Class 8 math chapter 3 MCQ and One word question with answer

Class 8 math chapter 3 MCQ and One word question

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MCQ question

1. Which of the following is a three-dimensional object?
a) Cube
b) Rectangular Prism
c) Rectangular Cube
d) Sphere

2. Which of the following has a two-dimensional measurement?
a) Rhombus
b) Triangle
c) Parallelogram
d) Cube

3. In which dimensional object is height added as the third dimension?
a) One-dimensional
b) Three-dimensional
c) Two-dimensional
d) Both b and c

6. How many dimensions does a classroom window have?
a) One
b) Two
c) Three
d) Zero

Answer: b) Two

7. How many dimensions does a classroom have?
a) 4
b) 3
c) 2
d) 1
Answer: c) 2

8. The length of the classroom is 2 feet more than its width. If the width is x feet, what is the length?
a) 2x feet
b) (2 – x) feet
c) (x + 2) feet
d) (x – 2) feet
Answer: c) (x + 2) feet

9. Which of the following is a binomial expression?
a) \frac{8}{3}
b) 4 × 3
c) 2x + 3
d) 3 + 2
Answer: c) 2x + 3

10. Which of the following is a binomial algebraic expression?
a) xy
b) 3x + 2
c) x
d) 2x × 3y
Answer: b) 3x + 2

11. The length of a rectangle is x and its width is y. If the length is three times the width, what is the length?
a) x = y + 3
b) x = 3y
c) x + y = 3
d) None of these
Answer: b) x = 3y

Solve the prblems 12 and 13 using the following figure

12. The length of land B is equal to the measurement of land A.
What is the length of land B?
a) 2(x + y)
b) 3(x + y)
c) x + y
d) x^2 + y^2
Answer: c) x + y

13. What is the sum of the length and width of land A called?
a) Monomial Expression
b) Binomial Expression
c) Trinomial Expression
d) Both a and b
Answer: b) Binomial Expression

Annual exam preparation questions: Part 1

14. Which dimension, when added to a rectangle, makes it a solid object?
a) Length
b) Width
c) Height
d) Perimeter
Answer: c) Height

15. A cube is an object of how many dimensions?
a) One
b) Three
c) Two
d) None of these
Answer: b) Three

16. Which of the following is the formula for the volume of a cube?
a) V = l^3
b) V = 3l
c) V = l^2
d) V = 3l^3
Answer: a) V = l^3

17. Which of the following is the formula for the volume of a rectangular cuboid?
a) V = \frac{l^3 w^3 h^3}{3}
b) V = lwh
c) V = (l + w + h)^3
d) V = 3(lwh)^3
Answer: b) V = lwh

18. If the length, width, and height of a rectangular cuboid are 2, 3, and 5 respectively, what is its volume?
a) 30 cubic units
b) 520 cubic units
c) 1000 cubic units
d) 3000 cubic units
Answer: a) 30 cubic units

19. How many dimensions does a square showcase have?
a) 2
b) 1
c) Zero
d) 3
Answer: a) 2

20. If there is a shelf placed in the middle along the length, width, and height of a showcase, how many compartments will be created?
a) 4
b) 8
c) 6
d) 2
Answer: b) 8

21. If one side of the shelf in the showcase is a and the other side is b, how many compartments of size a \times a \times b will be created?
a) 6
b) 4
c) 3
d) 2
Answer: c) 3

22. What is the pattern for the expansion of a binomial raised to the cube (binomial expansion)?
a) 1, 3, 3, 1
b) 1, 1, 3, 3
c) 3, 1, 3, 1
d) 3, 1, 1, 3
Answer: a) 1, 3, 3, 1

23. What is the formula for (a + b)^3 ?
a) (a + b)^3 = a^3 + b^3 + 3a^2b + 3ab^2
b) (a + b)^3 = a^3 - b^3 + 3ab(a + b)
c) (a + b)^3 = (a + b)(a^2 + 2ab + b^2)
d) All of the above
Answer: a) (a + b)^3 = a^3 + b^3 + 3a^2b + 3ab^2

24. If (a + b)^3 = (a + b) \times x , what is the value of x?
a) a^2 + 2ab + b^2
b) a^2 + ab + b^2
c) a^2 - ab + b^2
d) None of these
Answer: a) a^2 + 2ab + b^2

25. Which of the following is the formula for a^3 - 3a^2b + 3ab^2 - b^3 ?
a) (a + b)^3
b) (a - b)^3
c) a^3 - b^3
d) a^3 + b^3
Answer: b) (a - b)^3

