90209
Choose the correct answer from the given four options in the following questions: 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: D x\(^{2}\)y\(^{2}\). Given that, a= x\(^{3}\)y\(^{2}\) = x × x × x × y × y and b = xy\(^{3}\) = x × y × y × y \(\therefore\) HCF of a and b = HCF(x\(^{3}\)y\(^{2}\) xy\(^{2}\)) = x x y x y = xy\(^{2}\) [since, HCF is the product of the smallest power of each common prime facter involved in the numbers] Applying
REAL NUMBERS
90213
\(\frac{1}{\sqrt{2}}\) is:
1 )A fraction.
2 )A rational number.
3 )An irrational number.
4 )None of these.
Explanation:
Exp: C An irrational number. An irrational number is a number that is non-terminating and non-repeating. \(\frac{1}{\sqrt{2}}=\frac{1\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}}\) ...(Rationalising the denominator) \(=\frac{\sqrt{2}}{2}\) \(=\frac{1}2{}\times\sqrt{2}\) Now, \(\frac{1}2{}\) is rational but \(\sqrt2\) is irrational. Product of a rational number and an irrational number is irrational. Hence, \(\frac{1}{\sqrt2}\) is an irrational number. Never Active
REAL NUMBERS
90215
Choose the correct answer from the given four options in the following questions: The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is:
90223
If 112 = q × 6 + r, then the possible values of r, are:
1 )0, 1, 2, 3
2 )2, 3, 5
3 )1, 2, 3, 4
4 )0, 1, 2, 3, 4, 5 1Mark
Explanation:
Exp: D 0, 1, 2, 3, 4, 5 Solution: For the relation \(\text{x}=\text{qy}+\text{r},0\leq\text{r}<\text{y}\) So, here r lies between \(0\leq\text{r}<6\) Hence????, r = 0, 1, 2, 3, 4, 5
90209
Choose the correct answer from the given four options in the following questions: 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: D x\(^{2}\)y\(^{2}\). Given that, a= x\(^{3}\)y\(^{2}\) = x × x × x × y × y and b = xy\(^{3}\) = x × y × y × y \(\therefore\) HCF of a and b = HCF(x\(^{3}\)y\(^{2}\) xy\(^{2}\)) = x x y x y = xy\(^{2}\) [since, HCF is the product of the smallest power of each common prime facter involved in the numbers] Applying
REAL NUMBERS
90213
\(\frac{1}{\sqrt{2}}\) is:
1 )A fraction.
2 )A rational number.
3 )An irrational number.
4 )None of these.
Explanation:
Exp: C An irrational number. An irrational number is a number that is non-terminating and non-repeating. \(\frac{1}{\sqrt{2}}=\frac{1\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}}\) ...(Rationalising the denominator) \(=\frac{\sqrt{2}}{2}\) \(=\frac{1}2{}\times\sqrt{2}\) Now, \(\frac{1}2{}\) is rational but \(\sqrt2\) is irrational. Product of a rational number and an irrational number is irrational. Hence, \(\frac{1}{\sqrt2}\) is an irrational number. Never Active
REAL NUMBERS
90215
Choose the correct answer from the given four options in the following questions: The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is:
90223
If 112 = q × 6 + r, then the possible values of r, are:
1 )0, 1, 2, 3
2 )2, 3, 5
3 )1, 2, 3, 4
4 )0, 1, 2, 3, 4, 5 1Mark
Explanation:
Exp: D 0, 1, 2, 3, 4, 5 Solution: For the relation \(\text{x}=\text{qy}+\text{r},0\leq\text{r}<\text{y}\) So, here r lies between \(0\leq\text{r}<6\) Hence????, r = 0, 1, 2, 3, 4, 5
90209
Choose the correct answer from the given four options in the following questions: 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: D x\(^{2}\)y\(^{2}\). Given that, a= x\(^{3}\)y\(^{2}\) = x × x × x × y × y and b = xy\(^{3}\) = x × y × y × y \(\therefore\) HCF of a and b = HCF(x\(^{3}\)y\(^{2}\) xy\(^{2}\)) = x x y x y = xy\(^{2}\) [since, HCF is the product of the smallest power of each common prime facter involved in the numbers] Applying
REAL NUMBERS
90213
\(\frac{1}{\sqrt{2}}\) is:
1 )A fraction.
2 )A rational number.
3 )An irrational number.
4 )None of these.
Explanation:
Exp: C An irrational number. An irrational number is a number that is non-terminating and non-repeating. \(\frac{1}{\sqrt{2}}=\frac{1\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}}\) ...(Rationalising the denominator) \(=\frac{\sqrt{2}}{2}\) \(=\frac{1}2{}\times\sqrt{2}\) Now, \(\frac{1}2{}\) is rational but \(\sqrt2\) is irrational. Product of a rational number and an irrational number is irrational. Hence, \(\frac{1}{\sqrt2}\) is an irrational number. Never Active
REAL NUMBERS
90215
Choose the correct answer from the given four options in the following questions: The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is:
90223
If 112 = q × 6 + r, then the possible values of r, are:
1 )0, 1, 2, 3
2 )2, 3, 5
3 )1, 2, 3, 4
4 )0, 1, 2, 3, 4, 5 1Mark
Explanation:
Exp: D 0, 1, 2, 3, 4, 5 Solution: For the relation \(\text{x}=\text{qy}+\text{r},0\leq\text{r}<\text{y}\) So, here r lies between \(0\leq\text{r}<6\) Hence????, r = 0, 1, 2, 3, 4, 5
90209
Choose the correct answer from the given four options in the following questions: 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: D x\(^{2}\)y\(^{2}\). Given that, a= x\(^{3}\)y\(^{2}\) = x × x × x × y × y and b = xy\(^{3}\) = x × y × y × y \(\therefore\) HCF of a and b = HCF(x\(^{3}\)y\(^{2}\) xy\(^{2}\)) = x x y x y = xy\(^{2}\) [since, HCF is the product of the smallest power of each common prime facter involved in the numbers] Applying
REAL NUMBERS
90213
\(\frac{1}{\sqrt{2}}\) is:
1 )A fraction.
2 )A rational number.
3 )An irrational number.
4 )None of these.
Explanation:
Exp: C An irrational number. An irrational number is a number that is non-terminating and non-repeating. \(\frac{1}{\sqrt{2}}=\frac{1\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}}\) ...(Rationalising the denominator) \(=\frac{\sqrt{2}}{2}\) \(=\frac{1}2{}\times\sqrt{2}\) Now, \(\frac{1}2{}\) is rational but \(\sqrt2\) is irrational. Product of a rational number and an irrational number is irrational. Hence, \(\frac{1}{\sqrt2}\) is an irrational number. Never Active
REAL NUMBERS
90215
Choose the correct answer from the given four options in the following questions: The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is:
90223
If 112 = q × 6 + r, then the possible values of r, are:
1 )0, 1, 2, 3
2 )2, 3, 5
3 )1, 2, 3, 4
4 )0, 1, 2, 3, 4, 5 1Mark
Explanation:
Exp: D 0, 1, 2, 3, 4, 5 Solution: For the relation \(\text{x}=\text{qy}+\text{r},0\leq\text{r}<\text{y}\) So, here r lies between \(0\leq\text{r}<6\) Hence????, r = 0, 1, 2, 3, 4, 5
