If 3 digit numbers `A28, 3B9 and 62C` are divisible by a fixed constant 'K' where A, B, C are integers lying between 0 and 9, then determinant `|(A,3,6),(8,9,C),(2,B,2)|` is always divisible by

Suppose that digit numbers A28,3B9 and 62 C, where A,B and C are integers between 0 and 9 are divisible by a fixed integer k, prove that the determinant |{:(A,3,6),(8,9,C),(2,B,2):}| is also divisible by k.

The digits A,B,C are such that the three digit numbers A88, 6B8, 86 C are divisible by 72 the determinant |{:(A,6,8),(8,B,6),(8,8,C):}| is divisible by

The digits A,B,C are such that the three digit numbers A88, 6B8, 86 C are divisible by 72 the determinant |{:(A,6,8),(8,B,6),(8,8,C):}| is divisible by

The determinant Delta=|(a^2(a+b),a b,a c),(a b,b^2(a+k),b c),(a c,b c,c^2(1+k))| is divisible by

(a) How many numbers of two digits are divisible by 3 ? (b) How many numbers of three digits are divisible by 9 ?

How many numbers each lying between 100 and 1000 can be formed with the digits 2,3,4,0,8,9, no digit being repeated?

If n is a natural number, then 9^(2n)-4^(2n) is always divisible by (a) 5 (b) 13 (c) both 5 and 13 (d) none of these

The number of numbers divisible by 5 and lying between 40000 and 50000 that can be formed from the digits 0,3,4,5,8 and 9, when repetition of digits is not allowed is

The number of numbers divisible by 5 and lying between 40000 and 50000 that can be formed from the digits 0,3,4,5,8and 9 ,when repetition of digits is allowed is

Which of the following statements are true? If a number divisible by 3, it must be divisible by 9. If a number is divisible by 9, it must be divisible by 3. If a number is divisible by 4, it must be divisible by 8. If a number is divisible by 8,it must be divisible by 4. A number is divisible by 18, if it is divisible by both 3 and 6. If a number divisible by both 9 and 10, it must be divisible by 90.