90413
If two positive integers a and b are written as a = x\(^{3}\)y\(^{2}\) and b = xy\(^{3}\); x, y are prime numbers, then HCF (a, b) is:
1 )xy
2 )xy\(^{2}\)
3 )x\(^{3}\)y\(^{3}\)
4 )x\(^{2}\)y\(^{2}\)
Explanation:
Exp: B xy\(^{2}\) It is given that, \(\text{a}=\text{x}^3\text{y}^2=\text{x}\times\text{x}\times\text{x}\times\text{y}\times\text{y}\) \(\text{b}=\text{xy}^3=\text{x}\times\text{y}\times\text{y}\times\text{y}\) \(\text{HCF(a, b)}=\text{HCF}(\text{x}^3\text{y}^2,\text{xy}^3)=\text{x}\times\text{y}\times\text{y}=\text{xy}^2\) Hence, the correct answer is option B. Creating
REAL NUMBERS
90414
IF \(\frac{241}{4000}=\frac{241}{2^\text{m}\times5^\text{n}},\) Then:
1 )m = 4 and n = 5
2 )m = 3 and n = 2
3 )m = 5 and n = 3
4 )m = 2 and n = 5
Explanation:
Exp: C m = 5 and n = 3 \(\frac{241}{4000}=\frac{241}{2^\text{m}\times5^\text{m}}\) \(\Rightarrow\frac{241}{2^5\times5^3}=\frac{241}{2^\text{m}\times5^\text{n}}\) Comparing the denominators of both fractions, we have m = 5 and n = 3
REAL NUMBERS
90433
Choose the correct answer from the given four options in the following questions: The decimal expansion of the rational number \(\frac{14587}{1250}\) will terminate after:
1 )One decimal place.
2 )Two decimal places.
3 )Three decimal places.
4 )Four decimal places.
Explanation:
Exp: D Four decimal places. Rational number \(=\frac{14587}{1250}=\frac{14587}{2^{1}\times5^{4}}\) \(=\frac{14587}{10\times5^{3}}=\frac{(2)^{3}}{(2)^{3}}\) \(=\frac{14587\times8}{10\times1000}\) \(=\frac{1166969}{10000}=11.6696\) Hence, given rational number will terminate after four decimal places. \(\begin{array}{c|c} 2 & 1250 \\ \hline 5 & 625 \\ \hline 5 & 125 \\ \hline 5 & 25 \\ \hline 5 & 5 \\ \hline & 1 \end{array}\) Applying Medium **[Real Numbers]**
REAL NUMBERS
90435
If a = (2\(^{2}\) × 3\(^{3}\) × 5\(^{4}\)) and b = (2\(^{3}\) × 3\(^{2}\) × 5), then HCF (a, b) = ?
1 )90
2 )180
3 )360
4 )540
Explanation:
Exp: B 180 a = 2\(^{2}\) × 3\(^{3}\) × 5\(^{4}\) b = 2\(^{3}\) × 3\(^{2}\) × 5 HCF(a, b) = 2\(^{2}\) × 3\(^{2}\) × 5 = 180 Never Active Medium **[Real Numbers]**
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REAL NUMBERS
90413
If two positive integers a and b are written as a = x\(^{3}\)y\(^{2}\) and b = xy\(^{3}\); x, y are prime numbers, then HCF (a, b) is:
1 )xy
2 )xy\(^{2}\)
3 )x\(^{3}\)y\(^{3}\)
4 )x\(^{2}\)y\(^{2}\)
Explanation:
Exp: B xy\(^{2}\) It is given that, \(\text{a}=\text{x}^3\text{y}^2=\text{x}\times\text{x}\times\text{x}\times\text{y}\times\text{y}\) \(\text{b}=\text{xy}^3=\text{x}\times\text{y}\times\text{y}\times\text{y}\) \(\text{HCF(a, b)}=\text{HCF}(\text{x}^3\text{y}^2,\text{xy}^3)=\text{x}\times\text{y}\times\text{y}=\text{xy}^2\) Hence, the correct answer is option B. Creating
REAL NUMBERS
90414
IF \(\frac{241}{4000}=\frac{241}{2^\text{m}\times5^\text{n}},\) Then:
1 )m = 4 and n = 5
2 )m = 3 and n = 2
3 )m = 5 and n = 3
4 )m = 2 and n = 5
Explanation:
Exp: C m = 5 and n = 3 \(\frac{241}{4000}=\frac{241}{2^\text{m}\times5^\text{m}}\) \(\Rightarrow\frac{241}{2^5\times5^3}=\frac{241}{2^\text{m}\times5^\text{n}}\) Comparing the denominators of both fractions, we have m = 5 and n = 3
REAL NUMBERS
90433
Choose the correct answer from the given four options in the following questions: The decimal expansion of the rational number \(\frac{14587}{1250}\) will terminate after:
1 )One decimal place.
