151. Evaluate 9^ 32.
- 127
- 272
- 81
- 27
Answer: D) 27
Explanation: 9 = 3^2, so 9^ 32 = (3^2 )^ 32 = 3^3 = 27. SLO M-09-A-04 · Application
MCQs / Mathematics / Real Numbers
Real Numbers MCQs — Mathematics (page 7)
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.
152. Simplify (x^-2 )^5.
- x^-10
- x^-9
- x^-7
- x^3
Answer: A) x^-10
Explanation: (x^m)^n = x^mn, so the power is -2 5 = -10. SLO M-09-A-04 · Application
153. Find log9 3.
- 12
- - 12
- 1
- 32
Answer: A) 12
Explanation: log9 x = y means 9^y = x. Since 9^ 12 = 3, the answer is 12. SLO M-09-A-06 · Knowledge
154. Expand log (dfracx^2 yz ).
- 2log x + log y + log z
- 2log x + log y - log z
- log 2x + log y - log z
- 2log x log y - log z
Answer: B) 2log x + log y - log z
Explanation: Use log(mn) = log m + log n, log mn = log m - log n and log m^k = klog m. SLO M-09-A-08 · Application
155. Write 0.overline36 as a fraction in lowest terms.
- 3799
- 411
- 925
- 25
Answer: B) 411
Explanation: Let x = 0.overline36. Then 100x = 36.overline36, so 99x = 36 and x = 3699 = 411. SLO M-09-A-02 · Knowledge
156. The number 74 written in Roman numerals is:
- LXXXIV
- LXXIV
- LXXV
- LXXVI
Answer: B) LXXIV
Explanation: Write each place separately: 74 to LXXIV. SLO M-09-A-01 · Knowledge
157. Write 200 in simplest radical form.
- 2 10
- 10 2
- 11 2
- 10 4
Answer: B) 10 2
Explanation: 200 = 100 2, so 200 = 100 2 = 10 2. SLO M-09-A-04 · Application
158. Find log5 125.
- 6
- 3
- -3
- 4
Answer: B) 3
Explanation: log5 x = y means 5^y = x. Since 5^3 = 125, the answer is 3. SLO M-09-A-06 · Knowledge
159. The temperature in Murree at 6 a.m. is -12.75^circC. By noon it has risen by 5.5^circC. The noon temperature is:
- -18.25^circ C
- -7.25^circ C
- 18.25^circ C
- 7.25^circ C
Answer: B) -7.25^circ C
Explanation: -12.75 + 5.5 = -7.25. SLO M-09-A-09 · Application
160. Light travels about 300,000,000 m per second. In scientific notation this is:
- 3 10^8 m/s
- 30 10^8 m/s
- 3 10^7 m/s
- 3 10^9 m/s
Answer: A) 3 10^8 m/s
Explanation: There are 8 zeros after the 3, so it is 3 10^8 m/s. SLO M-09-A-05 · Understanding
161. Write 320,000 in scientific notation.
- 3.2 10^4
- 3.2 10^5
- 3.2 10^6
- 3.2 10^-5
Answer: B) 3.2 10^5
Explanation: Move the decimal point so that one non-zero digit is before it: 320,000 = 3.2 10^5 (left by 5 places). SLO M-09-A-05 · Understanding
162. Given log 2 = 0.3010 and log 3 = 0.4771, find log 12.
- 0.8781
- 1.3801
- 1.0791
- 0.1436
Answer: C) 1.0791
Explanation: log 12 = 2log 2 + log 3 = 1.0791. SLO M-09-A-08 · Application
163. The temperature in Murree at 6 a.m. is 3.5^circC. By noon it has fallen by 8.25^circC. The noon temperature is:
- -3.75^circ C
- 11.75^circ C
- -4.75^circ C
- 4.75^circ C
Answer: C) -4.75^circ C
Explanation: 3.5 - 8.25 = -4.75. SLO M-09-A-09 · Application
164. Write 10^-2 = 1100 in logarithmic form.
- log10 -2 = 1100
- log 1100 10 = -2
- log10 1100 = -2
- log 10 = -2
Answer: C) log10 1100 = -2
Explanation: a^y = x iff loga x = y. So 10^-2 = 1100 becomes log10 1100 = -2. SLO M-09-A-06 · Knowledge
165. Which property is shown by (14 3) 12 = 14 (3 12)?
- Associative property of multiplication
- Commutative property of addition
- Commutative property of multiplication
- Associative property of addition
Answer: A) Associative property of multiplication
Explanation: (14 3) 12 = 14 (3 12) is the associative property of multiplication. SLO M-09-A-03 · Knowledge
166. Write [3]54 in simplest form.
- 4 [3]2
- 2 [3]3
- 3 2
- 3 [3]2
Answer: D) 3 [3]2
Explanation: 54 = 27 2, so [3]54 = 3 [3]2. SLO M-09-A-04 · Application
167. Given log 2 = 0.3010 and log 3 = 0.4771, find log 18.
- 1.2552
- 1.5562
- 0.1436
- 0.8781
Answer: A) 1.2552
Explanation: log 18 = log 2 + 2log 3 = 1.2552. SLO M-09-A-08 · Application
168. Write 99,900 in scientific notation.
- 9.99 10^3
- 9.99 10^5
- 9.99 10^-4
- 9.99 10^4
Answer: D) 9.99 10^4
Explanation: Move the decimal point so that one non-zero digit is before it: 99,900 = 9.99 10^4 (left by 4 places). SLO M-09-A-05 · Understanding
169. Which of the following is a rational number?
- [3]5
- 7
- 0.overline3
- 32
Answer: C) 0.overline3
Explanation: 0.overline3 can be written as pq with q neq 0, so it is rational. The others are irrational. SLO M-09-A-02 · Knowledge
170. Write 3.004 10^2 as an ordinary number.
- 3,004
- 300.4
- 30.04
- 0.03004
Answer: B) 300.4
Explanation: Move the decimal point 2 places to the right: 300.4. SLO M-09-A-05 · Understanding
171. Evaluate 16^ 32.
- 256
- 164
- 24
- 64
Answer: D) 64
Explanation: 16 = 4^2, so 16^ 32 = (4^2 )^ 32 = 4^3 = 64. SLO M-09-A-04 · Application
172. Which property is shown by (3 + 13) + 4 = 3 + (13 + 4)?
- Commutative property of addition
- Associative property of multiplication
- Commutative property of multiplication
- Associative property of addition
Answer: D) Associative property of addition
Explanation: (3 + 13) + 4 = 3 + (13 + 4) is the associative property of addition. SLO M-09-A-03 · Knowledge
173. Write log6 36 = 2 in exponential form.
- 6^2 = 36
- 6^36 = 2
- 2^6 = 36
- 36^2 = 6
Answer: A) 6^2 = 36
Explanation: loga x = y iff a^y = x, so 6^2 = 36. SLO M-09-A-06 · Knowledge
174. A shopkeeper buys a watch for Rs. 800 and sells it for Rs. 920. His profit percentage is:
- 20%
- 13.04%
- 15%
- 120%
Answer: C) 15%
Explanation: Profit = 920 - 800 = 120. Profit % = 120800 100 = 15% (always on cost price). SLO M-09-A-09 · Application
175. Which rational number lies between 13 and 12?
- 512
- 730
- 35
- 1
Answer: A) 512
Explanation: The average 12 ( 13 + 12 ) = 512 always lies between them. SLO M-09-A-02 · Knowledge