297762
If A: The quotient of two integers is always a rational number, and R: \(\frac{1}{0}\) is not rational, then which of the following statements is true?
1 A is True and R is the correct explanation of A
2 A is False and R is the correct explanation of A
3 A is True and R is False
4 Both A and R are False
Explanation:
A is False and R is the correct explanation of A Since? \(\frac{1}{0}\) is not rational, the quotient of two integers is not rational.
RATIONAL NUMBERS
297763
If \(\frac{p}{q}\) and \(\frac{r}{s}\)are equivalent fraction, then we have
1 (a) p + s = q + r
2 (b) p ÷ s = q ÷ s
3 (c) pq = rs
4 (d) ps = rq
Explanation:
(d) ps = rq (d) ps = rq
RATIONAL NUMBERS
297764
\(\frac{5}{4}-\frac{7}{6}-\frac{-2}{3}=\)
1 \(\frac{3}{4}\)
2 \(-\frac{3}{4}\)
3 \(\frac{-7}{12}\)
4 \(\frac{7}{12}\)
Explanation:
\(\frac{3}{4}\) \(\frac{5}{4}-\frac{7}{6}-\frac{-2}{3}\) \(=\frac{5}{4}+\Big(\frac{-7}{6}\Big)+\frac{2}{3}\) \(\Big[-\Big(\frac{-2}{3}\Big)=\frac{2}{3}\Big]\) \(=\frac{5\times3+(-7)\times2+2\times4}{12}\) (LCM of 3, 4 and 6 = 12) \(=\frac{15-14+8}{12}\) \(=\frac{9}{12}\) \(=\frac{9\div3}{12\div3}\) (Dividing numerator and denominator by 3) \(=\frac{3}{4}\) Hence, the correct answer is option (a).
RATIONAL NUMBERS
297765
Choose the rational number which does not liebetween rational numbers \(-\frac{2}{5}\) and \(-\frac{1}{5}\)
1 \(-\frac{1}{4}\)
2 \(-\frac{3}{10}\)
3 \(\frac{3}{10}\)
4 \(-\frac{7}{10}\)
Explanation:
\(\frac{3}{10}\) Consider given the rational numbers \(-\frac{2}{5}\) and \(-\frac{1}{5}\) Now, given both rational numbers are negative numbers so the number which lies between them will be negative. so \(\frac{3}{10}\) will not lie between them,
RATIONAL NUMBERS
297767
Which one of the following is a rational number:
1 \((\sqrt{2})^{2}\)
2 \(2\sqrt{2}\)
3 \(2 + \sqrt{2}\)
4 \(\frac{\sqrt{2}}{2}\)
Explanation:
\((\sqrt{2})^{2}\) Observe that, \( (2^{\frac{1}{2}})^{2}=2\) \(\therefore\) it is a rational number. All other numbers are irrational.
297762
If A: The quotient of two integers is always a rational number, and R: \(\frac{1}{0}\) is not rational, then which of the following statements is true?
1 A is True and R is the correct explanation of A
2 A is False and R is the correct explanation of A
3 A is True and R is False
4 Both A and R are False
Explanation:
A is False and R is the correct explanation of A Since? \(\frac{1}{0}\) is not rational, the quotient of two integers is not rational.
RATIONAL NUMBERS
297763
If \(\frac{p}{q}\) and \(\frac{r}{s}\)are equivalent fraction, then we have
1 (a) p + s = q + r
2 (b) p ÷ s = q ÷ s
3 (c) pq = rs
4 (d) ps = rq
Explanation:
(d) ps = rq (d) ps = rq
RATIONAL NUMBERS
297764
\(\frac{5}{4}-\frac{7}{6}-\frac{-2}{3}=\)
1 \(\frac{3}{4}\)
2 \(-\frac{3}{4}\)
3 \(\frac{-7}{12}\)
4 \(\frac{7}{12}\)
Explanation:
\(\frac{3}{4}\) \(\frac{5}{4}-\frac{7}{6}-\frac{-2}{3}\) \(=\frac{5}{4}+\Big(\frac{-7}{6}\Big)+\frac{2}{3}\) \(\Big[-\Big(\frac{-2}{3}\Big)=\frac{2}{3}\Big]\) \(=\frac{5\times3+(-7)\times2+2\times4}{12}\) (LCM of 3, 4 and 6 = 12) \(=\frac{15-14+8}{12}\) \(=\frac{9}{12}\) \(=\frac{9\div3}{12\div3}\) (Dividing numerator and denominator by 3) \(=\frac{3}{4}\) Hence, the correct answer is option (a).
