1
VITEEE 2024
MCQ (Single Correct Answer)
+1
-0

$$ \int_0^\pi\left[\cos ^2\left(\frac{3 \pi}{8}-\frac{x}{4}\right)-\cos ^2\left(\frac{11 \pi}{8}+\frac{x}{4}\right)\right] d x$$ equals to

A
$\sqrt2$
B
$\sqrt3$
C
3
D
2
2
VITEEE 2024
MCQ (Single Correct Answer)
+1
-0

If the distance between the planes $8 x+12 y-14 z=2$ and $4 x+6 y-7 z=2$ can be expressed as $\frac{1}{\sqrt{N}}$, then the value of $\frac{N(N+1)}{2}$ is

A
4950
B
5050
C
5150
D
5151
3
VITEEE 2024
MCQ (Single Correct Answer)
+1
-0

The complex number $z$ satisfying $z+|z|$ $=1+7 i$, then the value of $|z|^2$ equals

A
625
B
169
C
49
D
25
4
VITEEE 2024
MCQ (Single Correct Answer)
+1
-0

Two red counters, three green counters and four blue counters are placed in a row in random order. The probability that no two blue counters are adjacent is

A
$\frac{7}{99}$
B
$\frac{7}{198}$
C
$\frac{5}{42}$
D
None of these
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