1
MHT CET 2021 20th September Evening Shift
+2
-0

The equation of the plane that contains the line of intersection of the planes. $$x+2 y+3 z-4=0$$ and $$2 x+y-z+5=0$$ and is perpendicular to the plane $$5 x+3 y-6 z+8=0$$ is

A
$$14 x+7 y-7 z-4=0$$
B
$$33 x+45 y+50 z-41=0$$
C
$$-33 x+45 y-50 z+41=0$$
D
$$5 x+31 y+50 z-41=0$$
2
MHT CET 2021 20th September Evening Shift
+2
-0

The vector equation of the line whose Cartesian equations are y = 2 and 4x $$-$$ 3z + 5 = 0 is

A
$$\overline{\mathrm{r}}=(2 \hat{\mathrm{j}}+\hat{\mathrm{k}})+\lambda(3 \hat{\mathrm{i}}-4 \hat{\mathrm{k}})$$
B
$$\overline{\mathrm{r}}=\left(2 \hat{\mathrm{j}}+\frac{5}{3} \hat{\mathrm{k}}\right)+\lambda(3 \hat{\mathrm{i}}+4 \hat{\mathrm{k}})$$
C
$$\bar{r}=(2 \hat{i}+\hat{k})+\lambda(3 \hat{i}+4 \hat{j})$$
D
$$\overline{\mathrm{r}}=\left(2 \hat{\mathrm{j}}+\frac{5}{3} \hat{\mathrm{k}}\right)+\lambda(3 \hat{\mathrm{i}}-4 \hat{\mathrm{k}})$$
3
MHT CET 2021 20th September Morning Shift
+2
-0

The Cartesian equation of the plane passing through the point $$(0,7,-7)$$ and containing the line $$\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}$$ is

A
$$2 x+y-z=14$$
B
$$x+2 y+z=7$$
C
$$x+y+z=0$$
D
$$2 x+y+z=0$$
4
MHT CET 2021 20th September Morning Shift
+2
-0

If the lines $$\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$$ and $$\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}$$ intersect, then the values of $$k$$ is

A
$$\frac{3}{2}$$
B
$$\frac{-3}{2}$$
C
$$\frac{-2}{9}$$
D
$$\frac{9}{2}$$
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