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 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{d x}{(x+2)\left(x^2+1\right)}=p \log |x+2|+q \log \left|x^2+1\right|+r \tan ^{-1} x+c$ then $p+q+r=$
A
$\frac{2}{5}$
B
$\frac{1}{2}$
C
$\frac{7}{10}$
D
16
3
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
Let R be a relation on natural numbers defined by $x+2 y=8, x, y \in N$. The domain of R is
A
$\{2,4,6,8\}$
B
$\{2,4,6\}$
C
$\{2,4,8\}$
D
$\{1,2,3\}$
4
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
Oil from a conical funnel is dripping at the rate of $5 \mathrm{~cm}^3 / \mathrm{s}$. If the radius and height of the funnel are 10 cm and 20 cm respectively, then the rate at which the oil level drops when it is 5 cm from the top is
A
$\frac{8}{45 \pi} \mathrm{~cm} / \mathrm{s}$
B
$-\frac{2 \pi}{45} \mathrm{~cm} / \mathrm{s}$
C
$-\frac{4 \pi}{45} \mathrm{~cm} / \mathrm{s}$
D
$-\frac{4}{45 \pi} \mathrm{~cm} / \mathrm{s}$
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