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

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

A
  $\frac{1}{2}$
B
$\frac{1}{4}$
C
$\frac{1}{6}$
D
$\frac{1}{8}$
2
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\quad \overline{\mathrm{a}}=\hat{\mathrm{i}}-\hat{\mathrm{k}}, \overline{\mathrm{b}}=x \hat{\mathrm{i}}+\hat{\mathrm{j}}+(1-x) \hat{\mathrm{k}} \quad$ and $\overline{\mathrm{c}}=y \hat{\mathrm{i}}+x \hat{\mathrm{j}}+(1+x-y) \hat{\mathrm{k}}$ then $\overline{\mathrm{a}} \cdot(\overline{\mathrm{b}} \times \overline{\mathrm{c}})$ depends on

A
only $x$
B
only $y$
C
neither $x$ nor $y$
D
both $x$ and $y$
3
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $\bar{a}, \bar{b}$ and $\bar{c}$ be three vectors having magnitudes 1,1 and 2 respectively. If $\overline{\mathrm{a}} \times(\overline{\mathrm{a}} \times \overline{\mathrm{c}})+\overline{\mathrm{b}}=\overline{0}$, then the acute angle between $\overline{\mathrm{a}}$ and $\overline{\mathrm{c}}$ is

A
$\frac{\pi}{3}$
B
$\frac{\pi}{6}$
C
$\frac{\pi}{4}$
D
$\frac{\pi}{12}$
4
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\overline{\mathrm{a}}$ and $\overline{\mathrm{c}}$ are unit vectors inclined at $\frac{\pi}{3}$ with each other and $(\overline{\mathrm{a}} \times(\overline{\mathrm{b}} \times \overline{\mathrm{c}})) \cdot(\overline{\mathrm{a}} \times \overline{\mathrm{c}})=5$, then the value of $5[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]=$

A
$-$10
B
10
C
50
D
$-$50
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