90342
Euclid’s division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy:
1 )1 < r < b
2 )0 < r = b
3 )0 = r < b
4 )0 < r < b
Explanation:
Exp: C 0 = r < b According to Euclid’s Division lemma, for a positive pair of integers there exists unique integers q and r, such that, a = bq + r, where 0 = r < b Understanding
REAL NUMBERS
90346
Let \(\text{x}=\frac{\text{p}}{\text{q}}\) be a rational number, such that the prime factorization of q is of the form 2n5m, where n,m are non-negative integers. Then x has a decimal expansion which terminates:
1 )True
2 )False
3 )Neither
4 )Either
Explanation:
Exp: A True The form of q is 2\(^{n}\) * 5\(^{m}\) q can be 1, 2, 5, 10, 20, 40.... Any integer divided by these numbers will always give a terminating decimal number.
REAL NUMBERS
90347
The decimal representation of \(\frac{71}{150}\) is:
1 )A terminating decimal.
2 )A non-terminating, repeating decimal.
3 )A non-terminating and non-repeating decimal.
4 )None of these.
Explanation:
Exp: B A non-terminating, repeating decimal. A number is a terminating decimal, if the denominator is of the form 2\(^{m}\) × 5\(^{n}\), where m and n are non-negative integers. The prime factorisation of the denominator is 2 × 3 × 50\(^{2}\) So, the denominator will be non- terminating. Since \(\frac{71}{150}\) is a rational number, it will surely be repeating. Never Active Medium **[Real Numbers]**
REAL NUMBERS
90350
The exponent of 2 in the prime factorisation of 144, is:
1 )4
2 )5
3 )6
4 )3
Explanation:
Exp: A 4 \(\begin{array}{c|c}2 &144\\\hline 2 & 72\\\hline 2 & 36\\\hline2 & 18\\\hline3 & 9\\\hline3 & 3 \\\hline&1 \end{array}\) 144 = 2\(^{4}\) × 3\(^{2}\) \(\therefore\) Exponant of 2 is 4
REAL NUMBERS
90351
The decimal expansion of the number \(\frac{14753}{1250}\) will terminate after:
1 )Three decimal places.
2 )One decimal place.
3 )Two decimal places.
4 )Four decimal places.
Explanation:
Exp: D Four decimal places. The prime factorisation of the denominator is 2 × 5\(^{2}\) Since 4 > 1, The decimal expansion will terminate after 4 decimal places. Never Active Medium **[Real Numbers]**
90342
Euclid’s division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy:
1 )1 < r < b
2 )0 < r = b
3 )0 = r < b
4 )0 < r < b
Explanation:
Exp: C 0 = r < b According to Euclid’s Division lemma, for a positive pair of integers there exists unique integers q and r, such that, a = bq + r, where 0 = r < b Understanding
REAL NUMBERS
90346
Let \(\text{x}=\frac{\text{p}}{\text{q}}\) be a rational number, such that the prime factorization of q is of the form 2n5m, where n,m are non-negative integers. Then x has a decimal expansion which terminates:
1 )True
2 )False
3 )Neither
4 )Either
Explanation:
Exp: A True The form of q is 2\(^{n}\) * 5\(^{m}\) q can be 1, 2, 5, 10, 20, 40.... Any integer divided by these numbers will always give a terminating decimal number.
REAL NUMBERS
90347
The decimal representation of \(\frac{71}{150}\) is:
1 )A terminating decimal.
2 )A non-terminating, repeating decimal.
3 )A non-terminating and non-repeating decimal.
4 )None of these.
Explanation:
Exp: B A non-terminating, repeating decimal. A number is a terminating decimal, if the denominator is of the form 2\(^{m}\) × 5\(^{n}\), where m and n are non-negative integers. The prime factorisation of the denominator is 2 × 3 × 50\(^{2}\) So, the denominator will be non- terminating. Since \(\frac{71}{150}\) is a rational number, it will surely be repeating. Never Active Medium **[Real Numbers]**
REAL NUMBERS
90350
The exponent of 2 in the prime factorisation of 144, is:
1 )4
2 )5
3 )6
4 )3
Explanation:
Exp: A 4 \(\begin{array}{c|c}2 &144\\\hline 2 & 72\\\hline 2 & 36\\\hline2 & 18\\\hline3 & 9\\\hline3 & 3 \\\hline&1 \end{array}\) 144 = 2\(^{4}\) × 3\(^{2}\) \(\therefore\) Exponant of 2 is 4
REAL NUMBERS
90351
The decimal expansion of the number \(\frac{14753}{1250}\) will terminate after:
1 )Three decimal places.