26. If a^3 - b^3 = (a - b)^3 + 3ab \cdot x , what is the value of x?
a) a - b
b) a + b
c) a^2 + ab + b^2
d) a^2b^2
Answer: c) a^2 + ab + b^2

27. If a^3 + b^3 = (a + b)^3 - 3ab \cdot P , what is the value of P?
a) a - b
b) a + b
c) (a - b)^2
d) (a + b)^2
Answer: d) (a + b)^2

28. Which of the following is correct?
a) a^3 + b^3 = (a + b)^3 + 3ab(a + b)
b) (a + b)^3 = (a + b)^3 - 3ab(a + b)
c) a^3 + b^3 = (a + b)(a^2 - ab + b^2)
d) a^3 - b^3 = (a - b)(a^2 - ab + b^2)
Answer: d) a^3 - b^3 = (a - b)(a^2 - ab + b^2)

29. What is the value of (2x + y)^3 ?
a) 2x^3 + 6x^2y + 6xy^2 + 2y^3
b) 8x^3 + 12x^2y + 6xy^2 + y^3
c) 2x^3 + 12x^2y + 3xy^2 + 2y^2
d) x^3 + 12x^2y + 3xy^2 + y^3
Answer: b) 8x^3 + 12x^2y + 6xy^2 + y^3

30. What is the value of (x - 1)^3 ?
a) x^3 - 3x^2 + 3x - 1
b) x^3 - 1 - 3(x + 1)x
c) x^3 - 3x^2 + 3x + 1
d) Both a and b
Answer: a) x^3 - 3x^2 + 3x - 1

Answer questions 31 and 32 based on the figure below.

The length of the cuboids M, N, and Q are x, y, and z respectively

31. What is the length of the P cuboid?
a) x + y + z
b) x - y + z
c) x + y
d) x - y
Answer: a) x + y + z

32. What type of quantity is the length of a cuboid?
a) Binomial
b) Trinomial
c) Polynomial
d) Quadratic
Answer: b) Trinomial

33. In the equation a^3 + b^3 + c^3 = (a + b + c)^3 - 3(a + b + c)(ab + bc + ca) + 3 \cdot x , what is the value of x?
a) 6abc
b) -6abc
c) 3abc
d) -3abc
Answer: b) -6abc

34. What is the factor of x^2 - 1 ?
a) x + 1
b) x^2 + 1
c) x - 1
d) Both a and c
Answer: d) Both a and c

35. What is a factor of a^3 - b^3 ?
a) a^2 - ab + b^2
b) a^2 - ab - b^2
c) a^2 + ab + b^2
d) a^2 + ab - b^2
Answer: a) a^2 - ab + b^2

36. How many factors does every quadratic quantity have at least?
a) 2
b) 4
c) 3
d) 5
Answer: a) 2

37. What is a factor of 12 \times 10 ?
a) 2 \times 6
b) 4 \times 8
c) 3 \times 4
d) Both a and b
Answer: d) Both a and b

38. If a cake with dimensions 8 \times 10 is cut along its length and width at intervals of 2 units, how many pieces of cake will there be?
a) 10
b) 15
c) 20
d) 30
Answer: d) 30

39. How many 4'' \times 2'' pieces are needed to cover a 12'' \times 10'' mesh?
a) 3
b) 5
c) 8
d) 15
Answer: d) 15

40. Which of the following is a factor of 1' \times 1' \times 6'' ?
a) 6'' \times 6'' \times 5''
b) 4'' \times 4'' \times 4''
c) 3' \times 3' \times 3'
d) 3'' \times 5'' \times 4''
Answer: d) 3'' \times 5'' \times 4''

41. How many 1' \times 1' \times 6'' egg boxes can fit in a 3' \times 3' \times 3' egg crate?
a) 7
b) 18
c) 27
d) 54
Answer: c) 27

42. What is the fundamental factor of (x + y)^3 ?
a) x + y
b) x - y
c) x^3 + y^3
d) x^2 + y^2
Answer: a) x + y

43. What is the factorization of x^3 + y^3 ?
a) (x - y)(x^2 + xy + y^2)
b) (x + y)(x^2 + xy + y^2)
c) (x + y)(x^2 - xy + y^2)
d) (x - y)(x^2 - xy + y^2)
Answer: b) (x + y)(x^2 + xy + y^2)

