1
MHT CET 2021 24th September Evening Shift
+2
-0

If $$G(3,-5, r)$$ is the centroid of $$\triangle A B C$$, where $$A \equiv(7,-8,1), B \equiv(p, q, 5), C \equiv(q+1,5 p, 0)$$ are vertices of the triangle $$A B C$$, then the values of $$p, q, r$$ are respectively

A
$$-2,3,2$$
B
$$-4,5,4$$
C
$$6,5,4$$
D
$$2,-2,3$$
2
MHT CET 2021 24th September Evening Shift
+2
-0

If the lines $$\frac{2 x-4}{\lambda}=\frac{y-1}{2}=\frac{z-3}{1}$$ and $$\frac{x-1}{1}=\frac{3 y-1}{\lambda}=\frac{z-2}{1}$$ are perpendicular to each other, then $$\lambda=$$

A
$$\frac{-7}{6}$$
B
$$\frac{6}{7}$$
C
$$\frac{-6}{7}$$
D
$$\frac{7}{6}$$
3
MHT CET 2021 24th September Evening Shift
+2
-0

The co-ordinates of the points on the line $$\frac{x+2}{1}=\frac{y-1}{2}=\frac{z+1}{-2}$$ at a distance of 12 units from the point A($$-$$2, 1, $$-$$1) are

A
$$(2,9,-9),(-6,-7,7)$$
B
$$(2,9,7),(6,5,-9)$$
C
$$(6,9,-5),(-10,9,-5)$$
D
$$(6,-7,3),(-10,9,3)$$
4
MHT CET 2021 24th September Evening Shift
+2
-0

If the vector equation of the plane $$\bar{r}=(2 \hat{i}+\hat{k})+\lambda \hat{i}+\mu(\hat{i}+2 \hat{j}-3 \hat{k})$$ in scalar product form is given by $$\overline{\mathrm{r}} \cdot(3 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})=\alpha$$ then $$\alpha=$$

A
2
B
3
C
1
D
0
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