176. Given log 2 = 0.3010 and log 3 = 0.4771, find log 5.
- 1.0000
- 0.8781
- 0.1436
- 0.6990
Answer: D) 0.6990
Explanation: log 5 = log 10 - log 2 = 0.6990. SLO M-09-A-08 · Application
MCQs / Mathematics / Real Numbers
Real Numbers MCQs — Mathematics (page 8)
230 multiple-choice questions on Real Numbers from Mathematics, each with the correct answer and, where available, a teacher's explanation. Read through them to revise the chapter, then practise the same questions one by one to test yourself.
177. Write 640,000,000 in scientific notation.
- 6.4 10^7
- 6.4 10^-8
- 6.4 10^9
- 6.4 10^8
Answer: D) 6.4 10^8
Explanation: Move the decimal point so that one non-zero digit is before it: 640,000,000 = 6.4 10^8 (left by 8 places). SLO M-09-A-05 · Understanding
178. The Roman numeral CDXLIX stands for:
- 439
- 459
- 449
- 549
Answer: C) 449
Explanation: Read left to right: a smaller symbol before a larger one is subtracted (e.g. CM = 900, XC = 90, IV = 4). So CDXLIX = 449. SLO M-09-A-01 · Knowledge
179. The characteristic of log 8.2 is:
- 0
- bar1
- 5
- 3
Answer: A) 0
Explanation: For a number ge 1 the characteristic is one less than the number of digits before the decimal point; for a number < 1 it is negative — one more than the number of zeros right after the decimal point (written with a bar). SLO M-09-A-07 · Knowledge
180. A phone bought for Rs. 2,400 is sold for Rs. 2,100. The loss percentage is:
- 12.5%
- 300%
- 14.29%
- 14.5%
Answer: A) 12.5%
Explanation: Loss = 300. Loss % = 3002400 100 = 12.5%. SLO M-09-A-09 · Application
181. Rationalise the denominator of dfrac6 3.
- 3 2
- 32
- 2 3
- 6 3
Answer: C) 2 3
Explanation: Multiply top and bottom by 3: 6 33 = 2 3. SLO M-09-A-04 · Application
182. Given log 2 = 0.3010 and log 3 = 0.4771, find log 24.
- 0.8781
- 0.1436
- 1.6811
- 1.3801
Answer: D) 1.3801
Explanation: log 24 = 3log 2 + log 3 = 1.3801. SLO M-09-A-08 · Application
183. If -4x 16, then:
- x < 4
- x 4
- x < -4
- x -4
Answer: C) x < -4
Explanation: Divide both sides by -4 and reverse the sign: x < 16-4 = -4. SLO M-09-A-03 · Knowledge
184. A shop has 56 of its stock left. It sells 310 of this. What fraction of the original stock is now left?
- 815
- 34
- 712
- 14
Answer: C) 712
Explanation: Left = 56 (1 - 310 ) = 712. SLO M-09-A-09 · Application
185. The Maya of Central America used a number system with base:
- 5
- 60
- 20
- 10
Answer: C) 20
Explanation: The Maya used a vigesimal (base-20) place-value system written with dots (ones) and bars (fives), and they had a symbol for zero (a shell). SLO M-09-A-01 · Knowledge
186. Which property is shown by 3 + (-3) = 0?
- Additive inverse
- Additive identity
- Additive property of inequality
- Additive property of equality
Answer: A) Additive inverse
Explanation: 3 + (-3) = 0 is the additive inverse. SLO M-09-A-03 · Knowledge
187. Write 0.overline07 as a fraction in lowest terms.
- 899
- 790
- 7100
- 799
Answer: D) 799
Explanation: Let x = 0.overline07. Then 100x = 7.overline07, so 99x = 7 and x = 799. SLO M-09-A-02 · Knowledge
188. Which of the following is an irrational number?
- pi
- 0.75
- 49
- 0.overline3
Answer: A) pi
Explanation: pi is irrational because pi is a non-terminating, non-recurring decimal. The others can be written as pq (e.g. 49 = 7, 0.overline3 = 13). SLO M-09-A-02 · Knowledge
189. A medicine in the blood decreases by 20% every hour: A = A0(0.80)^t. After about how many hours is half of it left?
- 2.5 hours
- 4.6 hours
- 3.1 hours
- 6.2 hours
Answer: C) 3.1 hours
Explanation: (0.80)^t = 0.5 Rightarrow t = log 0.5log 0.80 approx 3.1 hours. SLO M-09-A-08 · Application
190. Simplify log 8 + log 125.
- log 1000.5
- 3
- log 133
- 2
Answer: B) 3
Explanation: Combine with the laws of logarithms: sums become products, differences become quotients, and log 10 = 1. SLO M-09-A-08 · Application
191. The Roman numeral MCMXLVII stands for:
- 2047
- 1937
- 1957
- 1947
Answer: D) 1947
Explanation: Read left to right: a smaller symbol before a larger one is subtracted (e.g. CM = 900, XC = 90, IV = 4). So MCMXLVII = 1947. SLO M-09-A-01 · Knowledge
192. A bank pays a profit of 12% per year on savings. Profit on Rs. 50,000 for one year is:
- Rs. 4166.67
- Rs. 7,000
- Rs. 60,000
- Rs. 6,000
Answer: D) Rs. 6,000
Explanation: Profit = 12100 50000 = 6000. SLO M-09-A-09 · Application
193. Simplify (x^3 )^4.
- x^13
- x^-1
- x^12
- x^7
Answer: C) x^12
Explanation: (x^m)^n = x^mn, so the power is 3 4 = 12. SLO M-09-A-04 · Application
194. Sound level is L = 10 log ( II0 ) decibels. A sound 1,000,000,000,000 times as intense as I0 has a level of:
- 12 dB
- 130 dB
- 120 dB
- 1200 dB
Answer: C) 120 dB
Explanation: L = 10 log 10^12 = 10 12 = 120 dB. SLO M-09-A-08 · Application
195. Simplify dfrac2^n+2 - 2^n2^n.
- 4
- 2
- 3
- 2^2-2^n
Answer: C) 3
Explanation: 2^n(2^2 - 1)2^n = 4 - 1 = 3. SLO M-09-A-04 · Application
196. log 10000 =
- -4
- 4
- 5
- 3
Answer: B) 4
Explanation: 10000 = 10^4, so log 10000 = 4. SLO M-09-A-07 · Knowledge
197. A shopkeeper buys a watch for Rs. 4,000 and sells it for Rs. 4,500. His profit percentage is:
- 500%
- 12.5%
- 11.11%
- 17.5%
Answer: B) 12.5%
Explanation: Profit = 4500 - 4000 = 500. Profit % = 5004000 100 = 12.5% (always on cost price). SLO M-09-A-09 · Application
198. A medicine in the blood decreases by 10% every hour: A = A0(0.90)^t. After about how many hours is half of it left?
- 8.1 hours
- 5.0 hours
- 6.6 hours
- 13.2 hours
Answer: C) 6.6 hours
Explanation: (0.90)^t = 0.5 Rightarrow t = log 0.5log 0.90 approx 6.6 hours. SLO M-09-A-08 · Application
199. A common logarithm has base:
- 2
- e
- 1
- 10
Answer: D) 10
Explanation: Common logarithms (log x) use base 10. SLO M-09-A-07 · Knowledge
200. Given log 2 = 0.3010 and log 3 = 0.4771, find log 6.
- 0.7781
- 0.8781
- 0.1436
- 1.0791
Answer: A) 0.7781
Explanation: log 6 = log 2 + log 3 = 0.7781. SLO M-09-A-08 · Application