Q) Prove that 3√2 is an irrational number. Ans: Let us assume that 3√2 is a rational number Then we can represent 3√2 as ; where q ≠ 0 and let p, q are co-primes. 3√2 = ………………. (i) or it can be rearranged as √2 = Since, 3, a and b are integers, is […]
Prove that 3 root 2 is an irrational number. Read More »
Q) Find the greatest 3-digit number which is divisible by 18, 24 and 36. Ans: Here, this question is slightly tricky one. We need to first find lowest number and then find its largest multiple with 3 digits. Hence, we need to find LCM, not HCF. Let’s start with LCM of 18, 24, 36. By
Find the greatest 3-digit number which is divisible by 18, 24 and 36. Read More »
Q) A 2-digit number is seven times the sum of its digits. The number formed by reversing the digits is 18 less than the given number. Find the given number. Ans: Let’s consider X and Y are the digits of the given number. Hence the given number is 10 X + Y Also given that Number
Q) Solve :- = 2; = – 1, x, y > o Ans: Let’s consider, = A and = B therefore the given equations will be: Equation = 2 will become: 2 A + 3 B = 2 ………. (i) Similarly, = – 1 will become: 4 A – 9 B = -1
Solve 2 by root x + 3 by root y = 2 ; 4 by root x – 9 by root y = -1, x, y > o Read More »
Q) The sum of a two digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there? Ans: Let’s consider X and Y are the digits of the given number. Hence the given number is 10 X
The sum of a two digit number and the number obtained by reversing the digits is 66. Read More »
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,
Prove that root 2 is an irrational number. Read More »
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,
Prove that root 3 is an irrational number. Read More »