RATIONAL NUMBERS
297765
Choose the rational number which does not liebetween rational numbers \(-\frac{2}{5}\) and \(-\frac{1}{5}\)
1 \(-\frac{1}{4}\)
2 \(-\frac{3}{10}\)
3 \(\frac{3}{10}\)
4 \(-\frac{7}{10}\)
Explanation:
\(\frac{3}{10}\) Consider given the rational numbers \(-\frac{2}{5}\) and \(-\frac{1}{5}\) Now, given both rational numbers are negative numbers so the number which lies between them will be negative. so \(\frac{3}{10}\) will not lie between them,
RATIONAL NUMBERS
297767
Which one of the following is a rational number:
1 \((\sqrt{2})^{2}\)
2 \(2\sqrt{2}\)
3 \(2 + \sqrt{2}\)
4 \(\frac{\sqrt{2}}{2}\)
Explanation:
\((\sqrt{2})^{2}\) Observe that, \( (2^{\frac{1}{2}})^{2}=2\) \(\therefore\) it is a rational number. All other numbers are irrational.
297762
If A: The quotient of two integers is always a rational number, and R: \(\frac{1}{0}\) is not rational, then which of the following statements is true?
1 A is True and R is the correct explanation of A
2 A is False and R is the correct explanation of A
3 A is True and R is False
4 Both A and R are False
Explanation:
A is False and R is the correct explanation of A Since? \(\frac{1}{0}\) is not rational, the quotient of two integers is not rational.
RATIONAL NUMBERS
297763
If \(\frac{p}{q}\) and \(\frac{r}{s}\)are equivalent fraction, then we have
1 (a) p + s = q + r
2 (b) p ÷ s = q ÷ s
3 (c) pq = rs
4 (d) ps = rq
Explanation:
(d) ps = rq (d) ps = rq
RATIONAL NUMBERS
297764
\(\frac{5}{4}-\frac{7}{6}-\frac{-2}{3}=\)
1 \(\frac{3}{4}\)
2 \(-\frac{3}{4}\)
3 \(\frac{-7}{12}\)
4 \(\frac{7}{12}\)
Explanation:
\(\frac{3}{4}\) \(\frac{5}{4}-\frac{7}{6}-\frac{-2}{3}\) \(=\frac{5}{4}+\Big(\frac{-7}{6}\Big)+\frac{2}{3}\) \(\Big[-\Big(\frac{-2}{3}\Big)=\frac{2}{3}\Big]\) \(=\frac{5\times3+(-7)\times2+2\times4}{12}\) (LCM of 3, 4 and 6 = 12) \(=\frac{15-14+8}{12}\) \(=\frac{9}{12}\) \(=\frac{9\div3}{12\div3}\) (Dividing numerator and denominator by 3) \(=\frac{3}{4}\) Hence, the correct answer is option (a).
RATIONAL NUMBERS
297765
Choose the rational number which does not liebetween rational numbers \(-\frac{2}{5}\) and \(-\frac{1}{5}\)
1 \(-\frac{1}{4}\)
2 \(-\frac{3}{10}\)
3 \(\frac{3}{10}\)
4 \(-\frac{7}{10}\)
Explanation:
\(\frac{3}{10}\) Consider given the rational numbers \(-\frac{2}{5}\) and \(-\frac{1}{5}\) Now, given both rational numbers are negative numbers so the number which lies between them will be negative. so \(\frac{3}{10}\) will not lie between them,
RATIONAL NUMBERS
297767
Which one of the following is a rational number:
1 \((\sqrt{2})^{2}\)
2 \(2\sqrt{2}\)
3 \(2 + \sqrt{2}\)
4 \(\frac{\sqrt{2}}{2}\)
Explanation:
\((\sqrt{2})^{2}\) Observe that, \( (2^{\frac{1}{2}})^{2}=2\) \(\therefore\) it is a rational number. All other numbers are irrational.
NEET Test Series from KOTA - 10 Papers In MS WORD
WhatsApp Here
RATIONAL NUMBERS
297762
If A: The quotient of two integers is always a rational number, and R: \(\frac{1}{0}\) is not rational, then which of the following statements is true?
1 A is True and R is the correct explanation of A
2 A is False and R is the correct explanation of A
3 A is True and R is False
4 Both A and R are False
Explanation:
A is False and R is the correct explanation of A Since? \(\frac{1}{0}\) is not rational, the quotient of two integers is not rational.
