Question : The positive square root of [0.6 × 0.6 × 0.6 + 0.4 × 0.4 × 0.4 + 3 × 0.6 × 0.4 (0.6 + 0.4)] is equal to:
Option 1: 2.1736
Option 2: 1
Option 3: 0.21736
Option 4: 0.072
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Correct Answer: 1
Solution : 0.6 × 0.6 × 0.6 + 0.4 × 0.4 × 0.4 + 3 × 0.6 × 0.4 (0.6 + 0.4) = 0.63 + 0.43 + 3 × 0.6 × 0.4 (0.6 + 0.4) The equation is in the form of (a + b)3 = a3 + b3 + 3ab (a + b) So, 0.6 × 0.6 × 0.6 + 0.4 × 0.4 × 0.4 + 3 × 0.6 × 0.4 (0.6 + 0.4) = (0.6 + 0.4)3 = 13 = 1 Hence, the correct answer is 1.
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Question : The value of $\frac{1.6 \times 1.6 \times 1.6-0.6 \times 0.6 \times 0.6}{1.6 \times 1.6+1.6 \times 0.6+0.6 \times 0.6}$ is:
Option 1: 0
Option 3: –1
Option 4: 2
Question : Twenty-one times a positive number is less than its square. The value of the positive number is:
Option 1: 25
Option 2: 26
Option 3: 42
Option 4: 41
Question : A positive number, when decreased by 4, is equal to 21 times the reciprocal of this number. The number is:
Option 1: 3
Option 2: 7
Option 3: 5
Option 4: 9
Question : What is the sum of the first 20 terms of the following series? $1 \times 2+2 \times 3+3 \times 4+4 \times 5+\ldots \ldots$
Option 1: 3160
Option 2: 2940
Option 3: 3240
Option 4: 3080
Question : The intensity of any wave is proportional to which of the following?
Option 1: Amplitude
Option 2: The square of the amplitude
Option 3: The square root of the amplitude
Option 4: Cube of amplitude
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