Class 11 Mathematics

1. Into how many octants do the coordinate planes divide three-dimensional space?

• A. 8
• B. 4
• C. 6
• D. 12

2. The coordinates of origin in 3D space are:

• A. (0, 0, 0)
• B. (0, 0)
• C. (1, 1, 1)
• D. (0, 1, 0)

3. A point lies on the x-axis. What are its y and z coordinates?

• A. y = 0, z = 0
• B. x = 0, y = 0
• C. x = 0, z = 0
• D. x = 1, y = 1

4. The point (2, -3, 4) lies in which octant?

• A. IV octant
• B. I octant
• C. II octant
• D. V octant

5. Distance of point P(x, y, z) from the origin is given by:

• A. √(x² + y² + z²)
• B. x + y + z
• C. √(x² + y²)
• D. x² + y² + z²

6. Distance between points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂) is:

• A. √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²)
• B. (x₂ - x₁) + (y₂ - y₁) + (z₂ - z₁)
• C. √((x₂ + x₁)² + (y₂ + y₁)² + (z₂ + z₁)²)
• D. √((x₂ - x₁)² + (y₂ - y₁)²)

7. Find distance between points (1, 2, 3) and (4, 6, 3):

• A. 5
• B. 25
• C. √10
• D. 7

8. Midpoint of line joining (x₁, y₁, z₁) and (x₂, y₂, z₂) is:

• A. ((x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2)
• B. ((x₁-x₂)/2, (y₁-y₂)/2, (z₁-z₂)/2)
• C. (x₁+x₂, y₁+y₂, z₁+z₂)
• D. ((x₁+x₂)/3, (y₁+y₂)/3, (z₁+z₂)/3)

9. Coordinates of point dividing segment in ratio m : n internally are:

• A. ((mx₂ + nx₁)/(m+n), (my₂ + ny₁)/(m+n), (mz₂ + nz₁)/(m+n))
• B. ((mx₂ - nx₁)/(m-n), (my₂ - ny₁)/(m-n), (mz₂ - nz₁)/(m-n))
• C. ((mx₁ + nx₂)/(m+n), (my₁ + ny₂)/(m+n), (mz₁ + nz₂)/(m+n))
• D. ((x₁ + x₂)/m, (y₁ + y₂)/m, (z₁ + z₂)/m)

10. Coordinates of point dividing segment in ratio m : n externally are:

• A. ((mx₂ - nx₁)/(m-n), (my₂ - ny₁)/(m-n), (mz₂ - nz₁)/(m-n))
• B. ((mx₂ + nx₁)/(m+n), (my₂ + ny₁)/(m+n), (mz₂ + nz₁)/(m+n))
• C. ((nx₁ - mx₂)/(m-n), (ny₁ - my₂)/(m-n), (nz₁ - mz₂)/(m-n))
• D. ((mx₁ - nx₂)/(m-n), (my₁ - ny₂)/(m-n), (mz₁ - nz₂)/(m-n))

11. Centroid of a triangle with vertices (x₁, y₁, z₁), (x₂, y₂, z₂), and (x₃, y₃, z₃) is:

• A. ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3, (z₁+z₂+z₃)/3)
• B. ((x₁+x₂+x₃)/2, (y₁+y₂+y₃)/2, (z₁+z₂+z₃)/2)
• C. (x₁+x₂+x₃, y₁+y₂+y₃, z₁+z₂+z₃)
• D. ((x₁+x₂)/3, (y₁+y₂)/3, (z₁+z₂)/3)

12. The point (-3, 1, -2) lies in which octant?

• A. VI octant
• B. III octant
• C. VII octant
• D. II octant

13. In xy-plane, the z-coordinate of any point is always:

• A. 0
• B. 1
• C. Any constant
• D. Undefined

14. In yz-plane, which coordinate is always zero?

• A. x
• B. y
• C. z
• D. None

15. Distance of point P(3, 4, 5) from xy-plane is:

• A. 5 units
• B. 3 units
• C. 4 units
• D. √(3² + 4²) = 5

16. Distance of point P(3, 4, 5) from x-axis is:

• A. √(y² + z²) = √41
• B. 3
• C. 4
• D. 5

17. Find midpoint of line joining (2, 3, 4) and (4, 7, 8):

• A. (3, 5, 6)
• B. (6, 10, 12)
• C. (1, 2, 2)
• D. (2, 4, 4)

18. The octant in which all three coordinates are negative (-, -, -) is:

• A. VII octant
• B. VIII octant
• C. III octant
• D. V octant

19. Reflection of point (2, 3, 5) in xy-plane is:

• A. (2, 3, -5)
• B. (-2, 3, 5)
• C. (2, -3, 5)
• D. (-2, -3, -5)

20. Reflection of point (2, 3, 5) in yz-plane is:

• A. (-2, 3, 5)
• B. (2, -3, 5)
• C. (2, 3, -5)
• D. (-2, -3, 5)

21. Foot of perpendicular from point (2, 3, 4) on x-axis is:

• A. (2, 0, 0)
• B. (0, 3, 0)
• C. (0, 0, 4)
• D. (2, 3, 0)

22. Foot of perpendicular from point (2, 3, 4) on xy-plane is:

• A. (2, 3, 0)
• B. (2, 0, 4)
• C. (0, 3, 4)
• D. (2, 0, 0)

23. If points (1, 1, 1), (0, 0, 0) and (x, y, z) are collinear, then:

• A. x = y = z
• B. x + y + z = 0
• C. x + y = z
• D. x = y = -z

24. Distance between points (0, 0, 0) and (-3, 4, 12) is:

• A. 13
• B. 12
• C. 5
• D. √169 = 13

25. Centroid of triangle with vertices (1, 2, 3), (3, 0, 1), and (-1, 4, 2) is:

• A. (1, 2, 2)
• B. (3, 6, 6)
• C. (1, 3, 2)
• D. (2, 2, 2)

26. What is the equation of xz-plane?

• A. y = 0
• B. x = 0
• C. z = 0
• D. x + z = 0

27. Ratio in which yz-plane divides segment joining (2, 4, 5) and (3, 5, -4) is:

• A. -2 : 3 (externally)
• B. 2 : 3 (internally)
• C. 3 : 2 (internally)
• D. 1 : 2

28. Length of diagonal of a cuboid with sides a, b, c is:

• A. √(a² + b² + c²)
• B. a + b + c
• C. √(a² + b²)
• D. 2(ab + bc + ca)

29. Coordinates of point on z-axis at distance 5 from origin are:

• A. (0, 0, ±5)
• B. (±5, 0, 0)
• C. (0, ±5, 0)
• D. (5, 5, 5)

30. Signs of coordinates in Octant VIII (X O Y' Z') are:

• A. (+, -, -)
• B. (-, -, -)
• C. (+, +, -)
• D. (-, +, -)