This quiz works best with JavaScript enabled. Home > Cbse > Class 11 > Science > Mathematics > Class 11 Mathematics Chapter 12 Introduction To Three Dimensional Geometry – Quiz 2 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 11 Mathematics Chapter 12 Introduction To Three Dimensional Geometry Quiz 2 (56 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. X-axis is the intersection of two planes A) Xy and xz. B) Yz and zx. C) Xy and yz. D) None of these. Show Answer Correct Answer: A) Xy and xz. 2. What do skew lines in space contain? A) Neither parallel nor intersecting lines. B) Lines with equal direction cosines. C) Intersecting lines. D) Parallel lines. Show Answer Correct Answer: A) Neither parallel nor intersecting lines. 3. What is the angle between skew lines? A) 45 degrees. B) 60 degrees. C) 90 degrees. D) It varies. Show Answer Correct Answer: D) It varies. 4. Name a 3D shape that has 6 faces-only 2 that are squares. A) Pyramid. B) Rectangular prism. C) Cube. D) Triangular prism. Show Answer Correct Answer: B) Rectangular prism. 5. The lenght of the perpendicuiar drawn from the point P(3, 4, 5) on y-axis is A) . $5\sqrt{2}$. B) . 10. C) . $\sqrt{113}$. D) . $\sqrt{34}$. Show Answer Correct Answer: D) . $\sqrt{34}$. 6. L is the foot of the perpendicular drawn from a point P (3, 4, 5) on the xy-plane. The coordinates of point L are A) (3, 0, 0). B) (0, 4, 5). C) (3, 0, 5). D) None of these. Show Answer Correct Answer: D) None of these. 7. What is the length of foot of perpendicular drawn from the point P (3, 4, 5) on y-axis A) $\sqrt{41}$. B) $\sqrt{34}$. C) 5. D) None of these. Show Answer Correct Answer: B) $\sqrt{34}$. 8. The locus represented by xy + yz = 0 is: A) A pair of perpendicular lines. B) A pair of parallel lines. C) A pair of parallel planes. D) A pair of perpendicular planes. Show Answer Correct Answer: D) A pair of perpendicular planes. 9. The line x = 1, y = 2 is A) Parallel to Y-axis. B) Lies in a plane parallel to XY-plane. C) Parallel to Z-axis. D) Parallel to X-axis. Show Answer Correct Answer: C) Parallel to Z-axis. 10. The ratio in which the line joining (2, 4, 5) and (3, 5, -9) is divided by the yz-plane is A) . 3:2. B) . 2:3. C) .-2:3. D) . 4:-3. Show Answer Correct Answer: C) .-2:3. 11. State the octant in which the point P whose co-ordinates are (-4, -5, 3) lie. A) 4th octant. B) 3rd octant. C) 1st octant. D) 2nd octant. Show Answer Correct Answer: B) 3rd octant. 12. Direction ratios of the two lines are 3, 4, 5 and 4, -3, 5. Find the angle between them. A) $60^0$. B) $45^0$. C) $90^0$. D) $30^0$. Show Answer Correct Answer: A) $60^0$. 13. Flat shape which can be folded up into a three dimensional object. A) Rhombus. B) Triangular pyramid. C) Net. D) Rectangular prisim. Show Answer Correct Answer: C) Net. 14. Name the octant in which the points (4, -2, -5) lies. A) VII. B) VIII. C) IV. D) II. Show Answer Correct Answer: B) VIII. 15. Shawn is placing a fence around a circular garden with a 15-foot diameter. How many feet of fencing will Shawn need to buy to enclose the garden? Use 3.14 for $\pi$ A) 48 feet. B) 177 feet. C) 47 feet. D) 707 feetTags7.G.4. Show Answer Correct Answer: A) 48 feet. 16. Which shapes are used to create a tangram? A) Triangles. B) A square. C) A parallelogram. D) All of the above. Show Answer Correct Answer: D) All of the above. 