Q) Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers. Ans: Let’s take both numbers one by one and analyse: (i) 7 × 11 × 13 + 13 = 13 (7 x 11 + 1) = 13 […]
Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers. Read More »
Q) Can the number (15n), n being a natural number, end with the digit 0 ? Ans: For any number to end with the digit 0, it will be divisible by 10 Since 10 = 2 x 5, therefore, a number ending with digit 0 will be divisible by 2 and 5 both. Next, since
Can the number (15n), n being a natural number, end with the digit 0? Give reasons. Read More »
Q) If √2 is given as an irrational number, then prove that (5 – 2√2) is an irrational number. Ans: STEP BY STEP SOLUTION Let’s start by considering 5 – 2 √2 is a rational number. ∴ 5 – 2 √2 = (here p and q are integers and q ≠ 0) ∴ –
Q) Check whether 6n can end with the digit 0 for any natural number n. Ans: For any number to end with the digit 0, it will be divisible by 10 Since 10 = 2 x 5, therefore, a number ending with digit 0 will be divisible by 2 and 5 both. Next, since factors of
Check whether 6n can end with the digit 0 for any natural number n . Read More »
Q) In a 2-digit number, the digit at the unit’s place is 5 less than the digit at the ten’s place. The product of the digits is 36. Find the number. Ans: Let’s consider X is the digit at unit’s place and Y is the digit at ten’s place. The number will be 10 Y +
In a 2-digit number, the digit at the unit’s place is 5 less than the digit Read More »
Q) The sum of the digits of a 2-digit number is 14. The number obtained by interchanging its digits exceeds the given number by 18. Find the number. Ans: Let’s consider X and Y are the digits of the given number. Hence the given number is 10 X + Y ∴ the sum of the digits
Q) Prove that 5-2√3 is an irrational number. It is given that √3 is an irrational number. Ans: STEP BY STEP SOLUTION Let’s start by considering 5 – 2 √3 is a rational number. ∴ 5 – 2 √3 = (here p and q are integers and q ≠ 0) ∴ – 2 √3
Prove that 5-2√3 is an irrational number. It is given that √3 is an irrational number. Read More »
Q) Show that the number 5 × 11 × 17 + 3 × 11 is a composite number Ans: STEP BY STEP SOLUTION Let’s start solving the given expression: 5 ×11 × 17 + 3 × 11 = 11 (5 x 17 + 3) = 11 (88) = 11 x 11 x 8 it has
Show that the number 5×11×17+3×11 is a composite number Read More »
Q) In a teachers’ workshop, the number of teachers teaching French, Hindi and English are 48, 80 and 144 respectively. Find the minimum number of rooms required if in each room the same number of teachers are seated and all of them are of the same subject. Ans: STEP BY STEP SOLUTION The number of
Q) Find the smallest number that is divisible by each of 8, 9 and 10. Ans: Since, we need to find the smallest number which has to be multiple of the given numbers, clearly we need to find the LCM of 8,9, and 10 Let’s start with LCM of 8, 9, 10. By prime factorisation, we
Find the smallest number that is divisible by each of 8, 9 and 10. Read More »