101. The year 1999 written in Roman numerals is:
- MMIX
- MCMXCIX
- MM
- MMI
Answer: B) MCMXCIX
Explanation: Write each place separately: 1999 to MCMXCIX. SLO M-09-A-01 · Knowledge
MCQs / Mathematics / Real Numbers
Real Numbers MCQs — Mathematics (page 5)
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.
102. A family earns Rs. 84,000 a month. It spends 13 on rent and 38 on food. How much is left?
- Rs. 31,500
- Rs. 73,500
- Rs. 24,500
- Rs. 28,000
Answer: C) Rs. 24,500
Explanation: Fraction left = 1 - 13 - 38 = 724, and 724 84000 = 24500. SLO M-09-A-09 · Application
103. If log3 x = 4, then x =
- 64
- 81
- 12
- 27
Answer: B) 81
Explanation: x = 3^4 = 81. SLO M-09-A-06 · Knowledge
104. The word algebra comes from the title of a book by:
- Euclid
- Al-Khwarizmi
- Archimedes
- Brahmagupta
Answer: B) Al-Khwarizmi
Explanation: Al-Khwarizmi's book Al-Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabala gave us the word algebra (from al-jabr). SLO M-09-A-01 · Knowledge
105. Write 5^0 = 1 in logarithmic form.
- log5 0 = 1
- log 5 = 0
- log5 1 = 0
- log1 5 = 0
Answer: C) log5 1 = 0
Explanation: a^y = x iff loga x = y. So 5^0 = 1 becomes log5 1 = 0. SLO M-09-A-06 · Knowledge
106. Simplify dfracx^3 x^8x^5.
- x^16
- x^-10
- x^6
- x^19
Answer: C) x^6
Explanation: Add powers when multiplying and subtract when dividing: 3 + (8) - 5 = 6. SLO M-09-A-04 · Application
107. pH = -log[ H^+]. A solution has [ H^+] = 10^-8 mol/L. Its pH is:
- 8
- -8
- 2
- 10^8
Answer: A) 8
Explanation: pH = -log 10^-8 = 8. SLO M-09-A-08 · Application
108. For any valid base a, loga a =
- 1
- 0
- 10
- a
Answer: A) 1
Explanation: a^1 = a, so loga a = 1. SLO M-09-A-06 · Knowledge
109. The temperature in Murree at 6 a.m. is -4.5^circC. By noon it has risen by 7.25^circC. The noon temperature is:
- -11.75^circ C
- -2.75^circ C
- 11.75^circ C
- 2.75^circ C
Answer: D) 2.75^circ C
Explanation: -4.5 + 7.25 = 2.75. SLO M-09-A-09 · Application
110. Write 2.5 10^-3 as an ordinary number.
- 0.0025
- 2,500
- 0.025
- 0.00025
Answer: A) 0.0025
Explanation: Move the decimal point 3 places to the left: 0.0025. SLO M-09-A-05 · Understanding
111. Write 0.0000051 in scientific notation.
- 5.1 10^-7
- 5.1 10^-5
- 5.1 10^6
- 5.1 10^-6
Answer: D) 5.1 10^-6
Explanation: Move the decimal point so that one non-zero digit is before it: 0.0000051 = 5.1 10^-6 (right by 6 places). SLO M-09-A-05 · Understanding
112. log 0.001 =
- -2
- -3
- 3
- -4
Answer: B) -3
Explanation: 0.001 = 10^-3, so log 0.001 = -3. SLO M-09-A-07 · Knowledge
113. Find log7 49.
- 4
- 3
- -2
- 2
Answer: D) 2
Explanation: log7 x = y means 7^y = x. Since 7^2 = 49, the answer is 2. SLO M-09-A-06 · Knowledge
114. Which property is shown by 13 1 = 13?
- Multiplicative inverse
- Commutative property of addition
- Multiplicative identity
- Multiplicative property of equality
Answer: C) Multiplicative identity
Explanation: 13 1 = 13 is the multiplicative identity. SLO M-09-A-03 · Knowledge
115. Rationalise the denominator of dfrac10 5.
- 5 2
- 10 5
- 52
- 2 5
Answer: D) 2 5
Explanation: Multiply top and bottom by 5: 10 55 = 2 5. SLO M-09-A-04 · Application
116. pH = -log[ H^+]. A solution has [ H^+] = 10^-3 mol/L. Its pH is:
- 7
- 10^3
- 3
- -3
Answer: C) 3
Explanation: pH = -log 10^-3 = 3. SLO M-09-A-08 · Application
117. Given log 2 = 0.3010 and log 3 = 0.4771, find log 8.
- 0.8781
- 0.1436
- 1.2040
- 0.9030
Answer: D) 0.9030
Explanation: log 8 = 3log 2 = 0.9030. SLO M-09-A-08 · Application
118. Which of the following is an irrational number?
- 7
- 0.09
- 1.25
- 144
Answer: A) 7
Explanation: 7 is irrational because 7 is not a perfect square. The others can be written as pq (e.g. 49 = 7, 0.overline3 = 13). SLO M-09-A-02 · Knowledge
119. Which of the following is a rational number?
- 1+ 3
- 0.09
- 2
- 7
Answer: B) 0.09
Explanation: 0.09 can be written as pq with q neq 0, so it is rational. The others are irrational. SLO M-09-A-02 · Knowledge
120. A sound of 80 dB is how many times as intense as a sound of 50 dB? (L = 10log II0 )
- 3 times
- 1000 times
- 30 times
- 1.6 times
Answer: B) 1000 times
Explanation: The difference is 30 dB = 10 log I1I2, so log I1I2 = 3 and I1I2 = 10^3 = 1000. SLO M-09-A-08 · Application
121. Evaluate 32^- 25.
- - 645
- 12
- 4
- 14
Answer: D) 14
Explanation: 32 = 2^5, so 32^- 25 = (2^5 )^- 25 = 2^-2 = 14. SLO M-09-A-04 · Application
122. The Roman numeral MMXXIV stands for:
- 2124
- 2024
- 2034
- 2026
Answer: B) 2024
Explanation: Read left to right: a smaller symbol before a larger one is subtracted (e.g. CM = 900, XC = 90, IV = 4). So MMXXIV = 2024. SLO M-09-A-01 · Knowledge
123. Babylonian numbers were written on clay tablets in a script called:
- Latin
- cuneiform
- Devanagari
- hieroglyphics
Answer: B) cuneiform
Explanation: Babylonians pressed wedge-shaped marks into wet clay — this script is called cuneiform. SLO M-09-A-01 · Knowledge
124. If logx 64 = 3, then x =
- 5
- 4
- 12
- 3
Answer: B) 4
Explanation: x^3 = 64, so x = [3]64 = 4. SLO M-09-A-06 · Knowledge
125. Simplify 4 3 + 27.
- 5 6
- 5 27
- 8 3
- 7 3
Answer: D) 7 3
Explanation: 27 = 3 3, so the sum is 4 3 + 3 3 = 7 3. SLO M-09-A-04 · Application