17. What is the equation of a line through a point (x1, y1, z1) with direction cosines l, m, n? A) (x-x1)/l = (y-y1)/m = (z-z1)/n. B) (x-x1) + l = (y-y1) + m = (z-z1) + n. C) (x-x1) = l(y-y1) = m(z-z1) = n. D) (x-x1)-l = (y-y1)-m = (z-z1)-n. Show Answer Correct Answer: A) (x-x1)/l = (y-y1)/m = (z-z1)/n. 18. The triangle is called like that because ..... A) It's a shape. B) It has three angles. C) It has no angles. D) None of the above. Show Answer Correct Answer: B) It has three angles. 19. Kim's aquarium is a rectangular prism. If the aquarium has a length 48 inches, a width of 36 inches and a height of 30 inches, what is the aquarium's volume? A) 114 in$^{3}$. B) 51, 840 in$^{2}$. C) 114 in$^{2}$. D) 51, 840 in$^{3}$. Show Answer Correct Answer: D) 51, 840 in$^{3}$. 20. The cartesian equation of the line is $\frac{x-1}{2}=\frac{y+2}{3}=\frac{z-5}{-1}$ A) $\overrightarrow{r}=\left(i-2j+5k\right)+\lambda\left(2i+3j-k\right)$. B) $\overrightarrow{r}=\left(-i+2j-5k\right)+\lambda\left(2i+3j-k\right)$. C) $\overrightarrow{r}=\left(2i+3j-k\right)+\lambda\left(i-2j+5k\right)$. D) None of these. Show Answer Correct Answer: A) $\overrightarrow{r}=\left(i-2j+5k\right)+\lambda\left(2i+3j-k\right)$. 21. Find the coordinates of the point where the line $\frac{x-2}{3}=\\frac{y+1}{4}=\frac{z-2}{2}$ A) (2, -1, 2). B) (-2, 1, 2). C) (2, 1, 2). D) (-2, -1, -2). Show Answer Correct Answer: A) (2, -1, 2). 22. What are the direction cosines of a line, if direction ratios of the line are 2, -1.-2? A) $\frac{2}{3}, \frac{1}{3}, \frac{2}{3}$. B) $\frac{-2}{3}, \frac{-1}{3}, \frac{-2}{3}$. C) $\frac{3}{2}, \frac{-1}{3}, \\frac{-2}{3}$. D) $\frac{2}{3}, \frac{-1}{3}, \frac{-2}{3}$. Show Answer Correct Answer: D) $\frac{2}{3}, \frac{-1}{3}, \frac{-2}{3}$. 23. What is the volume of a 3-D shape with the following dimensions:L=10 in, W=3 in, & H=5 in? A) 150 in$^{2}$. B) 150 in$^{3}$. C) 1500 in$^{3}$. D) 500 in$^{3}$. Show Answer Correct Answer: B) 150 in$^{3}$. 24. What is the shortest distance between two lines? A) (x-x1)/a1-(y-y1)/b1-(z-z1)/c1 = (x-x2)/a2-(y-y2)/b2-(z-z2)/c2. B) (x-x1)/a1 + (y-y1)/b1 + (z-z1)/c1 = (x-x2)/a2 + (y-y2)/b2 + (z-z2)/c2. C) (x-x1)/a1 = (y-y1)/b1 = (z-z1)/c1 + (x-x2)/a2 = (y-y2)/b2 = (z-z2)/c2. D) (x-x1)/a1 = (y-y1)/b1 = (z-z1)/c1 and (x-x2)/a2 = (y-y2)/b2 = (z-z2)/c2. Show Answer Correct Answer: D) (x-x1)/a1 = (y-y1)/b1 = (z-z1)/c1 and (x-x2)/a2 = (y-y2)/b2 = (z-z2)/c2. 25. The perpendicular distance of the point P(6, 7, 8) from the XY-Plane is: A) 8. B) 7. C) 6. D) None of the above. Show Answer Correct Answer: A) 8. 26. A point on the x-axis. What are its y-coordinate and z-coordinate? A) Y = 0, z = 1. B) Y = 0, z = 0. C) Y = 1, z = 0. D) Y = 1, z= 1. Show Answer Correct Answer: B) Y = 0, z = 0. 27. If two lines are parallel, what can be said about their direction ratios? A) They are proportional. B) They are independent. C) They are perpendicular. D) They are equal. Show Answer Correct Answer: A) They are proportional. 