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Q) Find the HCF of 506 and 1155. Ans: By prime factorisation, we get: 506 = 2 x 11 x 23 1155 = 3 x 5 x 7 x 11 Since HCF is all the factors between the two numbers and here 11 is the only factor between the two numbers ∴ HCF = 11
real numbers
Q) Find the LCM and HCF of 404 and 96 and verify that LCM x HCF = product of the two numbers.120. Ans: By prime factorisation, we get: 404 = 22 x 101 96 = 25 x 3 ∴ LCM = 25 x 3 x 101 = 9696 And HCF = 22 = 4 Now
Q) ABCD is a rectangle if the value of AB= 12 is given, find the values of x and y. Ans: We know, opposite sides of a rectangle are equal, ∴ x + y = 12 —-(1) and, x – y = 8  —-(2) By elimination method, we subtract (2) from (1), Therefore, 2y =
ABCD is a rectangle if the value of AB=12 is given. Find the values of x and y. Read More »
Q) Mrs. Gupta arranged some snacks for her child’s birthday party. After the guest left she had some food left over. She did not want to waste food and so she contacted a local NGO. She gave 60 pieces of pastries,168 pieces of cookies, and 330 chocolate bars to the team. Now the NGO workers want
Mrs. Gupta arranged some snacks for her child’s birthday party. Read More »
Q)Â A number consists of two digits. Where the number is divided by the sum of its digits, the quotient is 7. If 27 is subtracted from the number, the digits interchange their places, find the number Ans:Â Let’s consider X and Y are the digits of the given number. Hence the given number is 10 X
A number consists of two digits. Where the number is divided by the sum of its digits, Read More »
Q) Solve for x and y: = -1; = 3 Ans: Let’s take the equations one by one: = -1 3X + 4 Y = – 6Â ………. (i) Similarly, = 3 We can write this as: = 3 3X – Y = 9 ….. (ii) By solving equations (i) and (ii), we get: X =
Solve for x and y : x / 2 + 2y / 3 = − 1; x − y / 3 = 3 Read More »
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
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:Â 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 :-Â Â = 2; = – 1, x, y > o Ans: Let’s consider, Â = 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 »