Maths Exercise
Number System
10 Practice Questions
Click a question to reveal the solution. Use search to filter.
1) Which fraction is the smallest: 7/8, 7/9, 4/5, 5/7?
▶
- a) 7/8
- b) 7/9
- c) 4/5
- d) 5/7
Compare decimal values or cross‑multiply: 7/9 ≈ 0.777…, 5/7 ≈ 0.714…, 4/5 = 0.8, 7/8 = 0.875. Smallest is 5/7.
2) The cube of 997 is close to which value?
▶
- a) 991,026,973
- b) 991,092,673
- c) 991,027,273
- d) 991,029,773
Use (1000−3)³ = 1000³ − 3×1000²×3 + 3×1000×3² − 3³ = 1,000,000,000 − 9,000,000 + 27,000 − 27 ≈ 991,027,000. Accurate value is 991,027,273.
3) A number divided by 899 leaves remainder 63. Dividing the same number by 29, remainder?
▶
- a) 10
- b) 5
- c) 4
- d) 2
Since 899 = 29×31, N = 899k + 63. Then N mod 29 = 63 mod 29 = 5.
4) 9e−11 divided by 8 leaves what remainder?
▶
- a) 0
- b) 1
- c) 3
- d) 7
Interpret e as a digit. 9e−11 mod 8 depends on e. Compute 90−11=79 mod 8=7; each +10 adds +2 mod 8. Try digits 0–9: remainder values cycle. If options given, pick matching remainder from the cycle.
5) 49^5 − 1 is exactly divisible by?
▶
- a) 48
- b) 50
- c) 29
- d) 98
Use a^n − 1 divisible by a − 1. With a = 49, divisible by 48. Also by factors of 49−1 = 48, i.e., 2, 3, 4, 6, 8, 12, 16, 24, 48.
6) If 5432e is divisible by 9, what is digit e?
▶
- a) 4
- b) 5
- c) 6
- d) 9
Sum of digits 5+4+3+2+e = 14+e must be multiple of 9 → e = 4.
7) A tank holds 135 L. One‑fourth is full. What part when it contains 80 L?
▶
- a) 2/3
- b) 16/27
- c) 5/9
- d) 3/8
Fraction filled = 80/135 = 16/27.
8) What is two‑third of half of 369?
▶
- a) 123
- b) 246
- c) 271⅜
- d) 184.5
Half of 369 is 184.5; two‑third of that is 123.
9) 5/7 of a number exceeds 1/7 of the same number by 10. The number?
▶
- a) 25
- b) 150
- c) 17.5
- d) 175
(5/7 − 1/7)N = 10 → (4/7)N = 10 → N = 17.5.
10) In a class, 3/5 students are girls; rest are boys. If 2/5 of girls and 1/6 of boys are absent, what fraction are present?
▶
- a) 52/75
- b) 51/75
- c) 2/3
- d) 7/10
Girls present: (1 − 2/5)×3/5 = 3/5×3/5 = 9/25. Boys share: 2/5; present = (1 − 1/6)×2/5 = 5/6×2/5 = 1/3. Total present = 9/25 + 1/3 = 27/75 + 25/75 = 52/75.
Power, Indices and Surd
Content to be provided.
Simplification
Content to be provided.
Miscellaneous
Content to be provided.
Algebra
Content to be provided.
LCM and HCF
Content to be provided.
Percentage
Content to be provided.
Profit and Loss
Content to be provided.
Discount
Content to be provided.
Trigonometry
Content to be provided.
Height and Distance
Content to be provided.
Geometry and Co-ordinate
Content to be provided.
Average
Content to be provided.
Ratio and Proportion
Content to be provided.
Partnership
Content to be provided.
Mixture and Alligation
Content to be provided.
Simple Interest
Content to be provided.
Compound Interest
Content to be provided.
Time and Work
Content to be provided.
Pipe and Cistern
Content to be provided.
Mensuration
Content to be provided.
Time, Distance and Train
Content to be provided.
Boat and Stream
Content to be provided.
Statistics and Data Interpretation (D.I.)
Content to be provided.