2 )One decimal place.
3 )Two decimal places.
4 )Four decimal places.
Explanation:
Exp: D Four decimal places. The prime factorisation of the denominator is 2 × 5\(^{2}\) Since 4 > 1, The decimal expansion will terminate after 4 decimal places. Never Active Medium **[Real Numbers]**
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REAL NUMBERS
90342
Euclid’s division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy:
1 )1 < r < b
2 )0 < r = b
3 )0 = r < b
4 )0 < r < b
Explanation:
Exp: C 0 = r < b According to Euclid’s Division lemma, for a positive pair of integers there exists unique integers q and r, such that, a = bq + r, where 0 = r < b Understanding
REAL NUMBERS
90346
Let \(\text{x}=\frac{\text{p}}{\text{q}}\) be a rational number, such that the prime factorization of q is of the form 2n5m, where n,m are non-negative integers. Then x has a decimal expansion which terminates:
1 )True
2 )False
3 )Neither
4 )Either
Explanation:
Exp: A True The form of q is 2\(^{n}\) * 5\(^{m}\) q can be 1, 2, 5, 10, 20, 40.... Any integer divided by these numbers will always give a terminating decimal number.
REAL NUMBERS
90347
The decimal representation of \(\frac{71}{150}\) is:
1 )A terminating decimal.
2 )A non-terminating, repeating decimal.
3 )A non-terminating and non-repeating decimal.
4 )None of these.
Explanation:
Exp: B A non-terminating, repeating decimal. A number is a terminating decimal, if the denominator is of the form 2\(^{m}\) × 5\(^{n}\), where m and n are non-negative integers. The prime factorisation of the denominator is 2 × 3 × 50\(^{2}\) So, the denominator will be non- terminating. Since \(\frac{71}{150}\) is a rational number, it will surely be repeating. Never Active Medium **[Real Numbers]**
REAL NUMBERS
90350
The exponent of 2 in the prime factorisation of 144, is:
1 )4
2 )5
3 )6
4 )3
Explanation:
Exp: A 4 \(\begin{array}{c|c}2 &144\\\hline 2 & 72\\\hline 2 & 36\\\hline2 & 18\\\hline3 & 9\\\hline3 & 3 \\\hline&1 \end{array}\) 144 = 2\(^{4}\) × 3\(^{2}\) \(\therefore\) Exponant of 2 is 4
REAL NUMBERS
90351
The decimal expansion of the number \(\frac{14753}{1250}\) will terminate after:
1 )Three decimal places.
2 )One decimal place.
3 )Two decimal places.
4 )Four decimal places.
Explanation:
Exp: D Four decimal places. The prime factorisation of the denominator is 2 × 5\(^{2}\) Since 4 > 1, The decimal expansion will terminate after 4 decimal places. Never Active Medium **[Real Numbers]**
90342
Euclid’s division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy:
1 )1 < r < b
2 )0 < r = b
3 )0 = r < b
4 )0 < r < b
Explanation:
Exp: C 0 = r < b According to Euclid’s Division lemma, for a positive pair of integers there exists unique integers q and r, such that, a = bq + r, where 0 = r < b Understanding
REAL NUMBERS
90346
Let \(\text{x}=\frac{\text{p}}{\text{q}}\) be a rational number, such that the prime factorization of q is of the form 2n5m, where n,m are non-negative integers. Then x has a decimal expansion which terminates:
1 )True
2 )False
3 )Neither
4 )Either
Explanation:
Exp: A True The form of q is 2\(^{n}\) * 5\(^{m}\) q can be 1, 2, 5, 10, 20, 40.... Any integer divided by these numbers will always give a terminating decimal number.
