if `6n` tickets numbered 0,1,2,....... 6n-1 are placed in a bag and three are drawn out , show that the chance that the sum of the numbers on then is equal to 6n is `(3n)/((6n-1)(6n-2))`

Out of (2n+1) tickets consecutively numbered, three are drawn at random. Find the chance that the numbers on them are in AP.

Statement-1: Out of 21 tickets with number 1 to 21, 3 tickets are drawn at random, the chance that the numbers on them are in AP is (10)/(133) . Statement-2: Out of (2n+1) tickets consecutively numbered three are drawn at ranodm, the chance that the number on them are in AP is (4n-10)/ (4n^(2)-1) .

Check whether 6^n can end with the digit 0 for any natural number n.

The natural numbers arearranged innthe form given below The rth group containing 2^(r-1) numbers. Prove that sum of the numbers in the nth group is 2^(n-2)[2^(n)+2^(n+1)-1] .

Check whether 6^(n) can end with the digit 0 for any natural number n

Three forces of magnitudes 2N, 3N and 6N act at corners of a cube along three sides as shown in figure. Find the resultant of these forces in N.

Write the first five terms of each of the sequences whose n^(th) terms are: a_(n) = (2n-3)/6

The number of positive integers satisfying the inequality .^(n+1)C(n-2)-.^(n+1)C(n-1)<=100 is

Suppose A is a complex number and n in N , such that A^n=(A+1)^n=1, then the least value of n is 3 b. 6 c. 9 d. 12

Find the sum of the series 1*n+2*(n-1)+3*(n-2)+4*(n-3)+....(n−1).2+n.1"