26. Simplify dfracx^4 x^6x^9.
- x
- x^-11
- x^15
- x^19
Answer: A) x
Explanation: Add powers when multiplying and subtract when dividing: 4 + (6) - 9 = 1. SLO M-09-A-04 · Application
MCQs / Mathematics / Real Numbers
Real Numbers MCQs — Mathematics (page 2)
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.
27. If -5x 20, then:
- x < 4
- x < -4
- x -4
- x 4
Answer: B) x < -4
Explanation: Divide both sides by -5 and reverse the sign: x < 20-5 = -4. SLO M-09-A-03 · Knowledge
28. A phone bought for Rs. 1,500 is sold for Rs. 1,200. The loss percentage is:
- 300%
- 25%
- 20%
- 22%
Answer: C) 20%
Explanation: Loss = 300. Loss % = 3001500 100 = 20%. SLO M-09-A-09 · Application
29. Write 0.049 in scientific notation.
- 4.9 10^2
- 4.9 10^-3
- 4.9 10^-1
- 4.9 10^-2
Answer: D) 4.9 10^-2
Explanation: Move the decimal point so that one non-zero digit is before it: 0.049 = 4.9 10^-2 (right by 2 places). SLO M-09-A-05 · Understanding
30. The decimal expansion of an irrational number is:
- non-terminating and non-recurring
- terminating
- always a whole number
- non-terminating and recurring
Answer: A) non-terminating and non-recurring
Explanation: Rational numbers give terminating or recurring decimals; irrational numbers never end and never repeat (e.g. pi = 3.14159ldots). SLO M-09-A-02 · Knowledge
31. If log2 x = 10, then x =
- 1024
- 20
- 100
- 512
Answer: A) 1024
Explanation: x = 2^10 = 1024. SLO M-09-A-06 · Knowledge
32. Who first gave written rules for calculating with zero and negative numbers (7th century CE)?
- Brahmagupta
- Fibonacci
- Pythagoras
- Euclid
Answer: A) Brahmagupta
Explanation: The Indian mathematician Brahmagupta, in his Brahmasphutasiddhanta (628 CE), gave rules such as a + 0 = a and a 0 = 0. SLO M-09-A-01 · Knowledge
33. A shirt marked at Rs. 2,400 is sold at a 15% discount. The sale price is:
- Rs. 2,385
- Rs. 2,760
- Rs. 2,040
- Rs. 360
Answer: C) Rs. 2,040
Explanation: Discount = 15% of 2400 = 360. Sale price = 2400 - 360 = 2040. SLO M-09-A-09 · Application
34. Write 6.02 10^3 as an ordinary number.
- 6,020
- 60,200
- 602
- 0.00602
Answer: A) 6,020
Explanation: Move the decimal point 3 places to the right: 6,020. SLO M-09-A-05 · Understanding
35. Which property is shown by 3 13 = 1?
- Multiplicative inverse
- Multiplicative property of equality
- Commutative property of addition
- Multiplicative identity
Answer: A) Multiplicative inverse
Explanation: 3 13 = 1 is the multiplicative inverse. SLO M-09-A-03 · Knowledge
36. The characteristic of log 56.7 is:
- 1
- 5
- 3
- bar1
Answer: A) 1
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
37. The Roman numeral MMMDCCCLXXXVIII stands for:
- 3898
- 3888
- 3878
- 3988
Answer: B) 3888
Explanation: Read left to right: a smaller symbol before a larger one is subtracted (e.g. CM = 900, XC = 90, IV = 4). So MMMDCCCLXXXVIII = 3888. SLO M-09-A-01 · Knowledge
38. If -3x 12, then:
- x -4
- x 4
- x < 4
- x < -4
Answer: D) x < -4
Explanation: Divide both sides by -3 and reverse the sign: x < 12-3 = -4. SLO M-09-A-03 · Knowledge
39. log 4.56, log 45.6 and log 456 all have the same:
- value
- mantissa
- sign
- characteristic
Answer: B) mantissa
Explanation: They differ only by powers of 10, so the decimal part (mantissa) is the same; only the characteristic changes (0, 1, 2). SLO M-09-A-07 · Knowledge
40. Find log10 10000.
- 5
- -4
- 8
- 4
Answer: D) 4
Explanation: log10 x = y means 10^y = x. Since 10^4 = 10000, the answer is 4. SLO M-09-A-06 · Knowledge
41. Write 0.overline12 as a fraction in lowest terms.
- 325
- 215
- 433
- 1399
Answer: C) 433
Explanation: Let x = 0.overline12. Then 100x = 12.overline12, so 99x = 12 and x = 1299 = 433. SLO M-09-A-02 · Knowledge
42. Write log10 1000 = 3 in exponential form.
- 10^3 = 1000
- 1000^3 = 10
- 3^10 = 1000
- 10^1000 = 3
Answer: A) 10^3 = 1000
Explanation: loga x = y iff a^y = x, so 10^3 = 1000. SLO M-09-A-06 · Knowledge
43. Simplify 3log 2 + log 5 - log 4.
- log 3
- 1
- log 6
- 2
Answer: B) 1
Explanation: Combine with the laws of logarithms: sums become products, differences become quotients, and log 10 = 1. SLO M-09-A-08 · Application
44. Write [3]128 in simplest form.
- 5 [3]2
- 2 [3]4
- 4 2
- 4 [3]2
Answer: D) 4 [3]2
Explanation: 128 = 64 2, so [3]128 = 4 [3]2. SLO M-09-A-04 · Application
45. Which chain of subsets is correct?
- mathbbN subset mathbbQ subset mathbbZ subset mathbbW subset mathbbR
- mathbbR subset mathbbQ subset mathbbZ subset mathbbW subset mathbbN
- mathbbN subset mathbbW subset mathbbZ subset mathbbQ subset mathbbR
- mathbbZ subset mathbbN subset mathbbW subset mathbbQ subset mathbbR
Answer: C) mathbbN subset mathbbW subset mathbbZ subset mathbbQ subset mathbbR
Explanation: Natural subset whole subset integers subset rationals subset reals. SLO M-09-A-02 · Knowledge
46. Which property is shown by 11(2 + 14) = 11 2 + 11 14?
- Commutative property of multiplication
- Commutative property of addition
- Distributive property of multiplication over addition
- Associative property of addition
Answer: C) Distributive property of multiplication over addition
Explanation: 11(2 + 14) = 11 2 + 11 14 is the distributive property of multiplication over addition. SLO M-09-A-03 · Knowledge
47. Write log2 128 = 7 in exponential form.
- 2^128 = 7
- 2^7 = 128
- 7^2 = 128
- 128^7 = 2
Answer: B) 2^7 = 128
Explanation: loga x = y iff a^y = x, so 2^7 = 128. SLO M-09-A-06 · Knowledge
48. ln (e^7 ) =
- e^7
- 1
- 70
- 7
Answer: D) 7
Explanation: ln and e^x undo each other: ln(e^7) = 7. SLO M-09-A-07 · Knowledge
49. Which feature makes the Hindu–Arabic numeral system much easier to calculate with than Roman numerals?
- It has a separate symbol for every number
- It is based on 60
- It uses letters as numbers
- Place value together with a symbol for zero
Answer: D) Place value together with a symbol for zero
Explanation: With ten digits, place value and zero, any number can be written and calculations can be done column by column. SLO M-09-A-01 · Knowledge
50. ln 1 =
- e
- undefined
- 1
- 0
Answer: D) 0
Explanation: e^0 = 1, so ln 1 = 0. SLO M-09-A-07 · Knowledge