28. To calculate the amount of cardboard needed to make a cereal box, which of the following should you find: A) Area. B) Perimenter. C) Volume. D) Surface Area. Show Answer Correct Answer: D) Surface Area. 29. Identify the net of a pyramid from the given options:a) b) c) A) . B) . C) . D) . Show Answer Correct Answer: A) . 30. The side of a 3D shape is called a ..... ? A) Angle. B) Vertices. C) Face. D) Edge. Show Answer Correct Answer: C) Face. 31. Planes 3x-2y-z =-1 and 15x-10y-5z + 4 = 0 are A) Intersecting. B) Perpendicular. C) Parallel. D) None of these. Show Answer Correct Answer: C) Parallel. 32. What is the vector equation of a line passing through a point A and parallel to a vector b? A) R = a + $\lambda$b. B) R = a + b. C) R = a-$\lambda$b. D) R = $\lambda$a + b. Show Answer Correct Answer: A) R = a + $\lambda$b. 33. What 3D shape does the net shown in the image represent? A) Cube. B) Cylinder. C) Sphere. D) Pyramid. Show Answer Correct Answer: A) Cube. 34. Which are the examples of objects in cylindrical shape? A) Candles only. B) Test tubes only. C) Coins only. D) All of the above. Show Answer Correct Answer: D) All of the above. 35. The centroid of the triangle with vertices (5, -6, 3), (2, -2, 1) and (2, 5, 2) is A) . (-3, 1, -2). B) . (3, 1, -2). C) . (3, -1, 2). D) . (-3, 1, 2). Show Answer Correct Answer: C) . (3, -1, 2). 36. A point is on the x-axis. Which of the following represent the point? A) (0, x, 0). B) (0, 0, x). C) (x, 0, 0). D) None of the above. Show Answer Correct Answer: C) (x, 0, 0). 37. What is the name of a 3D shape that has 8 vertices and 12 edges? A) Cube. B) Sphere. C) Cylinder. D) Pyramid. Show Answer Correct Answer: A) Cube. 38. Which option does not give an example of object in spherical shape? A) Ball. B) Moon. C) Earth. D) Orange. Show Answer Correct Answer: C) Earth. 39. Name That Polyhedron-a prism with two identical, triangular bases. A) Quadrilateral. B) Triangular Prism. C) Rhombus. D) Triangular pyramid. Show Answer Correct Answer: B) Triangular Prism. 40. Jim made a rectangular prism whose length is 4 in, height 10 in and width 6 in. Find the volume of a rectangular prism A) 250 in$^{3}$. B) -240 in$^{3}$. C) 240 cm$^{3}$. D) 240 in$^{3}$. Show Answer Correct Answer: D) 240 in$^{3}$. 41. I am a solid shape. I have only one curved face, no edge and no corner. Who am I? A) Sphere. B) Cube. C) Cone. D) Cuboid. Show Answer Correct Answer: A) Sphere. 42. How can you determine if three points A, B, and C are collinear in three-dimensional space? A) By measuring the distances between the points. B) By calculating the angles between the points. C) By checking if the direction ratios of AB and AC are proportional. D) By finding the midpoints of the segments. Show Answer Correct Answer: C) By checking if the direction ratios of AB and AC are proportional. 43. What is the relationship between direction cosines and the unit vector of a line? A) Direction cosines are the squares of the unit vector components. B) Direction cosines are the components of the unit vector. C) Direction cosines are always greater than 1. D) Direction cosines have no relation to unit vectors. Show Answer Correct Answer: B) Direction cosines are the components of the unit vector. 44. A soda can is what shape? A) Cone. B) Sphere. C) Cylinder. D) Cube. Show Answer Correct Answer: C) Cylinder. 