Three Dimensional Geometry is an important topic in the Mathematics section in MHT CET exam. Practising this topic will increase your score overall and make your conceptual grip on MHT CET exam stronger.
This article gives you a full set of MHT CET PYQs for Three Dimensional Geometry with explanations for effective preparation. Practice of MHT CET Mathematics PYQs including Three Dimensional Geometry questions regularly will improve accuracy, speed, and confidence in the MHT CET 2026 exam.
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MHT CET PYQs for Three Dimensional Geometry with Solutions
1.
Find the area of a circle whose radius is 7 cm.- \( 49\pi \, \text{cm}^2 \)
- \( 14\pi \, \text{cm}^2 \)
- \( 49 \, \text{cm}^2 \)
- \( 154 \, \text{cm}^2 \)
2.
The area of a triangle with base 12 cm and height 5 cm is?- 30 cm\(^2\)
- 60 cm\(^2\)
- 24 cm\(^2\)
- 12 cm\(^2\)
3.
Direction cosines of the line $\frac{x+2}{2} = \frac{2y-5}{3}, z = -1$ is- $\frac{4}{5}, \frac{3}{5}, 0$
- $\frac{3}{5}, \frac{4}{5}, \frac{1}{5}$
- $-\frac{3}{5}, \frac{4}{5}, 0$
- $\frac{4}{5}, -\frac{2}{5}, \frac{1}{5}$
4.
The angle between two lines x +1 =y + 3 =z - 4 and \(\frac {x-4}{1}\) = \(\frac {y+2}{2}\) = \(\frac {z+1}{2}\) is
cos-1\((\frac {4}{9})\)
cos-1\((\frac {2}{9})\)
cos-1\((\frac {1}{9})\)
cos-1\((\frac {5}{9})\)
5.
If the position vectors of the points A and B are 3\(\hat {i}\) + \(\hat {j}\) + 2\(\hat {k}\) and \(\hat {i}\) -2\(\hat {j}\) -4\(\hat {k}\) respectively, then the equation of the plane through B and perpendicular to AB is
\(2x + 3y + 6z + 28 = 0\)
\(2x + 3y + 6z – 11 = 0\)
\(2x – 3y – 6z – 32 = 0\)
\(2x + 3y + 6z + 9 = 0\)
6.
Find the length of the diagonal of a rectangle with length 6 cm and breadth 8 cm.- 10 cm
- 12 cm
- 14 cm
- 8 cm
7.
The equation of the plane through $(-1, 1 , 2 ) $ whose normal makes equal acute angles with co-ordinate axes is- $\vec{r} . (\hat{i} + \hat{j} + \hat{k} ) = 2 $
- $\vec{r} . (\hat{i} + \hat{j} + \hat{k} ) = 6 $
- $\vec{r} . ( 3 \hat{i} - 3 \hat{j} + 3\hat{k} ) = 2 $
- $\vec{r} . (\hat{i} - \hat{j} + \hat{k} ) = 3 $
8.
If $A$ and $B$ are foot of perpendicular drawn from point $Q (a, b, c)$ to the planes $yz$ and $zx$, then equation of plane through the points $A, B$ and $O$ is ___________- $\frac{x}{a}+\frac{y}{b}-\frac{z}{c}=0$
- $\frac{x}{a}-\frac{y}{b} + \frac{z}{c}=0$
- $\frac{x}{a} - \frac{y}{b} - \frac{z}{c}=0$
- $\frac{x}{a} + \frac{y}{b} + \frac{z}{c}=0$
9.
The length of the perpendicular drawn from the point \((1, 2, 3)\) to the line \((X - 6)/3 = (y - 7)/2 = (Z - 7)/-2\) is:- \(4 \, \text{units}\)
- \(5 \, \text{units}\)
- \(6 \, \text{units}\)
- \(7 \, \text{units}\)
10.
In a triangle ABC, with usual notations ∠A = 60°, then (1 + \(\frac {a}{c}\) + \(\frac {b}{c}\))(1 + \(\frac {c}{b}\) - \(\frac {a}{b}\)) = ?
- 3
\(\frac {1}{2}\)
\(\frac {3}{2}\)
- 1
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