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Class 11 Mathematics Chapter 12 Introduction To Three Dimensional Geometry Quiz 1 (25 MCQs)

Quiz Instructions

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1. What is the name of a 3D shape that has 6 faces, all of which are squares?

Correct Answer: A) Cube.

2. A plane is parallel to yz-plane so it is perpendicular to:

Correct Answer: A) X-axis.

3. The x-axis and y-axis taken together determine a plane known as

Correct Answer: A) XY-plane.

4. What is the formula for the direction cosines of a line segment joining two points P(x1, y1, z1) and Q(x2, y2, z2)?

Correct Answer: C) (x2-x1) / PQ, (y2-y1) / PQ, (z2-z1) / PQ.

5. Distance of the plane 2x-3y + 4z-6 = 0 from the origin is

Correct Answer: B) $\frac{6}{\sqrt{29}}$.

6. Which octant do the point (-5, 4, 3) lie?

Correct Answer: B) Octant II.

7. Two storage boxes with the same length and different heights and widths are shown below. What is the total volume, in cubic inches, of both storage boxes?

Correct Answer: D) 97$^{1}$/$_{2}$ cubic inches.

8. Find the equation of the line passing through the point (-1, 7, 2) and perpendicular to the plane 3x-y + 4z = 11.

Correct Answer: C) $\frac{x+1}{3}=\frac{y-7}{-1}=\frac{z-2}{4}$.

9. The point (-2, -3, -4) lies in the

Correct Answer: B) Seventh octant.

10. The length of a building is 60 feet. The length of the building on a scale drawing is 4 inches. Which ratio describes the scale of the drawing?

Correct Answer: B) 1 inch:15 feet.

11. The distance of point P(3, 4, 5) from the yz plane is

Correct Answer: A) 3 units.

12. I am a Solid shape. I have two flat and one curved face. I have two curved edges and no corner. Who am I?

Correct Answer: D) Cylinder.

13. The coordinates of a point are (-2, 0, 3), the point lies on

Correct Answer: C) XZ-plane.

14. The point of intersection of the line $\frac{x-1}{3}=\frac{y+2}{4}=\frac{z-3}{-2}$

Correct Answer: B) (10, 10, -3).

15. If direction cosines of a line are $\frac{1}{a}, \frac{1}{a}, \frac{1}{a}$

Correct Answer: C) $\pm\sqrt{3}$.

16. Coordinate planes divide the space into ..... octants.

Correct Answer: C) 8.

17. Which 2D shape has no sides and is not a polygon?

Correct Answer: A) Circle.

18. The vector equation of x-axis is

Correct Answer: C) $\overrightarrow{r}=\lambda i$.

19. The distance of point P(3, 4, 5) from the yz-plane is

Correct Answer: A) 3 units.

20. In a three dimensional space, the equation 3x-4y = 0 represents

Correct Answer: C) A plane containing Z axis.

21. Which set of measurements could be the lengths of three segments that form a triangle?

Correct Answer: D) 7 cm, 2 cm, 6 cm.

22. Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the x z-plane

Correct Answer: D) (17/3, 0, 23/3).

23. Determine the approximate height of a cone with volume 124 in$^{3 }$and radius 7 in.

Correct Answer: A) 2.4 in.

24. Any point on YZ-plane will be of the form

Correct Answer: B) (0, y, z).

25. The XY-plane, YZ-plane and XZ-plane are

Correct Answer: B) Mutually perpendicular to each other.

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