2 )Two decimal places.
3 )Three decimal places.
4 )Four decimal places.
Explanation:
Exp: D Four decimal places. Rational number \(=\frac{14587}{1250}=\frac{14587}{2^{1}\times5^{4}}\) \(=\frac{14587}{10\times5^{3}}=\frac{(2)^{3}}{(2)^{3}}\) \(=\frac{14587\times8}{10\times1000}\) \(=\frac{1166969}{10000}=11.6696\) Hence, given rational number will terminate after four decimal places. \(\begin{array}{c|c} 2 & 1250 \\ \hline 5 & 625 \\ \hline 5 & 125 \\ \hline 5 & 25 \\ \hline 5 & 5 \\ \hline & 1 \end{array}\) Applying Medium **[Real Numbers]**
REAL NUMBERS
90435
If a = (2\(^{2}\) × 3\(^{3}\) × 5\(^{4}\)) and b = (2\(^{3}\) × 3\(^{2}\) × 5), then HCF (a, b) = ?
1 )90
2 )180
3 )360
4 )540
Explanation:
Exp: B 180 a = 2\(^{2}\) × 3\(^{3}\) × 5\(^{4}\) b = 2\(^{3}\) × 3\(^{2}\) × 5 HCF(a, b) = 2\(^{2}\) × 3\(^{2}\) × 5 = 180 Never Active Medium **[Real Numbers]**
90413
If two positive integers a and b are written as a = x\(^{3}\)y\(^{2}\) and b = xy\(^{3}\); x, y are prime numbers, then HCF (a, b) is:
1 )xy
2 )xy\(^{2}\)
3 )x\(^{3}\)y\(^{3}\)
4 )x\(^{2}\)y\(^{2}\)
Explanation:
Exp: B xy\(^{2}\) It is given that, \(\text{a}=\text{x}^3\text{y}^2=\text{x}\times\text{x}\times\text{x}\times\text{y}\times\text{y}\) \(\text{b}=\text{xy}^3=\text{x}\times\text{y}\times\text{y}\times\text{y}\) \(\text{HCF(a, b)}=\text{HCF}(\text{x}^3\text{y}^2,\text{xy}^3)=\text{x}\times\text{y}\times\text{y}=\text{xy}^2\) Hence, the correct answer is option B. Creating
REAL NUMBERS
90414
IF \(\frac{241}{4000}=\frac{241}{2^\text{m}\times5^\text{n}},\) Then:
1 )m = 4 and n = 5
2 )m = 3 and n = 2
3 )m = 5 and n = 3
4 )m = 2 and n = 5
Explanation:
Exp: C m = 5 and n = 3 \(\frac{241}{4000}=\frac{241}{2^\text{m}\times5^\text{m}}\) \(\Rightarrow\frac{241}{2^5\times5^3}=\frac{241}{2^\text{m}\times5^\text{n}}\) Comparing the denominators of both fractions, we have m = 5 and n = 3
REAL NUMBERS
90433
Choose the correct answer from the given four options in the following questions: The decimal expansion of the rational number \(\frac{14587}{1250}\) will terminate after:
1 )One decimal place.
2 )Two decimal places.
3 )Three decimal places.
4 )Four decimal places.