RATIONAL NUMBERS
297763
If \(\frac{p}{q}\) and \(\frac{r}{s}\)are equivalent fraction, then we have
1 (a) p + s = q + r
2 (b) p ÷ s = q ÷ s
3 (c) pq = rs
4 (d) ps = rq
Explanation:
(d) ps = rq (d) ps = rq
RATIONAL NUMBERS
297764
\(\frac{5}{4}-\frac{7}{6}-\frac{-2}{3}=\)
1 \(\frac{3}{4}\)
2 \(-\frac{3}{4}\)
3 \(\frac{-7}{12}\)
4 \(\frac{7}{12}\)
Explanation:
\(\frac{3}{4}\) \(\frac{5}{4}-\frac{7}{6}-\frac{-2}{3}\) \(=\frac{5}{4}+\Big(\frac{-7}{6}\Big)+\frac{2}{3}\) \(\Big[-\Big(\frac{-2}{3}\Big)=\frac{2}{3}\Big]\) \(=\frac{5\times3+(-7)\times2+2\times4}{12}\) (LCM of 3, 4 and 6 = 12) \(=\frac{15-14+8}{12}\) \(=\frac{9}{12}\) \(=\frac{9\div3}{12\div3}\) (Dividing numerator and denominator by 3) \(=\frac{3}{4}\) Hence, the correct answer is option (a).
RATIONAL NUMBERS
297765
Choose the rational number which does not liebetween rational numbers \(-\frac{2}{5}\) and \(-\frac{1}{5}\)
1 \(-\frac{1}{4}\)
2 \(-\frac{3}{10}\)
3 \(\frac{3}{10}\)
4 \(-\frac{7}{10}\)
Explanation:
\(\frac{3}{10}\) Consider given the rational numbers \(-\frac{2}{5}\) and \(-\frac{1}{5}\) Now, given both rational numbers are negative numbers so the number which lies between them will be negative. so \(\frac{3}{10}\) will not lie between them,
RATIONAL NUMBERS
297767
Which one of the following is a rational number:
1 \((\sqrt{2})^{2}\)
2 \(2\sqrt{2}\)
3 \(2 + \sqrt{2}\)
4 \(\frac{\sqrt{2}}{2}\)
Explanation:
\((\sqrt{2})^{2}\) Observe that, \( (2^{\frac{1}{2}})^{2}=2\) \(\therefore\) it is a rational number. All other numbers are irrational.
297762
If A: The quotient of two integers is always a rational number, and R: \(\frac{1}{0}\) is not rational, then which of the following statements is true?
1 A is True and R is the correct explanation of A
2 A is False and R is the correct explanation of A
3 A is True and R is False
4 Both A and R are False
Explanation:
A is False and R is the correct explanation of A Since? \(\frac{1}{0}\) is not rational, the quotient of two integers is not rational.
RATIONAL NUMBERS
297763
If \(\frac{p}{q}\) and \(\frac{r}{s}\)are equivalent fraction, then we have
1 (a) p + s = q + r
2 (b) p ÷ s = q ÷ s
3 (c) pq = rs
4 (d) ps = rq
Explanation:
(d) ps = rq (d) ps = rq
RATIONAL NUMBERS
297764
\(\frac{5}{4}-\frac{7}{6}-\frac{-2}{3}=\)
1 \(\frac{3}{4}\)
2 \(-\frac{3}{4}\)
3 \(\frac{-7}{12}\)
4 \(\frac{7}{12}\)
Explanation:
\(\frac{3}{4}\) \(\frac{5}{4}-\frac{7}{6}-\frac{-2}{3}\) \(=\frac{5}{4}+\Big(\frac{-7}{6}\Big)+\frac{2}{3}\) \(\Big[-\Big(\frac{-2}{3}\Big)=\frac{2}{3}\Big]\) \(=\frac{5\times3+(-7)\times2+2\times4}{12}\) (LCM of 3, 4 and 6 = 12) \(=\frac{15-14+8}{12}\) \(=\frac{9}{12}\) \(=\frac{9\div3}{12\div3}\) (Dividing numerator and denominator by 3) \(=\frac{3}{4}\) Hence, the correct answer is option (a).
RATIONAL NUMBERS
297765
Choose the rational number which does not liebetween rational numbers \(-\frac{2}{5}\) and \(-\frac{1}{5}\)
1 \(-\frac{1}{4}\)
2 \(-\frac{3}{10}\)
3 \(\frac{3}{10}\)
4 \(-\frac{7}{10}\)
Explanation:
\(\frac{3}{10}\) Consider given the rational numbers \(-\frac{2}{5}\) and \(-\frac{1}{5}\) Now, given both rational numbers are negative numbers so the number which lies between them will be negative. so \(\frac{3}{10}\) will not lie between them,
RATIONAL NUMBERS
297767
Which one of the following is a rational number:
1 \((\sqrt{2})^{2}\)
2 \(2\sqrt{2}\)
3 \(2 + \sqrt{2}\)
4 \(\frac{\sqrt{2}}{2}\)
Explanation:
\((\sqrt{2})^{2}\) Observe that, \( (2^{\frac{1}{2}})^{2}=2\) \(\therefore\) it is a rational number. All other numbers are irrational.