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
The value of $\lim _\limits{x \rightarrow 0} \frac{(1-x)^n-1}{x}=$
A
n
B
0
C
$-$n
D
1
3
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
$m \neq 1$
4
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
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