Explanation:
Exp: D Four decimal places. Rational number \(=\frac{14587}{1250}=\frac{14587}{2^{1}\times5^{4}}\) \(=\frac{14587}{10\times5^{3}}=\frac{(2)^{3}}{(2)^{3}}\) \(=\frac{14587\times8}{10\times1000}\) \(=\frac{1166969}{10000}=11.6696\) Hence, given rational number will terminate after four decimal places. \(\begin{array}{c|c} 2 & 1250 \\ \hline 5 & 625 \\ \hline 5 & 125 \\ \hline 5 & 25 \\ \hline 5 & 5 \\ \hline & 1 \end{array}\) Applying Medium **[Real Numbers]**
REAL NUMBERS
90435
If a = (2\(^{2}\) × 3\(^{3}\) × 5\(^{4}\)) and b = (2\(^{3}\) × 3\(^{2}\) × 5), then HCF (a, b) = ?
1 )90
2 )180
3 )360
4 )540
Explanation:
Exp: B 180 a = 2\(^{2}\) × 3\(^{3}\) × 5\(^{4}\) b = 2\(^{3}\) × 3\(^{2}\) × 5 HCF(a, b) = 2\(^{2}\) × 3\(^{2}\) × 5 = 180 Never Active Medium **[Real Numbers]**
90413
If two positive integers a and b are written as a = x\(^{3}\)y\(^{2}\) and b = xy\(^{3}\); x, y are prime numbers, then HCF (a, b) is:
1 )xy
2 )xy\(^{2}\)
3 )x\(^{3}\)y\(^{3}\)
4 )x\(^{2}\)y\(^{2}\)
Explanation:
Exp: B xy\(^{2}\) It is given that, \(\text{a}=\text{x}^3\text{y}^2=\text{x}\times\text{x}\times\text{x}\times\text{y}\times\text{y}\) \(\text{b}=\text{xy}^3=\text{x}\times\text{y}\times\text{y}\times\text{y}\) \(\text{HCF(a, b)}=\text{HCF}(\text{x}^3\text{y}^2,\text{xy}^3)=\text{x}\times\text{y}\times\text{y}=\text{xy}^2\) Hence, the correct answer is option B. Creating
REAL NUMBERS
90414
IF \(\frac{241}{4000}=\frac{241}{2^\text{m}\times5^\text{n}},\) Then:
1 )m = 4 and n = 5
2 )m = 3 and n = 2
3 )m = 5 and n = 3
4 )m = 2 and n = 5
Explanation:
Exp: C m = 5 and n = 3 \(\frac{241}{4000}=\frac{241}{2^\text{m}\times5^\text{m}}\) \(\Rightarrow\frac{241}{2^5\times5^3}=\frac{241}{2^\text{m}\times5^\text{n}}\) Comparing the denominators of both fractions, we have m = 5 and n = 3
REAL NUMBERS
90433
Choose the correct answer from the given four options in the following questions: The decimal expansion of the rational number \(\frac{14587}{1250}\) will terminate after:
1 )One decimal place.
2 )Two decimal places.
3 )Three decimal places.
4 )Four decimal places.
Explanation:
Exp: D Four decimal places. Rational number \(=\frac{14587}{1250}=\frac{14587}{2^{1}\times5^{4}}\) \(=\frac{14587}{10\times5^{3}}=\frac{(2)^{3}}{(2)^{3}}\) \(=\frac{14587\times8}{10\times1000}\) \(=\frac{1166969}{10000}=11.6696\) Hence, given rational number will terminate after four decimal places. \(\begin{array}{c|c} 2 & 1250 \\ \hline 5 & 625 \\ \hline 5 & 125 \\ \hline 5 & 25 \\ \hline 5 & 5 \\ \hline & 1 \end{array}\) Applying Medium **[Real Numbers]**
REAL NUMBERS
90435
If a = (2\(^{2}\) × 3\(^{3}\) × 5\(^{4}\)) and b = (2\(^{3}\) × 3\(^{2}\) × 5), then HCF (a, b) = ?
1 )90
2 )180
3 )360
4 )540
Explanation:
Exp: B 180 a = 2\(^{2}\) × 3\(^{3}\) × 5\(^{4}\) b = 2\(^{3}\) × 3\(^{2}\) × 5 HCF(a, b) = 2\(^{2}\) × 3\(^{2}\) × 5 = 180 Never Active Medium **[Real Numbers]**