1
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The shortest distance between lines $\bar{r}=(\hat{i}+2 \hat{j}-\hat{k})+\lambda(2 \hat{i}+\hat{j}-3 \hat{k})$ and $\bar{r}=(2 \hat{i}-\hat{j}+2 \hat{k})+\mu(\hat{i}-\hat{j}+\hat{k})$ is

A
$\frac{4 \sqrt{2}}{19}$ units
B
$\frac{3 \sqrt{2}}{\sqrt{19}}$ units
C
$\frac{5 \sqrt{2}}{\sqrt{19}}$ units
D
$\frac{2 \sqrt{2}}{\sqrt{19}}$ units
2
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The graphical solution set of the system of inequations $x+y \geq 1,7 x+9 y \leq 63, y \leq 5, x \leq 6$, $x \geq 0, y \geq 0$ is represented by

MHT CET 2024 10th May Evening Shift Mathematics - Linear Programming Question 13 English

A
Fig. 1
B
Fig. 2
C
Fig. 3
D
Fig. 4
3
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$\tan \left(\cos ^{-1} \frac{1}{\sqrt{2}}+\tan ^{-1} \frac{1}{2}\right)=$

A
1
B
2
C
3
D
4
4
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $x^2 y^2=\sin ^{-1} x+\cos ^{-1} x$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at $x=1$ and $y=2$ is

A
$\frac{1}{2}$
B
$2$
C
$-\frac{1}{2}$
D
$-2$
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