Q) The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 2 16/21, find the fraction. Ans: Let the Numerator be A, then by given 1st condition, denominator = 2 A + 1 Hence the fraction is: And its reciprocal will be: By […]
The denominator of a fraction is one more than twice the numerator. If the sum of the Read More »
Q)Teaching Mathematics through activities is a powerful approach that enhances students’ understanding and engagement. Keeping this in mind, Ms. Mukta planned a prime number game for class 5 students. She announces the number 2 in her class and asked the first student to multiply it by a prime number and then pass it to second
Teaching Mathematics through activities is a powerful approach that enhances students’ Read More »
Q) Can the number (8n), 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 (8n), n being a natural number, end with the digit 0? Give reasons. Read More »
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 »