1
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Domain of definition of the real valued function $f(x)=\sqrt{\sin ^{-1}(2 x)+\frac{\pi}{6}}$ is

A
$\left[-\frac{1}{4}, \frac{1}{2}\right]$
B
$\left[\frac{-3}{2}, \frac{1}{2}\right]$
C
$\left[\frac{-3}{2}, \frac{1}{9}\right]$
D
$\left[-\frac{1}{4}, \frac{3}{4}\right]$
2
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The value of m , such that $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-m}{2}$ lies in the plane $2 x-4 y+z=7$, is

A
7
B
$-$7
C
no real value
D
4
3
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Suppose that $\bar{p}, \bar{q}$ and $\overline{\mathrm{r}}$ are three non-coplanar vectors in $\mathbb{R}^3$. Let the components of a vector $\overline{\mathrm{s}}$ along $\overline{\mathrm{p}}, \overline{\mathrm{q}}$ and $\overline{\mathrm{r}}$ be 4,3 and 5 respectively. If the components of this vector $\overline{\mathrm{s}}$ along $(-\overline{\mathrm{p}}+\overline{\mathrm{q}}+\overline{\mathrm{r}}),(\overline{\mathrm{p}}-\overline{\mathrm{q}}+\overline{\mathrm{r}})$ and $(-\overline{\mathrm{p}}-\overline{\mathrm{q}}+\overline{\mathrm{r}})$ are $x$, $y$ and $z$ respectively, then the value of $2 x+y+z$ is

A
10
B
6
C
9
D
8
4
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$\int \frac{x^4+x^2+1}{x^2-x+1} d x$ is equal to

A
$\frac{x^3}{3}-\frac{x^2}{2}+x+\mathrm{c}$, (where c is a constant of integration)
B
$\frac{x^3}{3}+\frac{x^2}{2}+x+\mathrm{c}$, (where c is a constant of integration)
C
$\frac{x^3}{3}-\frac{x^2}{2}-x+\mathrm{c}$, (where c is a constant of integration)
D
$\frac{x^3}{3}+\frac{x^2}{2}-x+\mathrm{c}$, ( where c is a constant of integration)
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