Simplification
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= 5 × 2 4 3 5 30 = 5 × 30 = 5 6 5 Correct Option: D
= 5 × 2 4 3 5 30 = 5 × 30 = 5 6 5
- The simplified value of [(0.111)3 + (0.222)3 – (0.333)3 + (0.333)3 (0.222)]3 is :
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Using (x) of Basic Formulae
If a + b + c = 0, then
a3 + b3 + c3 = 3abc
Here, 0.111 + 0.222 + (–0.333) = 0
∴ (0.111)3 + (0.222)3 + (–0.333)3
= –3 × 0.111 × 0.222 × 0.333
= – (0.333)2 × 0.222
∴ Expression
= [–(0.333)2 × 0.222 + (0.333)2 × 0.222]3 = 0Correct Option: B
Using (x) of Basic Formulae
If a + b + c = 0, then
a3 + b3 + c3 = 3abc
Here, 0.111 + 0.222 + (–0.333) = 0
∴ (0.111)3 + (0.222)3 + (–0.333)3
= –3 × 0.111 × 0.222 × 0.333
= – (0.333)2 × 0.222
∴ Expression
= [–(0.333)2 × 0.222 + (0.333)2 × 0.222]3 = 0
- 8.7–[7.6 − {6.5 − (5.4 − 4.3 − 2)}] is simplified to :
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Expression
= 8.7 – [7.6 – {6.5 – (5.4 – 4.3 − 2)}]
=8.7 – [7.6 – {6.5 – (5.4 – 2.3)}]
=8.7 – [7.6 – {6.5 – 3.1}]
=8.7 – [7.6 – 3.4}]
= 8.7 – 4.2 = 4.5Correct Option: C
Expression
= 8.7 – [7.6 – {6.5 – (5.4 – 4.3 − 2)}]
=8.7 – [7.6 – {6.5 – (5.4 – 2.3)}]
=8.7 – [7.6 – {6.5 – 3.1}]
=8.7 – [7.6 – 3.4}]
= 8.7 – 4.2 = 4.5
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upto three-places of decimals yieldsThe simplification of 1 + 1 + 1 + 1 + 1 8 82 83 84 85
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Expression = 0.125 +
0.015625 + 0.001953125 +
0.00024414 + 0.000030517
= 0.1428 ≈ 0.143Correct Option: A
Expression = 0.125 +
0.015625 + 0.001953125 +
0.00024414 + 0.000030517
= 0.1428 ≈ 0.143
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Expression
= 1 + 19 − 5 2 4 6 = 6 + 57 − 10 = 53 = 4 5 12 12 12 Correct Option: C
Expression
= 1 + 19 − 5 2 4 6 = 6 + 57 − 10 = 53 = 4 5 12 12 12
