2.

Simplification
1 13 19
1. What is 6 th of 3 ? (c) (d)
22 22
(a) 6 (b) 3 19. If 217 × 15 = 3255, then 2.17 × 0.15 is
(c) 1/2 (d) 1/3 (a) 32.55 (b) 0.3255
2. What is 10-(-8) equal to ? (c) 3.255 (d) 325.5
(a) 2 (b) 18 20. 24.315 × 256.2 × 0.0019 is the same as
(c) 10 (d) 8 (a) 243.15×2.562×0.019
3. Multiply 0.932 by 100. (b) 24.315×25.62×0.00019
(a) 932 (b) 9.32 (c) 2.4315×2.562×0.019
(c) 93.2 (d) 9320 (d) 0.24315x25.62×0.019
4. Divide 0.045 by 100. 21. If 13 + 23 + 33 +…..+ 93 = 2025, then find the value of
(a) 0.0045 (b) 0.00045 (0.1)3 +(0.2)3 +……+(0.9)3
(c) 0.000045 (d) 0.45 (a) 2.025 (b) 202.5
4𝑥 (c) 20.25 (d) 0.2025
5. If 2 x =5 and 3y=8, then is equal to
9𝑦 22. If 12 + 22 + 32 +…...+ 92 = 385, then find the value of
5 5
(a) (b) (0.11)2 + (0.22)2 +…..+ (0.99)2
18 16
5 5 (a) 4.6585 (b) 0.46585
(c) (d)
12 8 (c) 2.46585 (d) 1.46585
6. The sum of first 50 positive integers 1275. What is the 23. If x # y = x + y, then find the value of (3#4) # 3.
sum of the integers from 51 to 100? (a) 6 (b) 7
(a) 2525 (b) 2550 (c) 10 (d) 8
(c) 3250 (d) 3775 𝑎2
1 1 1 1 1 1 24. If a + b be defined by the relation , where b≠0. Find
7. ( − ) + ( − ) + ( + )is equal to 𝑏
2 3 3 4 4 2 the value of (24 +16) +4.
1
(a) 0 (b) (a) 324 (b) 320
4
1
(c) (d) 1 (c) 280 (d) 290
2 1 1
1.5 2 25. If = 1.6. Find the value of .
8. ( ) is equal to 0.625 0.00625
2.5
(a) 0.06 (b) 0.36 (a) 0.016 (b) 160
(c) 0.21 (d) 0.41 (c) 1.6 (d) 0.16
9. Find 3 + 0.3 + 0.03 + 0.003 26. If x=2y and y= 2z/3, what is the value of z in terms of x.
2𝑥 3𝑥
(a) 3.360 (b) 3.333 (a) (b)
3 4
(c) 3.630 (d) 3.033 4𝑥 3𝑥
1
10. Simplify 15.876 – (2.49 + 4.056) ÷ . (c) (d)
2 3 2
(a) 2.784 (b) 3.052 (0.83)6
27. is approximately equal to
(c) 2.984 (d) 3.152 (0.83)7
0.48÷0.12+0.04×25 (a) -1 (b) 0
11. Simplify . (c) 1 (d) 2
0.05
(a) 100 (b) 110 15
28. If x is positive and 6-x2 =, then √𝑥 = ?
(c) 90 (d) 105 16
23 19 81 9
12. Simplify × × 85. (a) (b)
19 17 16 4
(a) 110 (b) 125 3 √3
(c) 115 (d) 120 (c) (d)
2 2
𝑃
13. Find P in the expression, if 1 = 1. 29. Find the value of
1 1+√5 1−√5
[( 2 ) − ( 2 )].
1+
1+
𝑃 √5
1−𝑃
1 (a) √5 (b) 2√5
(a) 2 (b) (c) 5 (d) 1
4
1 18
(c) 1 (d) 30. (0.1254) is equal to
2
3 1 3 60
÷ × (a) 0.0052 (b) 0.03135
2 2 2 1
14. Simplify 3 1 3 ÷ (c) 0.03762 (d) 0.0418
÷ 𝑜𝑓 8
2 2 2 31. Simplify [1 − 2(3 − 4) − 1]−1
(a) 18 (b) 21 1 1
(a) (b)
(c) 16 (d)24 4 3
(3+3+3+3)/3 1 1
15. Find the value of . (c) (d)
5+5+5+5/5 2 6
1 3 1 1 3 1 7 3
(a) (b) 32. Simplify [ + { − ( − )}].
4 4 2 2 4 2 8 4
5 9 27 9
(c) (d) (a) (b)
4 4
5+5×19−15−7 32 32
16. Find the value of . 15 13
13×13−156 (c) (d)
32 32
(a) 4 (b) 8 1
(c) 6 (d) 9 33. Simplify 1 + 1 .
2+
17. Simplify 1 ÷ [1 + 1 ÷ {1 + 1 ÷ (1 ÷ 1)}]. 3+
1
3 2 3
(a) (b) 19 17
2 5 (a) (b)
2 5 23 23
(c) (d) 33 11
3 2 (c) (d)
1 1 23 23
18. Simplify 2 + 4.
4 2 3
5 9 34. Find 𝑥, if 6 − [5 − {𝑥 − (2 − )}] = 3 .
