Which of the following is false:

(i) $\"|\"4 + 2\"|\" = \"|\"4\"|\" + \"|\"2\"|\"$
(ii) $\"|\"2 - 4\"|\" = \"|\"2\"|\" + \"|\"4\"|\"$
(iii) $\"|\"4 - 2\"|\" = \"|\"4\"|\" - \"|\"2\"|\"$
(iv) $\"|\"(- 2) + (- 4)\"|\" = \"|\"- 2\"|\" + \"|\"- 4\"|\"$

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Solution

(i) |4|+ |2| = 6 = |4| + |2|; True
(ii) |2 − 4| = |−2| = 2 ≠ 2 + 4 = 6; False
(iii) |4 − 2| = 2 = |4| − |2|; True
(iv) |(−2) + (−4)| = |−6| = 6 = |−2| + |(−4)|; True

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Similar questions

Which of the following is false:
(i) $| 4 + 2 | = | 4 | + | 2 |$
(ii) $| 2 - 4 | = | 2 | + | 4 |$
(iii) $| 4 - 2 | = | 4 | - | 2 |$
(iv) $| (- 2) + (- 4) | = | - 2 | + | - 4 |$

Rationalize the denominator and simplify:

(i) $\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}$

(ii) $\frac{5 + 2 \sqrt{3}}{7 + 4 \sqrt{3}}$

Q. In the following list of numerals, how many 2's are followed by 1's but not preceded by 4 ?
4 2 1 2 1 4 2 1 1 2 4 4 4 1 2 2 1 2 1 4 4 2 1 4 2 1 2 1 2 4 1 4 2 1 2 4 1 4 6

Question 22

Which of the following is an example of distributive property of multiplication over addition for rational numbers.
(a) $- \frac{1}{4} \times {\frac{2}{3} + (\frac{- 4}{7})} = [- \frac{1}{4} \times \frac{2}{3}] + [- \frac{1}{4} \times (\frac{- 4}{7})]$
(b) $- \frac{1}{4} \times {\frac{2}{3} + (\frac{- 4}{7})} = [\frac{1}{4} \times \frac{2}{3}] - (\frac{- 4}{7})$
(c) $- \frac{1}{4} \times {\frac{2}{3} + (\frac{- 4}{7})} = \frac{2}{3} + (- \frac{1}{4}) \times \frac{- 4}{7}$
(d) $- \frac{1}{4} \times {\frac{2}{3} + (\frac{- 4}{7})} = {\frac{2}{3} + (\frac{- 4}{7})} - \frac{1}{4}$

Q. Name the octants in which the following points lie:

(1, 2, 3), (4, - 2, 3) (4, - 2, - 5), (4, 2, - 5), (- 4, 2, - 5), (- 4, 2, 5), (- 3, - 1, 6), (2, - 4, - 7)

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Which of the following is false: (i) 4+2=4+2 (ii) 2-4=2+4 (iii) 4-2=4-2 (iv) -2+-4=-2+-4

(i) |4|+ |2| = 6 = |4| + |2|; True(ii) |2 − 4| = |−2| = 2 ≠ 2 + 4 = 6; False(iii) |4 − 2| = 2 = |4| − |2|; True(iv) |(−2) + (−4)| = |−6| = 6 = |−2| + |(−4)|; True

Which of the following is false:

(i) $\"|\"4 + 2\"|\" = \"|\"4\"|\" + \"|\"2\"|\"$
(ii) $\"|\"2 - 4\"|\" = \"|\"2\"|\" + \"|\"4\"|\"$
(iii) $\"|\"4 - 2\"|\" = \"|\"4\"|\" - \"|\"2\"|\"$
(iv) $\"|\"(- 2) + (- 4)\"|\" = \"|\"- 2\"|\" + \"|\"- 4\"|\"$

(i) |4|+ |2| = 6 = |4| + |2|; True
(ii) |2 − 4| = |−2| = 2 ≠ 2 + 4 = 6; False
(iii) |4 − 2| = 2 = |4| − |2|; True
(iv) |(−2) + (−4)| = |−6| = 6 = |−2| + |(−4)|; True