1
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
A shopkeeper sells three varieties of fruit juice. He has a large number of bottles of same size of each variety. The number of different ways of displaying all the three varieties on the shelf with 5 places in a row and each display must have at least one bottle of each variety is
A
150
B
120
C
60
D
90
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 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
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