1
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\bar{a}=a_1 \hat{i}+a_2 \hat{j}+a_3 \hat{k}, \quad \bar{b}=b_1 \hat{i}+b_2 \hat{j}+b_3 \hat{k}$, $\bar{c}=c_1 \hat{i}+c_2 \hat{j}+c_3 \hat{k}$ and $\left[\begin{array}{lll}3 \bar{a}+\bar{b} & 3 \bar{b}+\bar{c} & 3 \bar{c}+\bar{a}\end{array}\right]=\lambda\left|\begin{array}{lll}\overline{\mathrm{a}} \cdot \hat{\mathrm{i}} & \overline{\mathrm{a}} \cdot \hat{\mathrm{j}} & \overline{\mathrm{a}} \cdot \hat{\mathrm{k}} \\ \overline{\mathrm{b}} \cdot \hat{\mathrm{i}} & \overline{\mathrm{b}} \cdot \hat{\mathrm{j}} & \overline{\mathrm{b}} \cdot \hat{\mathrm{k}} \\ \overline{\mathrm{c}} \cdot \hat{\mathrm{i}} & \overline{\mathrm{c}} \cdot \hat{\mathrm{j}} & \overline{\mathrm{c}} \cdot \hat{\mathrm{k}}\end{array}\right|,$ then the value of $\lambda$ is

A
27
B
28
C
4
D
3
2
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The domain of the function $\mathrm{f}(x)=\frac{\sin ^{-1}(x-3)}{\sqrt{9-x^2}}$ is

A
$(2,3)$
B
$[2,3)$
C
$[2,3]$
D
$(2,3]$
3
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\bar{a}=2 \hat{i}+2 \hat{j}+3 \hat{k}, \quad \bar{b}=-\hat{i}+2 \hat{j}+\hat{k}$ and $\bar{c}=3 \hat{i}+\hat{j}$ are the vectors such that $\overline{\mathrm{a}}+\lambda \overline{\mathrm{b}}$ is perpendicular to $\bar{c}$, then value of $\lambda$ is

A
6
B
$-$6
C
8
D
$-$8
4
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The area (in sq. units) bounded between the parabolas $x^2=\frac{y}{4}$ and $x^2=9 y$ and the line $y=2$ is

A
$20 \sqrt{2}$
B
$\frac{10 \sqrt{2}}{3}$
C
$\frac{20 \sqrt{2}}{3}$
D
$10 \sqrt{2}$
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