Usha Martin World School, Patna
Session: 2016-17
QUESTION BANK
Class: VIII
Sub. : MATHS
All questions are compulsory.
1. The product of a monomial and a binomial is a
(a) Monomial (b) binomial (c) trinomial
(d) none of these
2. In a polynomial, the exponents of the variables are always
(a) Integers
(b) positive integers
(c) Non-negative integers
(d) non-positive integers
3. Which of the following is a binomial?
(a) 7 × a+ a
(b) 6a2+ 7b+ 2c
(c) 4a× 3b× 2c
(d) 6 (a2+ b)
4. Area of a rectangle with length 4ab and breadth 6b2is
(a) 24a2b2
(b) 24ab3
(c) 24ab2
(d) 24ab
5. Volume of a rectangular box (cuboid) with length = 2ab, breadth = 3ac and height = 2ac is
(a) 12a3bc2
(b) 12a3bc
(c) 12a2bc
(d) 2ab+3ac+ 2ac
𝑦
6. Coefficient of y in the term – 3 is
(a) – 1
(b) – 3
(c)−
1
3
7. Number of factors of (a+ b) 2 is
(a) 4
(b) 3
8. Add:
(i) 7a2bc, – 3abc2, 3a2bc, 2abc2
(ii) 9ax, + 3by– cz, – 5by+ ax+ 3cz
(iii) xy2z2+ 3x2y2z– 4x2yz2, – 9x2y2z + 3xy2z2+ x2yz2
(iv) 5x2– 3xy+ 4y2– 9, 7y2+ 5xy– 2x2+ 13
9. Multiply the following:
(i) 7pqr, (p– q +r)
(ii) x2y2z2, (xy– yz +zx)
(iii) (p+ 6), (q– 7)
3
(d)
1
3
(c) 2
(d) 1
2
(iv) 2p 2 + 3q2, (2p2–3q2)
10. Simplify
(i) (3x+ 2y) 2 + (3x– 2y)2
(ii) (x2 – 4) + (x2+ 4) + 16
11. Expand the following, using suitable identities.
(i) (x+ 3) (x+ 7)
(ii) (x2+ y2) (x2– y2)
12. Using suitable identities, evaluate the following.
(i) 104 × 97
(ii) (729)2– (271)2
13. Factorize the following expressions.
(i) x3y2+ x2y3– xy4+ xy
(ii) a3+ a2+ a+ 1
(iii) a2x2 + 2abx + b2
(iv) a2x3+ 2abx2+ b2x
(v) x2– 8x+ 16
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(vi) x2+ 9x+ 20
(vii) 25ax2– 25a
(viii) y4– 625
14. The following expressions are the areas of rectangles. Find the possible lengths and breadths of these rectangles.
(i) x2– 6x+ 8
(ii) x2– 3x + 2
15. Factorise the expressions and divide them as directed:
(i) (2x3– 12x2+ 16x) ÷ (x– 2) (x– 4)
(ii) (x4– 16) ÷ (x3+ 2x2+ 4x+ 8)
16. The curved surface area of a cylinder is 2π(y2– 7y+ 12) and its radius is (y– 3). Find the height of the cylinder
(C.S.A. of cylinder = 2πrh).
17. The area of a circle is given by the expression (πx2+ 6πx+ 9π). Find the radius of the circle.
18. The height of a triangle is x4+ y4 and its base is 14xy. Find the area of the triangle.
19. The base of a parallelogram is (2x+ 3 units) and the corresponding height is (2x– 3 units). Find the area of the
parallelogram in terms of x. What will be the area of parallelogram of x= 30 units.
20. If a2+ b2 = 74 and ab= 35, then find a+ b.
21. Find the length of the side of the given square if area of the square is 625 square units and then find the value of
x.
21. A circle of maximum possible size is cut from a square sheet of board. Subsequently, a square of maximum
possible size is cut from the resultant circle. What will be the area of the final square?
