Q) Prove that √5 is an irrational number. Ans: Let us assume that √5 is a rational number Let √5 = ; where q ≠ 0 and let p, q are co-primes. 5q2 = p2………………. (i) It means p2 is divisible by 5 p is divisible by 5 Hence, we can write that p = 5a, […]
Prove that root 5 is an irrational number. Read More »
Q) The two numbers are in the ratio of 2 : 3 and their LCM is 180. What is the HCF of the these numbers? Ans: Let us consider, the two number be 2x & 3x in the ratio of 2 : 3. Therefore the LCM of these two numbers = 6x Since, its given
Q) Prove that 6 – √7 is an irrational number, given that √7 is an irrational number. Ans: Let us assume that 6 – √7 is a rational number Let 6 – √7 = ; q ≠ 0 and p, q are integers √7 = Since, p and q are integers; Therefore 6q – p is
Q) Prove that 4n can never end with digit 0, where n is a natural number. Ans: Let’s assume that 4n ends with 0. Since now it ends with zero, it is multiple of 10 and hence, it must be divisible by 2 and 5 both. This clearly means, that the factors of 4n should include
Prove that 4^n can never end with digit 0, where n is a natural number. Read More »
Q) Three bells ring at intervals of 6, 12 and 18 minutes. If all the three bells rang at 6 a.m., when will they ring together again? Ans: VIDEO SOLUTION STEP BY STEP SOLUTION The three bells will ring together again when the time gap is perfect multiple of each bell’s interval Therefore, we will take
Q) Find by prime factorisation the LCM of the numbers 18180 and 7575. Also, find the HCF of the two numbers. Ans: By prime factorisation, we get: 18180 = 22 x 32 x 5 x 101 and 7575 = 3 x 52 x 101 LCM = 22 x 32 x 52 x 101 LCM =
Q) Prove that 2 + √3 is an irrational number, given that √3 is an irrational number. Ans: Let us assume that 2 + √3 is a rational number Let 2 + √3 = ; q ≠ 0 and p, q are integers √3 = Since, p and q are integers; Therefore p – 2q is
Prove that 2 + √3 is an irrational number, given that √3 is an irrational number. Read More »
Q) Find the least number which when divided by 12, 16 and 24 leaves remainder 7 in each case. Ans: Let’s start with LCM of 12, 16, 24: We get LCM as 48 Since remainder is 7, It means the number is 7 more than LCM Hence, the required number is 48 + 7 =
Q) Prove that √5 is an irrational number. Ans: Let √5 be a rational number. Therefore √5 = p/q, where q ≠ 0 and let p & q be co-primes. ⇒ 5q² = p² ⇒ p² is divisible by 5 ⇒ p is divisible by 5………………….. ……………….. (i) ⇒ p = 5a, where a is some
Prove that root 5 is an irrational number. Read More »
Q) Find the greatest number which divides 85 and 72 leaving remainders 1 and 2 respectively. Ans: Question is asking for highest number which is dividing other numbers…. . clearly, we need to find HCF Since there are remainders after dividing, hence if we subtract remainder from the given number, we will get the actual