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

The coefficient of the third term in the expansion of $$\left(x^2-\frac{1}{4}\right)^n$$, when expanded in the descending power of $$x$$ is 31, then $$n$$ is

A
31
B
16
C
30
D
32
2
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If }|\vec{a} \times \vec{b}|^2+|\vec{a} \cdot \vec{b}|^2=144 ~\&~|\vec{a}|=4 \text { then }|\vec{b}|= $$

A
3
B
12
C
8
D
16
3
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } \sin A=\frac{4}{5} \text { and } \cos B=\frac{-12}{13} \text { where } A \text { and } B \text { lie in first and third quadrant respectively. Then } \cos (A+B)= $$

A
$$ \frac{16}{65} $$
B
$$ \frac{-56}{65} $$
C
$$ \frac{56}{65} $$
D
$$ \frac{-16}{65} $$
4
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int_\limits{-1}^1 \frac{d}{d x}\left(\tan ^{-1} \frac{1}{x}\right) d x \text { is } $$

A
$$ \frac{\pi}{4} $$
B
$$ -\frac{\pi}{2} $$
C
$$ -\frac{\pi}{4} $$
D
$$ \frac{\pi}{2} $$
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