1
MHT CET 2021 20th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$\overline{\mathrm{a}}, \overline{\mathrm{b}} , \overline{\mathrm{c}}$$ are three vectors which are perpendicular to $$\overline{\mathrm{b}}+\overline{\mathrm{c}}, \overline{\mathrm{c}}+\overline{\mathrm{a}}$$ and $$\overline{\mathrm{a}}+\overline{\mathrm{b}}$$ respectively, such that $$|\bar{a}|=2,|\bar{b}|=3,|\bar{c}|=4$$, then $$|\bar{a}+\bar{b}+\bar{c}|=$$

A
29
B
3
C
9
D
$$\sqrt{29}$$
2
MHT CET 2021 20th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$(2 \hat{\mathrm{i}}+6 \hat{\mathrm{i}}+27 \hat{\mathrm{k}}) \times(\hat{\mathrm{i}}+\lambda \hat{\mathrm{j}}+\mu \hat{\mathrm{k}})=\overline{0}$$, then $$\lambda$$ and $$\mu$$ are respectively

A
$$\frac{17}{2}, 3$$
B
$$3, \frac{17}{2}$$
C
$$3, \frac{27}{2}$$
D
$$\frac{27}{2}, 3$$
3
MHT CET 2020 19th October Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathbf{a}=3 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, \mathbf{b}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+7 \hat{\mathbf{k}}$ and $\mathbf{c}=7 \hat{\mathbf{i}}-\hat{\mathbf{j}}+23 \hat{\mathbf{k}}$ are three vectors, then which of the following statement is true.

A
$\mathbf{a}$ and $b$ are collinear
B
a, b, c are mutually perpendicular
C
a, b and c are coplanar
D
a, b and c are non-coplanar
4
MHT CET 2020 19th October Evening Shift
MCQ (Single Correct Answer)
+2
-0

$\mathbf{a}$ and $\mathbf{b}$ are non-collinear vectors. If $p=(2 x+1) a-b$ and $q=(x-2) a+b$ are collinear vectors, then $x=$

A
$\frac{1}{3}$
B
$-\frac{1}{3}$
C
$-3$
D
3
MHT CET Subjects
EXAM MAP