14 17 2
(a) (b) (a)
5
(b)
3
22 22 2 2
2. Simplification
7 11 3 5
(c) (d) (a) (b)
2 23
8 8
35. Simplify 0.00175 ÷ 0.025 ÷ 0.07.
(a) 1 (b) 0.1 7 1
(c) 10 (d) 0.01 (c) (d)
8 8
36. What least fraction should be added to
1
+ 1 + 48. If 2494 ÷ 14.5=172, then 24.94  1.45 is equal to
2×3 3×4
1 1 (a) 1.72 (b) 17.2
4×5
+ ⋯ + 21×22, so that the result is unity. (c) 172 (d) 0.172
3 6 5−√21
(a) (b) 1
11 11 49. If 𝑥= then 𝑥 2 + is equal to
2 𝑥2
5 7
(c) (d) 22 25
11 11 (a) (b)
𝑥 3 𝑦−𝑥 7 2
37. If = , then find the value of . (c) 23 (d) 25
𝑦 4 𝑦+𝑥
1 1 50. 3 tables and 2 chair cost Rs.3500 while 5 tables and 2
(a) (b)
7 5 chairs cost Rs.5500. The cost of a table (in rupees) is
1 1 (a) Rs.500 (b) Rs.1000
(c) (d)
9 4 (c) Rs.1200 (d) Rs.1500
38. (16÷4) ÷ 4 is equal to (𝑥−𝑦) 4
(a) 4 (b) 1 51. If x and y are positive integers and = , then
3.5 7
1
(c) (d) 16 (a) y < x (b) y > x
4 (c) y = x (d) y ≥ x
39. 16 ÷ (4÷4) is equal to
52. In a fraction, if 2 is subtracted from the denominator, the
(a) 4 (b) 1
1
fraction becomes 1. If 1 is subtracted from both the
(c) (d) 16 numerator and the denominator, the fraction becomes
4
(214)3 −(186)3 3/4. What is the denominator for the fraction?
40. Find the value of (a) 6 (b) 7
(214)2 +(214)(186)+(186)2
(c) 8 (d) 9
(a) 28 (b) 26
53. If x+y-z=m and if, x-y+z=n, then x is equal to
(c) 22 (d) 24
𝑥 2 −1
(a) (m+n)/2 (b) m-n
41. If = 8. Find 𝑥 (c) 2m+n (d) m+n
𝑥+1
(a) 8 (b) 9 54. It is required to change a rupee coin into 2 paise and 5
(c) 6 (d) 4 paise coins with the total number of coins equal to 26.
42. Find the value of Find the number of each type of coins.
0.049×0.049×0.049+0.051×0.051×0.051 (a) 10 and 16 (b) 12 and 14
0.049×0.049−0.049×0.051+0.051×0.051 (c) 10 and 20 (d) 14 and 14
(a)0.1 (b) 0.01 55. Given that (9/2)x+3y=21 and (1/2)x ‒8y=4. Find the
(c) 0.5 (d) 0.05 value of 12x ‒ 12y.
2125×2125×2125+875×875×875 (a) 12 (b) 30
43. Find the value of (c) 25 (d) 60
2125×2125−2125×875+875×875
(a) 2 × 103 (b) 3 ×103 56. Let A=(x+1)/(x‒1) and B=(x‒1)/(x +1). Determine the
(c) 1 × 103 (d) 4×103 value of A-B.
(4.256−1.744)2 +(4.256+1.744)2 (a) 0 (b) x/(x2‒1)
44. Find the value of
4.256×4.256+1.744×1.744 (c) 4x/(x2‒1) (d) None of these
(a)8 (b) 2 57. If the numerator of a fraction is doubled and the
(c) 4 (d) 6 denominator is increased by 3, the new fraction is 3/5.
4 3 3 3 What is the original fraction, if its denominator is more
( ) −( ) than twice the numerator by 1?
7 7
45. Simply
4 2 3 2 (a) 3/7 (b) 6/13
( ) −( ) (c) 1/3 (d) 5/11
7 7
37 39 58. For what value if x, 8 + (x ‒ 3)2 have the least value?
(a) (b)
49 49 (a) -3 (b) 0
33 36
(c) (d) (c) 3 (d) 5
41 49 59. 3.7 (107) is equal to
46. Simplify
24 × 24 × 24 + 32 × 32 × 32 + 45 × 45 × 45 − 3 × 24 × 32 × 45 (a) 370000 (b) 3700000
(c) 37000000 (d) 370000000
24 × 24 + 32 × 32 + 45 × 45 − 24 × 32 − 32 × 45 − 45 × 24 2
(a) 105 (b) 101 60. (√5 + √5 ) is equal to
(c) 103 (d) 107 (a) 5 (b) 10
47. Simplify (c) 15 (d) 20
1 1 1 1 1 1
(1 + ) (1 − ) (1 + ) (1 − ) (1 + ) (1 − )
4 4 5 5 6 6

Ans Key
(1-10) cbcbc ddbba
(11-20) accaa ccaba
(21-30) aacab bccdc
(31-40) cacaa babda
(41-50) babba bcbcb
(51-60) adaad caccd