Q) Prove that (√2 + √3)2 is an irrational number, given that √6 is an irrational number. Ans: STEP BY STEP SOLUTION Let’s start by considering (√2 + √3)2 is a rational number (by the method of contradiction) If (√2 + √3)2 is a rational number, then it can be expressed in the form of , […]
Prove that (√2 + √3)2 is an irrational number, given that √6 is an irrational number. Read More »
Q) Prove that is an irrational number. It is given that √3 is an irrational number. Ans: STEP BY STEP SOLUTION Let’s start by considering is a rational number. ∴ = (here p and q are integers and q ≠ 0) ∴ (2 – √3) = 5 ∴ √3 = 2 – 5
Q) Prove that (2 + √3) / 5 is an irrational number. It is given that √3 is an irrational number. Ans: STEP BY STEP SOLUTION Let’s start by considering is a rational number. ∴ (here p and q are integers and q ≠ 0) ∴ ∴ ∴ Since p and q are integers,
Q) In a school, there are two sections of class X. There are 40 students in the first section and 48 students in the second section. Determine the minimum number of books required for their class library so that they can be distributed equally among students of both sections. Ans: STEP-BY-STEP SOLUTION To get a
Q) A 2-digit number is such that the product of its digits is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number. Ans: Step 1: Let’s consider X and Y are the digits of the given number. Hence the given number is 10 X + Y ∴ the
A 2-digit number is such that the product of its digits is 18. When 63 is subtracted Read More »
Q) Three bells ring at intervals of 9, 12 and 15 minutes respectively. If they start tolling together, after what time will they next toll together? Ans: 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 LCM of three time
Q) The H.C.F of 85 and 238 is expressible in the form 85m -238. Find the value of m. Ans: By prime factorisation, we solve 85 and 238 one by one: 85 = 5 x 17 238 = 2 x 7 x 17 Hence the HCF of these two numbers = 17 Since it is
The H.C.F of 85 and 238 is expressible in the form 85m -238. Find the value of m. Read More »
Q) Find the H.C.F and L.C.M of 480 and 720 using the Prime factorisation method. Ans: VIDEO SOLUTION STEP BY STEP SOLUTION Step 1: By prime factorisation, we solve 480 and 720 one by one: ∴ 480 = 2 x 2 x 2 x 2 x 2 x 3 x 5 = 25 x 3
Find the H.C.F and L.C.M of 480 and 720 using the Prime factorisation method. Read More »
Q) The sum of two numbers is 18 and the sum of their reciprocals is 9/40. Find the numbers. Ans: Let the numbers be X and Y Step 1: By first condition: X + Y = 18 ………… (i) Step 2: By second condition: ∴ ∴ 40 (Y + X) = 9 X Y e
The sum of two numbers is 18 and the sum of their reciprocals is 9/40. Find the numbers. Read More »
Q) Sum of two numbers is 105 and their difference is 45. Find the numbers. Ans: Let the numbers be X and Y Step 1: By first condition: X + Y = 105 ………… (i) By second condition: X – Y = 45 ………. (ii) Step 2: By adding these two equations, we get: (X
Sum of two numbers is 105 and their difference is 45. Find the numbers. Read More »