power indices and surds Model Questions & Answers, Practice Test for ssc chsl tier 1 2024
ssc chsl tier 1 2024 SYLLABUS WISE SUBJECTS MCQs
Number System
Simplification
Power, Indices And Surds
Time & Work
Time & Distance
Mensuration
If x = $y^a , y = z^b and z = x^c$ , then the value of abc is
Answer: (c)
x = $y^a , y = z^b and z = x^c$ {given}
From x = $y^a$
⇒x = $(z^b)^a$
x = $z^{ab}$
⇒x = $(x^c)^{ab}$
∴ x = $x^{abc}$
Hence, abc = 1.
If $5^{x+1} – 5^{x–1}$ = 600, then what is the value of $10^{2x}$ ?
Answer: (d)
$5^{x+1} –5^{x–1}$ = 600
$5^{x–1}(25 – 1) = 600⇒5^{x –1} = 25⇒x = 3$
$10^{2x} = 10^6$ = 1000000
If $(3.7)^x = (0.037)^y$ = 10000, then what is the value of $1/x - 1/y$ ?
Answer: (a)
Given, $(3.7)^x = (0.037)^y$ = 10000
⇒$(3.7)^x = 10^4 and (0.037)^y = 10^4$
⇒37 = $10^{4/x + 1} and 37 = 10^{4/y + 3}$
⇒$10^{4/x + 1} = 10^{4/y + 3}⇒4/x + 1 = 4/y + 3$
∴ $4/x - 4/y = 3 - 1⇒1/x - 1/y = 1/2$
The number $√{0.0001}$ is
Answer: (b)
$√{0.0001} = √{00001}/{10000} = 1/{100}$ = 0.01
So, it is a rational number.
The sum of the square of a number and the square of the reciprocal of the number, is thrice the difference of the square of the number and the square of the reciprocal of the number. What is the number?
Answer: (b)
Let number be x, then its reciprocal be $1/x$.
According to question,
$x^2 + 1/{x^2} = 3 (x^2 - 1/{x^2})$
∴ $x^2 + 1/{x^2} = 3x^2 - 3/{x^2}⇒2x^2 = 4/{x^2}$
⇒$x^4 = 2⇒x = (2)^{1/4}$
ssc chsl tier 1 2024 IMPORTANT QUESTION AND ANSWERS
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Time & Distance Aptitude Questions Test For SSC CHSL 2024 »
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Number System Aptitude MCQ Test For SSC CHSL [2024] Tier 1 »
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Simplification Aptitude MCQ Test For SSC CHSL 2024 Tier 1 »
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Mensuration Aptitude Questions Test: SSC CHSL 2024 Tier 1 »
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Surds & Indices Aptitude Questions: SSC CHSL 2024 Tier 1 »
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Time & Work Aptitude Questions Test: SSC CHSL 2024 Tier 1 »
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