90447
The number of possible pairs of number, whose product is 5400 and the HCF is 30 is:
1 )1
2 )2
3 )3
4 )4
Explanation:
Exp: B 2 Given that product of the number is 5400 = 30 × 3 × 2 × 30. \(\therefore\) Possible pairs as per the requirment are (1) 30 × (3 × 2 × 30) = 30 × 180 (2) (30 ×3) × (2 × 30) = 90 × 60 \(\therefore\) Total number of pairs = 2
REAL NUMBERS
90450
The product of a rational number and an irrational number is:
1 )an irrational number only
2 )none of these
3 )both rational and irrational number
4 )a rational number only
Explanation:
Exp: C both rational and irrational number The product of a rational number and an irrational number can be either a rational number or an irrational number. \(\text{e.g} \sqrt{5}\times\sqrt{2}=\sqrt{10}\) which irrational \(\text{but}\sqrt{8}\times\sqrt{2}=\sqrt{16}\) = 4 which is a rational number Thus, the product of two irrational numbers can be either rational or irrational similarly, the product of rational and irrational numbers can be either rational or irrational \(5\times\sqrt{2}=5\sqrt{2}\) which is a rational number \(\text{but }4\times\sqrt{4}=4\times2=8\) which is rational.
90447
The number of possible pairs of number, whose product is 5400 and the HCF is 30 is:
1 )1
2 )2
3 )3
4 )4
Explanation:
Exp: B 2 Given that product of the number is 5400 = 30 × 3 × 2 × 30. \(\therefore\) Possible pairs as per the requirment are (1) 30 × (3 × 2 × 30) = 30 × 180 (2) (30 ×3) × (2 × 30) = 90 × 60 \(\therefore\) Total number of pairs = 2
REAL NUMBERS
90450
The product of a rational number and an irrational number is:
1 )an irrational number only
2 )none of these
3 )both rational and irrational number
4 )a rational number only
Explanation:
Exp: C both rational and irrational number The product of a rational number and an irrational number can be either a rational number or an irrational number. \(\text{e.g} \sqrt{5}\times\sqrt{2}=\sqrt{10}\) which irrational \(\text{but}\sqrt{8}\times\sqrt{2}=\sqrt{16}\) = 4 which is a rational number Thus, the product of two irrational numbers can be either rational or irrational similarly, the product of rational and irrational numbers can be either rational or irrational \(5\times\sqrt{2}=5\sqrt{2}\) which is a rational number \(\text{but }4\times\sqrt{4}=4\times2=8\) which is rational.
90447
The number of possible pairs of number, whose product is 5400 and the HCF is 30 is:
1 )1
2 )2
3 )3
4 )4
Explanation:
Exp: B 2 Given that product of the number is 5400 = 30 × 3 × 2 × 30. \(\therefore\) Possible pairs as per the requirment are (1) 30 × (3 × 2 × 30) = 30 × 180 (2) (30 ×3) × (2 × 30) = 90 × 60 \(\therefore\) Total number of pairs = 2
REAL NUMBERS
90450
The product of a rational number and an irrational number is:
1 )an irrational number only
2 )none of these
3 )both rational and irrational number
4 )a rational number only
Explanation:
Exp: C both rational and irrational number The product of a rational number and an irrational number can be either a rational number or an irrational number. \(\text{e.g} \sqrt{5}\times\sqrt{2}=\sqrt{10}\) which irrational \(\text{but}\sqrt{8}\times\sqrt{2}=\sqrt{16}\) = 4 which is a rational number Thus, the product of two irrational numbers can be either rational or irrational similarly, the product of rational and irrational numbers can be either rational or irrational \(5\times\sqrt{2}=5\sqrt{2}\) which is a rational number \(\text{but }4\times\sqrt{4}=4\times2=8\) which is rational.
90447
The number of possible pairs of number, whose product is 5400 and the HCF is 30 is:
1 )1
2 )2
3 )3
4 )4
Explanation:
Exp: B 2 Given that product of the number is 5400 = 30 × 3 × 2 × 30. \(\therefore\) Possible pairs as per the requirment are (1) 30 × (3 × 2 × 30) = 30 × 180 (2) (30 ×3) × (2 × 30) = 90 × 60 \(\therefore\) Total number of pairs = 2
REAL NUMBERS
90450
The product of a rational number and an irrational number is:
1 )an irrational number only
2 )none of these
3 )both rational and irrational number
4 )a rational number only
Explanation:
Exp: C both rational and irrational number The product of a rational number and an irrational number can be either a rational number or an irrational number. \(\text{e.g} \sqrt{5}\times\sqrt{2}=\sqrt{10}\) which irrational \(\text{but}\sqrt{8}\times\sqrt{2}=\sqrt{16}\) = 4 which is a rational number Thus, the product of two irrational numbers can be either rational or irrational similarly, the product of rational and irrational numbers can be either rational or irrational \(5\times\sqrt{2}=5\sqrt{2}\) which is a rational number \(\text{but }4\times\sqrt{4}=4\times2=8\) which is rational.