REAL NUMBERS
90347
The decimal representation of \(\frac{71}{150}\) is:
1 )A terminating decimal.
2 )A non-terminating, repeating decimal.
3 )A non-terminating and non-repeating decimal.
4 )None of these.
Explanation:
Exp: B A non-terminating, repeating decimal. A number is a terminating decimal, if the denominator is of the form 2\(^{m}\) × 5\(^{n}\), where m and n are non-negative integers. The prime factorisation of the denominator is 2 × 3 × 50\(^{2}\) So, the denominator will be non- terminating. Since \(\frac{71}{150}\) is a rational number, it will surely be repeating. Never Active Medium **[Real Numbers]**
REAL NUMBERS
90350
The exponent of 2 in the prime factorisation of 144, is:
1 )4
2 )5
3 )6
4 )3
Explanation:
Exp: A 4 \(\begin{array}{c|c}2 &144\\\hline 2 & 72\\\hline 2 & 36\\\hline2 & 18\\\hline3 & 9\\\hline3 & 3 \\\hline&1 \end{array}\) 144 = 2\(^{4}\) × 3\(^{2}\) \(\therefore\) Exponant of 2 is 4
REAL NUMBERS
90351
The decimal expansion of the number \(\frac{14753}{1250}\) will terminate after:
1 )Three decimal places.
2 )One decimal place.
3 )Two decimal places.
4 )Four decimal places.
Explanation:
Exp: D Four decimal places. The prime factorisation of the denominator is 2 × 5\(^{2}\) Since 4 > 1, The decimal expansion will terminate after 4 decimal places. Never Active Medium **[Real Numbers]**
90342
Euclid’s division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy:
1 )1 < r < b
2 )0 < r = b
3 )0 = r < b
4 )0 < r < b
Explanation:
Exp: C 0 = r < b According to Euclid’s Division lemma, for a positive pair of integers there exists unique integers q and r, such that, a = bq + r, where 0 = r < b Understanding
REAL NUMBERS
90346
Let \(\text{x}=\frac{\text{p}}{\text{q}}\) be a rational number, such that the prime factorization of q is of the form 2n5m, where n,m are non-negative integers. Then x has a decimal expansion which terminates:
1 )True
2 )False
3 )Neither
4 )Either
Explanation:
Exp: A True The form of q is 2\(^{n}\) * 5\(^{m}\) q can be 1, 2, 5, 10, 20, 40.... Any integer divided by these numbers will always give a terminating decimal number.
REAL NUMBERS
90347
The decimal representation of \(\frac{71}{150}\) is:
1 )A terminating decimal.
2 )A non-terminating, repeating decimal.
3 )A non-terminating and non-repeating decimal.
4 )None of these.
Explanation:
Exp: B A non-terminating, repeating decimal. A number is a terminating decimal, if the denominator is of the form 2\(^{m}\) × 5\(^{n}\), where m and n are non-negative integers. The prime factorisation of the denominator is 2 × 3 × 50\(^{2}\) So, the denominator will be non- terminating. Since \(\frac{71}{150}\) is a rational number, it will surely be repeating. Never Active Medium **[Real Numbers]**
REAL NUMBERS
90350
The exponent of 2 in the prime factorisation of 144, is:
1 )4
2 )5
3 )6
4 )3
Explanation:
Exp: A 4 \(\begin{array}{c|c}2 &144\\\hline 2 & 72\\\hline 2 & 36\\\hline2 & 18\\\hline3 & 9\\\hline3 & 3 \\\hline&1 \end{array}\) 144 = 2\(^{4}\) × 3\(^{2}\) \(\therefore\) Exponant of 2 is 4
REAL NUMBERS
90351
The decimal expansion of the number \(\frac{14753}{1250}\) will terminate after:
1 )Three decimal places.
2 )One decimal place.
3 )Two decimal places.
4 )Four decimal places.
Explanation:
Exp: D Four decimal places. The prime factorisation of the denominator is 2 × 5\(^{2}\) Since 4 > 1, The decimal expansion will terminate after 4 decimal places. Never Active Medium **[Real Numbers]**