45. The coordinates of a point are (0, -1, 0), the point lies on A) X-axis. B) Y-axis. C) Z-axis. D) None of these. Show Answer Correct Answer: B) Y-axis. 46. What do you call a triangle with two sides are equal? A) Obtuse Triangle. B) Right Triangle. C) Scalene Triangle. D) Isosceles Triangle. Show Answer Correct Answer: D) Isosceles Triangle. 47. Find the distance between the given parallel planes:-2x-3y + z = 4 and-6x-9y + 3z = 11 A) $\frac{1}{\sqrt{126}}units$. B) $\frac{1}{126}units$. C) $\frac{1}{\sqrt{116}}units$. D) $\frac{1}{116}units$. Show Answer Correct Answer: A) $\frac{1}{\sqrt{126}}units$. 48. Which 3D shape has 5 faces, with 4 of them being triangular and 1 being a pentagon? A) Triangular pyramid. B) Hexagonal prism. C) Square pyramid. D) Octagonal pyramid. Show Answer Correct Answer: A) Triangular pyramid. 49. The direction cosines of the normal to the plane 5y + 4 = 0 are A) 0, -4/5, 0. B) 0, 1, 0. C) 0, -1, 0. D) None of these. Show Answer Correct Answer: C) 0, -1, 0. 50. The image of the point P(1, 3, 4) in the plane 2x-y + z = 0 is: A) (3, 5, -2). B) (3, -5, 2). C) (-3, 5, 2). D) (3, 5, 2). Show Answer Correct Answer: C) (-3, 5, 2). 51. Name a 3D shape that has only 2 faces. A) Cylinder. B) Sphere. C) Cone. D) Pyramid. Show Answer Correct Answer: C) Cone. 52. What is the distance between parallel lines? A) |b(x(a2-a1))|/|a + b + c|. B) |b(x(a2-a1))|/|a|. C) |b(x(a2-a1))|/|b|. D) |b(x(a2-a1))|/|c|. Show Answer Correct Answer: C) |b(x(a2-a1))|/|b|. 53. A silo in the shape of a cylinder is partially filled with corn to feed cows. The corn fills 50% of the height of the silo. What is the approximate volume of the part of the silo that is filled with corn if the silo is 12 feet in diameter and 60 feet high? A) 27, 143.36 ft$^{3}$. B) 3391.2 ft$^{3}$. C) 6, 785.84 ft$^{3}$. D) 13, 571.68 ft$^{3}$. Show Answer Correct Answer: B) 3391.2 ft$^{3}$. 54. The end-points of a diameter of a sphere are (2, -1, 4) and (0, 5, -4), then the centre of the sphere is A) . (0, 1, 2). B) . (1, -3, 4). C) . (0, 0, 0). D) . (1, 2, 0). Show Answer Correct Answer: D) . (1, 2, 0). 55. Name That Polyhedron-a prism with two identical rectangular bases. A) Rectangular Prism. B) Area. C) Volume. D) Rectangular pyramid. Show Answer Correct Answer: A) Rectangular Prism. 56. What is the shortest distance between two skew lines? A) The sum of their lengths. B) The length of the perpendicular drawn from one line to the other. C) The distance between their direction cosines. D) The distance between their direction ratios. Show Answer Correct Answer: B) The length of the perpendicular drawn from one line to the other. ← PreviousRelated QuizzesScience QuizzesClass 11 QuizzesClass 11 Mathematics Chapter 12 Introduction To Three Dimensional Geometry Quiz 1Class 11 Mathematics Chapter 1 Sets QuizClass 11 Mathematics Chapter 10 Straight Lines QuizClass 11 Mathematics Chapter 11 Conic Sections QuizClass 11 Mathematics Chapter 13 Limits And Derivatives QuizClass 11 Mathematics Chapter 14 Mathematical Reasoning QuizClass 11 Mathematics Chapter 15 Statistics QuizClass 11 Mathematics Chapter 16 Probability Quiz 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books