This Article consist of most important ” Surds and Indices Questions and Answers ” that are mostly asked in all competitive exams. We collected these questions from the students who appeared in exams. Now try to solve these questions.
Surds and Indices Questions and Answers
Question : 1 If 3^(x – y) = 27 and 3^(x + y) = 243, then x is equal to:
A. 0
B. 2
C. 4
D. 6
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Correct Answer : C
Explanation :
3^x – y = 27 = 3^3 x – y = 3 ….(i)
3^x + y = 243 = 3^5 x + y = 5 ….(ii)
On solving (i) and (ii), we get x = 4.
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Question : 2 If 5^a = 3125, then the value of 5^(a – 3) is:
A. 25
B. 125
C. 625
D. 1625
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Correct Answer : A
Explanation :
5^a = 3125 5^a = 55
a = 5.
5^(a – 3) = 5^(5 – 3) = 5^2 = 25
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Question : 3 Given that 10^(0.48) = x, 10^(0.70) = y and x^z = y^2, then the value of z is close to:
A. 1.45
B. 1.88
C. 2.9
D. 3.7
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Correct Answer : C
Explanation :
x^z = y^2 10^(0.48z) = 10^(2 x 0.70) = 10^1.40
0.48z = 1.40
z = 140/48 = 35/12 = 2.9 (approx.)
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Question : 4 If(a/b)^x-1 = (b/a)^x-3, then the value of x is:
A. 1/2
B. 1
C. 2
D. 7/2
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Correct Answer : C
Explanation :
(a/b)^x-1 = (b/a)^x-3
(a/b)^x-1 = (a/b)^-(x-3)
x – 1 = 3 – x
2x = 4
x = 2.
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Question : 5 (17)^3.5 x (17)^? = 178
A. 2.29
B. 2.75
C. 4.25
D. 4.5
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Correct Answer : C
Explanation :
Let (17)^3.5 x (17)^x = 178.
Then, (17)^3.5 + x = 178.
3.5 + x = 8
x = (8 – 3.5)
x = 4.5
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