Write the set of values of `n` for which the statement `P(n):2n < n!` is true.

Write the value of n for which n t h terms of the A.P.s 3,10,17. And 63,65,67. are equal.

find the value of P(n,n-1)

If P(n) is the statement n^3+n is divisible 3 is the statement P(3) true ? Is the statement P(4) true?

Find whether the following statements are true or false. If the statement is false, then write its correct statement: (i) If P={m,n} and Q={n,m},then PxxQ={(m,n),(n,m)} . (ii) If A and B are non-empty sets, then AxxB is a non-empty set of the ordered pairs (x,y) such that x in A and y in B .

Write down the fourth term in the binomial expansion of (px + (1)/(x) )^(n) . If this term is independent of x , find the value of n. With this value of n , calculate the value of p given that the fourth term is equal to (5)/(2) .

A set contains (2n+1) elements. If the number of subsets of this set which contain atmost n elements is 4096, then n is

State whether each of the following statements are true or false. If the statement is false re-write the given statement correctly: (i) If p={m , n}a n d\ Q={n , m},\ t h e n\ PxxQ={(m , n),\ (n , m)} (ii) If A and B are non empty sets then AxxB is a non empty set of ordered pairs (x , y) such that x in B\ a n d\ y in Adot (iii) If A={1,2},\ B={3,4},\ t h e n\ Axx(Bnnvarphi)=varphidot

If P(n) is the statement n(n+1)(n+2) is divisible is 12 prove that the statements P(3) and P(4) are true, but that P(5) is not true.

Let P_n denotes the number of ways in which three people can be selected out of 'n' people sitting in a row, if no two of them are consecutive. If P_(n+1)- P_n=15 then the value of 'n is____.

If P(n) is the statement n^2+n is even, and if P(r) is true then P(r+1) is true.