powers surds and indices Model Questions & Answers, Practice Test for ssc chsl tier 1 2023
ssc chsl tier 1 2023 SYLLABUS WISE SUBJECTS MCQs
Number System
Simplification
Powers Surds & Indices
Ratio Proportion & Partnership
Percentages
Profit & Loss
Time & Work
Time & Distance
Simple Interest & Compound Interest
Mensuration: Area & Volumes
If $4^{√x}^√x$ = 256 then the value of x is
Answer: (c)
$4^{{√x}^{{√x}}=256=4^4$
⇒${√x}^{√x}=4=2^2⇒√x=2⇒x=4$
$81^{2.5} × 9^{4.5} ÷ 3^{4.8} = 9^{?}$
Answer: (e)
${81^{2.5} × 9 ^{4.5}}/{3^{4.8}} = 9^{?}$
⇒${(3^4)^{2.5} × (3^2)^{4.5}}/{3^{4.8}} = 9^{?}⇒{{3^{10} × 3^{9}}/{3^{4.8}} = 9^{?}$
⇒$3^{10+9-4.8} = 9^{?}⇒3^{14.2} = 3^{2x?}$
⇒2 × ? = 14.2⇒? = ${14.2}/2$ = 7.1
$(49)^3 ÷ (7)^2$ = ?
Answer: (b)
? = $(49)^3 ÷ (7)^2 = {49 × 49 × 49}/{7 × 7}$ = 2401
If $3^x/{1+3^x}=1/9$, the value of $9^x/{1+9^x}$ is
Answer: (c)
$ 3^x/{1+3^x}=1/9$
$⇒3^x.9=1+3^x⇒3^x(9-1)=1$
$⇒3^x=1/8⇒9^x=1/64$
$∴ 9^x/{1+9^x}=1/64/{1+1/64}={1/64}/{65/64}=1/65$
$6^4 × 36^2 ÷ 216 = 6^{(?)}$
Answer: (c)
${6^4 × 6^4}/{6^3} = 6^{?} =⇒6^{8– 3} = 6^{?}⇒6^{?} = 6^5⇒? = 5$
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