Simplification
- (0.5 × 5 + 0.25 × 0.5 + 0.5 × 4 + 0.5 × 0.75) is equal to
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Expression
= 0.5 (5 + 0.25 + 4 + 0.75)
= 0.5 × 10 = 5Correct Option: A
Expression
= 0.5 (5 + 0.25 + 4 + 0.75)
= 0.5 × 10 = 5
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is equal to
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0.01 − 0.0001 + 1 = 0.0099 + 1 0.0001 0.0001
= 99 + 1 = 100Correct Option: D
0.01 − 0.0001 + 1 = 0.0099 + 1 0.0001 0.0001
= 99 + 1 = 100
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If 1120 = 80, then P is equal to √P
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80 × √P = 1120
⇒ √P = 1120 = 14 80
⇒ P = (14)2 = 196Correct Option: C
80 × √P = 1120
⇒ √P = 1120 = 14 80
⇒ P = (14)2 = 196
- (32)3 + (79)3 − (111)3 + 3 × 32 × 79 × 111 is equal to
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Using (x) of Basic Formulae
Let, 32 = a
79 = b, –111 = c
When (a + b + c) = 0
then a3 + b3 + c3 − 3abc = 0
Here, a + b + c = 32 + 79 – 111 = 0
∴ (32)3 + (79)3 − (111)3 + 3 × 32 × 79 × 111 = 0Correct Option: B
Using (x) of Basic Formulae
Let, 32 = a
79 = b, –111 = c
When (a + b + c) = 0
then a3 + b3 + c3 − 3abc = 0
Here, a + b + c = 32 + 79 – 111 = 0
∴ (32)3 + (79)3 − (111)3 + 3 × 32 × 79 × 111 = 0
- Simplify :
[0.9 – {2.3 – 3.2 – (7.1 – 5.4 – 3.5)}]
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[0.9 – {2.3 – 3.2 – (7.1 – 8.9)}]
= [0.9 – {2.3 – 3.2 + 1.8}]
= [0.9 – 0.9] = 0Correct Option: C
[0.9 – {2.3 – 3.2 – (7.1 – 8.9)}]
= [0.9 – {2.3 – 3.2 + 1.8}]
= [0.9 – 0.9] = 0
