1
MHT CET 2025 26th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

The tangent to the ellipse $9 x^2+16 y^2=288$ making equal intercepts on the co-ordinate axes intersects the X -axis and the Y -axis in the points $A$ and $B$ respectively. Then $A(\triangle O A B)=$ (where O is origin)

A

$\frac{25}{2}$ sq. units

B

25 sq. units

C

$\frac{25 \sqrt{5}}{2}$ sq. units

D

$25 \sqrt{5}$ sq. units

2
MHT CET 2025 26th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

The distance of the point $\mathrm{A}(3,-4,5)$ from the plane $2 x+5 y-6 z=16$ measured along the line $\frac{x}{2}=\frac{y}{1}=\frac{z}{-2}$ is

A
$\frac{60}{7}$ units
B
$\frac{7}{60}$ units
C
$\frac{1}{7}$ units
D
$\frac{2}{7}$ units
3
MHT CET 2025 26th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

The direction cosines of a normal to the plane passing through $(4,2,3),(-1,4,2)$ and $(3,2,1)$ are …..

A

$\quad \frac{-2}{\sqrt{101}}, \frac{3}{\sqrt{101}}, \frac{8}{\sqrt{101}}$

B

$\frac{-3}{\sqrt{49}}, \frac{2}{\sqrt{49}}, \frac{6}{\sqrt{49}}$

C

$\quad \frac{-4}{\sqrt{101}}, \frac{-9}{\sqrt{101}}, \frac{2}{\sqrt{101}}$

D

$\frac{4}{22}, \frac{-12}{22}, \frac{18}{22}$

4
MHT CET 2025 26th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

The unit vectors perpendicular to the plane determined by the points $\mathrm{A}(1,-1,2), \mathrm{B}(2,0,-1)$, $\mathrm{C}(0,2,1)$ is

A

$\pm\left(\frac{3 \hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}}{\sqrt{11}}\right)$

B

$\pm\left(\frac{-\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}}{\sqrt{6}}\right)$

C

$\pm\left(\frac{2 \hat{i}+\hat{j}+\hat{k}}{\sqrt{6}}\right)$

D

$\pm\left(\frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}}{\sqrt{3}}\right)$

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