Q) National Art convention got registrations from students from all parts of the country, of which 60 are interested in music, 84 are interested in dance and 108 students are interested in handicrafts. For optimum cultural exchange, organisers wish to keep them in minimum number of groups such that each group consists of students interested […]
National Art convention got registrations from students from all parts of the country Read More »
Q) Prove that √2 is an irrational number. Ans: Let us assume that √2 is a rational number Let √2 = ; where q ≠ 0 and let p, q are co-primes. 2q2 = p2………………. (i) It means p2 is divisible by 2 p is divisible by 2 Hence, we can write that p = 2a,
Q) The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change together next? Ans: The three traffic light will change together again when the time gap is perfect multiple of each light’s interval. Therefore,
Q) Using prime factorisation, find HCF and LCM of 96 and 120. Ans: By prime factorisation, we get: 96 = 25 x 3 and 120 = 23 x 3 x 5 ∴ LCM = 25 x 3 x 5 = 480 And HCF = 23 x3 = 24 Therefore, LCM of given numbers is 480
Using prime factorisation, find HCF and LCM of 96 and 120. Read More »
Q) Prove that √3 is an irrational number. Ans: Let us assume that √3 is a rational number Let √3 = ; where q ≠ 0 and let p, q are co-primes. 3q2 = p2………………. (i) It means p2 is divisible by 3 p is divisible by 3 Hence, we can write that p = 3a,
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,
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