Question
The number of five–digit telephone numbers having
at least one of their digits repeated isSolution
The number of five–digit telephone numbers which can be formed using the digits of 0, 1, 2,...., 9 is 105. The number of five-digit telephone numbers which have none of their digits repeated is 10P5 = 10 × 9 × 8 × 7 × 6 = 30240 Hence the required number =105 - 30240 = 69760
Two numbers add up to 18, and the sum of their reciprocals is 5/2. Calculate the square of the product of the two numbers.
Find the number of zeros in 58!.
If 893x2 is divisible by 56, and x > 6, find x.
A and B are positive integers. If A + B + AB = 65, then what is the difference between A and B (A, B ≤ 15)?
- 65% of 'A' is (13/5) of 'B'. Find the value of A:B, given that 'A' and 'B' are co-prime numbers.
Find the difference between of the greatest among the numbers 0.82, 0.802, 0.85, 0.085 with the smallest among the numbers 0.3, 0.03, 0.203, 2.03
Find the remainder when '323323323' is divided by 17.
If the expression (px3 + x2 - 2x - q) is divisible by (x-1) and (x + 1), what are the values of
p and q respectively ?
- The sum of two numbers is 144. Their LCM is 540 and HCF is 15. What is the smaller number?
Which of the following pairs is NOT coprime?
