Number System
कुल प्रश्न: 77 | पेज 8
71. Find the highest common factor (HCF) of 2/3, 8/9, 16/81, and 10/27.
सही उत्तर: [A]
हल (Solution):
Correct Answer: A) 2/81
Solution:
HCF of fractions = (HCF of Numerators) / (LCM of Denominators).
HCF of (2, 8, 16, 10) = 2.
LCM of (3, 9, 81, 27) = 81. HCF = 2/81.
Correct Answer: A) 2/81
Solution:
HCF of fractions = (HCF of Numerators) / (LCM of Denominators).
HCF of (2, 8, 16, 10) = 2.
LCM of (3, 9, 81, 27) = 81. HCF = 2/81.
72. Which of the following is an irrational number?
सही उत्तर: [C]
हल (Solution):
Correct Answer: C) √3
Solution:
√3 cannot be expressed as a simple fraction p/q.
Correct Answer: C) √3
Solution:
√3 cannot be expressed as a simple fraction p/q.
73. If the sum of two numbers is 14 and their difference is 10, find the product of the two numbers.
सही उत्तर: [B]
हल (Solution):
Correct Answer: B) 24
Solution:
a+b = 14, a-b = 10. Adding them gives 2a=24 -> a=12.
b = 2. Product = 12 * 2 = 24
Correct Answer: B) 24
Solution:
a+b = 14, a-b = 10. Adding them gives 2a=24 -> a=12.
b = 2. Product = 12 * 2 = 24
74. How many numbers between 200 and 600 are exactly divisible by 4, 5, and 6?
सही उत्तर: [B]
हल (Solution):
Correct Answer: B) 6
Solution:
LCM of 4, 5, 6 = 60.
Numbers divisible by 60 between 200 and 600 are: 240, 300, 360, 420, 480, 540. (Total 6).
Correct Answer: B) 6
Solution:
LCM of 4, 5, 6 = 60.
Numbers divisible by 60 between 200 and 600 are: 240, 300, 360, 420, 480, 540. (Total 6).
75. Simplify: 1 + 1/(1 + 1/(1 + 1/3))
सही उत्तर: [A]
हल (Solution):
Correct Answer: A) 11/7
Solution:
Bottom up: 1 + 1/3 = 4/3.
Next step: 1 + 1/(4/3) = 1 + 3/4 = 7/4.
Final step: 1 + 1/(7/4) = 1 + 4/7 = 11/7.
Correct Answer: A) 11/7
Solution:
Bottom up: 1 + 1/3 = 4/3.
Next step: 1 + 1/(4/3) = 1 + 3/4 = 7/4.
Final step: 1 + 1/(7/4) = 1 + 4/7 = 11/7.
76. What is the value of 0.333... + 0.444... ?
सही उत्तर: [D]
हल (Solution):
Correct Answer: D) Both A and B
Solution:
0.333... = 3/9 = 1/3.
0.444... = 4/9.
Sum = 3/9 + 4/9 = 7/9, which is also written as 0.777...
Correct Answer: D) Both A and B
Solution:
0.333... = 3/9 = 1/3.
0.444... = 4/9.
Sum = 3/9 + 4/9 = 7/9, which is also written as 0.777...
77. If n is a natural number, then (6n^2 + 6n) is always divisible by:
सही उत्तर: [C]
हल (Solution):
Correct Answer: C) 6 and 12
Solution:
6n^2 + 6n = 6n(n+1).
'n' and 'n+1' are consecutive integers, so one of them must be even. Therefore, n(n+1) is always divisible by 2.
So, 6 * 2 = 12. The expression is always divisible by both 6 and 12.
Correct Answer: C) 6 and 12
Solution:
6n^2 + 6n = 6n(n+1).
'n' and 'n+1' are consecutive integers, so one of them must be even. Therefore, n(n+1) is always divisible by 2.
So, 6 * 2 = 12. The expression is always divisible by both 6 and 12.