3
(a) 4 of original square.
1
(c) 4 of original square.
1
(b) 2 of original square.
2
(d) 3 of original square.
22. What is the area of the largest triangle that can be fitted into a rectangle of length l units and width w units?
(a) lw/2
(b) lw/3
(c) lw/6
(d) lw/4
1
23. If the height of a cylinder becomes 4 of the original height and the radius is doubled, then which of the following
will be true?
(a) Volume of the cylinder will be doubled.
(b) Volume of the cylinder will remain unchanged.
(c) Volume of the cylinder will be halved.
1
(d) Volume of the cylinder will be 4 of the original volume.
24. The dimensions of a godown are 40 m, 25 m and 10 m. If it is filled with cuboidal boxes each of dimensions 2 m ×
1.25 m × 1 m, then the number of boxes will be
(a) 1800
(b) 2000
(c) 4000
(d) 8000
25. The volume of a cylinder whose radius r is equal to its height is
1
(a)4 πr3
(b)πr3/32
(c) πr3
(d) πr3/8
26. If R is the radius of the base of the hat, then the total outer surface area of the hat is
(a) πr (2h+ R)
(b) 2πr(h + R)
2
(c) 2πrh+ πR
(d) None of these
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Figure A
27. The area of a rectangular field is 48 m2 and one of its sides is 6m.
How long will a lady take to cross the field diagonally at the rate of 20 m/minute?
28. The area of a trapezium with equal non-parallel sides is 168 m2. If the lengths of the parallel sides are 36 m and
20 m, find the length of the non-parallel sides.
29. The areas of two circles are in the ratio 49:64. Find the ratio of their circumferences.
30. Find the perimeter of the given figure A.
31. Find the length of the largest pole that can be placed in a room of dimensions 12 m × 4 m × 3 m.
32. In 2n, n is known as
(a) Base
(b) Constant
(c) x
(d) Variable
2
33. The reciprocal of ( 5 )-1 is
2
(a) 5
(b)
5
2
5
2
(c) − 2
(d) − 5
34. The standard form for 0.000064 is
(a) 64 × 104
(b) 64 × 10-4
(c) 6.4 × 105
(d) 6.4 × 10-5
35. The usual form for 2.03 × 10-5
(a) 0.203
(b) 0.00203
(c) 203000
(d) 0.0000203
36. Divide 293 by 1000000 and express the result in standard form.
37. By what number should we multiply (–29)0 so that the product becomes (+29)0.
38.
2n ∗ 26
2−3
= 218 , find the value of ‘n’.
39. 132. The planet Uranus is approximately 2,896,819,200,000 metres away from the Sun. What is this distance in
standard form?
40. One Fermi is equal to 10-15 metre. The radius of a proton is 1.3 Fermis. Write the radius of a proton in metres in
standard form.
41. Write 390000000 in the standard form.
42. If x varies inversely as y and x = 20 when y = 600, find y when x = 400.
2
16
43. L varies directly as M and L is equal to 5, when M = 3 . Find L when M= 3 .
44. If x varies inversely as y and y = 60 when x = 1.5. Find x. when y = 4.5.
45. A contractor undertook a contract to complete a part of a stadium in 9 months with a team of 560 persons. Later
on, it was required to complete the job in 5 months. How many extra persons should he employ to complete the
work?
46. There are 20 grams of protein in 75 grams of sauted fish. How many grams of protein is in 225 gm of that fish?
47. 30 persons can reap a field in 17 days. How many more persons should be engaged to reap the same field in 10
days?
48. The cost of 27 kg of iron is Rs 1,080, what will be the cost of 120 kg of iron of the same quality?
49. Suppose that the division (x ÷5) leaves a remainder 4 and the division (x ÷ 2) leaves a remainder 1. Find the ones
digit of x.
50. If24x is a multiple of 3, where x is a digit, what is the value of x?
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