1
MHT CET 2020 19th October Evening Shift
MCQ (Single Correct Answer)
+2
-0

The equations of planes parallel to the plane $x+2 y+2 z+8=0$, which are at a distance of 2 units from the point $(1,1,2)$ are

A
$x+2 y+2 z-5=0$ or $x+2 y+2 z-3=0$
B
$x+2 y+2 z-6=0$ or $x+2 y+2 z-7=0$
C
$x+2 y+2 z-13=0$ or $x+2 y+2 z-1=0$
D
$x+2 y+2 z+3=0$ or $x+2 y+2 z-5=0$
2
MHT CET 2020 19th October Evening Shift
MCQ (Single Correct Answer)
+2
-0

The equation of a plane containing the point $(1,-1,2)$ and perpendicular to the planes $2 x+3 y-2 z=5$ and $x+2 y-3 z=8$ is

A
$r(4 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})=15$
B
$\mathbf{r}(5 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}+2 \hat{\mathbf{k}})=5$
C
$\mathbf{r}(5 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-\hat{\mathbf{k}})=5$
D
$\mathbf{r}(5 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}-\hat{\mathbf{k}})=7$
3
MHT CET 2020 19th October Evening Shift
MCQ (Single Correct Answer)
+2
-0

The equation of the line passing through $(1,2,3)$ and perpendicular to the lines $x-1=\frac{y+2}{2}=\frac{z+4}{4}$ and $\frac{x-1}{2}=\frac{y-2}{2}=z+3$ is

A
$x-1=\frac{y-2}{2}=\frac{z-3}{4}$
B
$\frac{x-1}{4}=\frac{2-y}{5}=\frac{z-3}{2}$
C
$\frac{x-1}{6}=\frac{y-2}{7}=\frac{z-3}{2}$
D
$\frac{x-1}{6}=\frac{2-y}{7}=\frac{z-3}{2}$
4
MHT CET 2020 16th October Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the plane $$2 x+3 y+5 z=1$$ intersects the co-ordinate axes at the points $$A, B, C$$, then the centroid of $$\triangle A B C$$ is

A
$$(2,3,5)$$
B
$$\left(\frac{1}{6}, \frac{1}{9}, \frac{1}{15}\right)$$
C
$$\left(\frac{3}{2}, 1, \frac{3}{5}\right)$$
D
$$\left(\frac{1}{2}, \frac{1}{3}, \frac{1}{5}\right)$$
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