1
MHT CET 2025 19th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

The domain of the function $\mathrm{f}(x)={ }^{7-x} \mathrm{P}_{x-1}$ is

A
R
B
$\quad x \in \mathbb{R}-\{1\}$
C
$\{1,2,3,4\}$
D
$\quad\{1,2,3,4,5,6\}$
2
MHT CET 2025 19th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \frac{x+\sin x}{1+\cos x} d x= $$

A
$x \cos x+\mathrm{c}$, where c is the constant integration
B
$x \tan x+\mathrm{c}$, where c is the constant integration
C
$x \tan \frac{x}{2}+c$, where $c$ is the constant integration
D
$x \sec ^2 \frac{x}{2}+\mathrm{c}$, where c is the constant integration
3
MHT CET 2025 19th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\bar{a}, \bar{b}, \bar{c}$ are three vectors such that $|\bar{a}|=3$, $|\bar{b}|=5,|\bar{c}|=7$ then $|\bar{a}-\bar{b}|^2+|\bar{b}-\bar{c}|^2+|\bar{c}-\bar{a}|^2$ does not exceed

A
83
B
249
C
166
D
105
4
MHT CET 2025 19th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

Total number of 3-digit numbers, whose g.c.d with 36 is 2 , is

A
140
B
150
C
165
D
170

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