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
Simplify : $^3√2+^4√64+^4√2500+^6√8$
Answer: (c)
$3√2+^4√{16×4}+^4√{625×4}+^6√2^3$
= $√2+^4√{2^4×2^2}+^4√{5^4×2^2}+^6√2^3$
= $3√2+2√^4 2^2+5√^4 2^2+√^6 2^3$
= $3√2+2√2+5√2+√2$
= $(3+2+5+1)√2=11√2$
$(31)^{31} × (31)^{– 27}$ = ?
Answer: (b)
? = $(31)^{31} × (31)^{– 27}$
? = $(31)^{31 – 27}$
? = $(31)^4$
? = $(961)^2$
$8^7 × 2^6 ÷ 8^{2.4} = 8^{?}$
Answer: (d)
$8^{?} = 8^7 × 2^6 ÷ 8^{2.4}$
$8^{?} = 8^7 × {8^2/8^{2.4}$ or $8^{?} = 8^{7 + 2 – 2.4}$
$8^{?} = 8^{6.6}$ or ? = 6.6
The value of $(-1/126)^{-2/3}$ is :
Answer: (d)
$(-1/216)^{-2/3}=(-1/6^3)^{-2/3}=(-1/6)^{-2}=(-6)^2$=36
$(4 × 4)^3 ÷ (512 ÷ 8)^4 × (32 × 8)^4 = (2 × 2)^{? + 4}$
Answer: (c)
$(4 × 4)^3 ÷ (512 ÷ 8)^4 × (32 × 8)^4 = (2 × 2)^{? + 4}$
⇒$(16)^3 ÷ (64)^4 × (256)^4 = (4)^{? + 4}$
⇒$(4)^{2 × 3} ÷ (4)^{3 × 4} × (4)^{4 × 4} = (4)^{? + 4}$
⇒$(4)^6$ ÷$(4)^{12} × (4)^{16} = (4)^{? + 4}$
⇒$(4)^{6 – 2 + 16} = (4)^{? + 4}⇒(4)^{10} = (4)^{? + 4}$⇒10 = ? + 4
∴ ? = 6
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