44. What is the LCM of x^3 y, xy^3, x^3 y^3 ?
a) x^3 y^3
b) x^3 y
c) xy^3
d) x^3 y^3
Answer: a) x^3 y^3

45. What is the GCD of x^3 y, x^2, xy^3 ?
a) x^3 y^3
b) xy^3
c) x
d) y^3
Answer: c) x

46. What is the GCD of 70^3 and 80^3 ?
a) 56
b) 1
c) 10^3
d) 70^3
Answer: b) 1

47. What is the GCD of x and y when the expression is r \times x^4 \times y^4 ?
a) x y^4
b) x y
c) r^4
d) r^2
Answer: c) r^4

Question 1: What dimension is a rectangle?
Answer: Three-dimensional

Question 2: How many dimensions does a rectangle have?
Answer: Two

Question 3: Which geometric shape is a special case of a rectangle?
Answer: Square

Question 4: What additional dimension is added to a three-dimensional object?
Answer: Height

Question 5: What do you call a three-dimensional object that includes length, width, and height?
Answer: Solid (Cuboid)

Question 6: If the length is x and the width is y, and the length is 2 feet more than the width, what is the length?
Answer: x = y + 2

Question 7: If a binomial has two terms, what is it called?
Answer: Binomial

Question 8: What is it called when a quantity has two terms?
Answer: Binomial expression

Question 9: What is the dimension of a cube and a rectangular solid?
Answer: Three-dimensional

Question 10: If the length of a cube is l, what is its volume?
Answer: l^3

Question 11: What is the volume of a rectangular cuboid when the length, width, and height are l, w, and h respectively?
Answer: lwh

Question 12: What is the volume of a unit length cube?
Answer: One cubic unit

Question 13: What is the dimension of a square showcase?
Answer: 31

Question 14: What is the volume of a square showcase with a side length of 2 units?
Answer: 8 cubic units

Question 15: What will be the volume of a square showcase if the length, width, and height are 3 units and 4 units respectively, and there is a cut along both sides?
Answer: 343 cubic units

Question 16: Why is a pattern needed?
Answer: A pattern is needed to create designs.

Question 17: What is the cube of the sum of a and b?
Answer: (a + b)^3

Question 18: What is (a + b)^3 = ?
Answer: (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

Question 19: How many terms are generated when a binomial is cubed?
Answer: 4 terms

Question 20: According to the formula for the cube of a binomial difference, what is the value of (6−1)³?
Answer: 125

Question 21: What is the cube of the difference of x and y?
Answer: (x - y)^3

Question 22: What is (a - b)^3 = ?
Answer: (a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3

Question 23: What is a^3 + b^3 + 3ab(a + b) = ?
Answer: (a + b)^3

Question 24: What is (a + b)(a^2 - ab + b^2) = ?
Answer: a^3 + b^3

Question 25: What is a^3 - b^3 - 3ab(a - b) = ?
Answer: (a - b)^3

Question 26: What is (a - b)(a^2 + ab + b^2) = ?
Answer: a^3 - b^3

Question 27: What is a quantity with three terms called?
Answer: Trinomial expression

Question 28: What type of trinomial expression is x + y + z ?
Answer: A trinomial with three variables

Question 29: If the dimensions of a cuboid are length x, width y, and height z, what is x + y + z called?
Answer: Trinomial expression

Question 30: What is a number called when it divides another number exactly, with no remainder?
Answer: factor

Question 31: If one factor of x^2 - 1 is (x + 1) , what is the other factor?
Answer: x - 1

Question 32: If one factor of a^3 + b^3 is (a^2 - ab + b^2) , what is the other factor?
Answer: (a + b)

Question 33: If the dimensions of a cuboid are pqr, xyz , how many equal parts can the cuboid be divided into?
Answer: \frac{xyz}{pqr}

Question 35: What is the fundamental factor of (x + y)^3 ?
Answer: x + y

Question 36: What is the product of the common prime factors of two or more algebraic expressions called?
Answer: The greatest common divisor (gcd) of the expressions

Question 37: What is the gcd of x^3, x^2y, x^2y^2 ?
Answer: x^2

Question 38: What is the lcm of x^3y^2, x^2y^2, x^2y ?
Answer: x^3y^2

Question 39: What is the gcd of 30^3 and 20^3 ?
Answer: 10^3

Question 40: What is the gcd of x^3y^3 and xy^3 ?
Answer: xy