Two natural numbers r,s and drawn one at a time, without replacement from the set S={1,2,3,………..,n}. Find the `P[r le p/s le p]`, where `p in S`.

If P(n) is the statement : ''^nC_r len ! for 1 le r len ", then : find P(n +1) .

There are two sets A and B each of which consists of three numbers in GP whose product is 64 and R and r are the common ratios sich that R=r+2 . If (p)/(q)=(3)/(2) , where p and q are sum of numbers taken two at a time respectively in the two sets. The value of r^(R)+R^(r) is

Name the element with electronic configuration 1s2 2s2 2p6 3s1

Name the element with electronic configuration 1s2 2s2 2p6 3s2

Name the element with electronic configuration 1s2 2s2 2p6 3s2

lf r, s, t are prime numbers and p, q are the positive integers such that their LCM of p,q is r^2 t^4 s^2, then the numbers of ordered pair of (p, q) is (A) 252 (B) 254 (C) 225 (D) 224

If P(n) is the statement ‘‘2^n ge n’’ , prove that P(r +1) is true whenever P(r) is true.

Prove that if r le s le n , then ""^nP_s is divisible by ""^nP_r .

Consider the following relations: R = {(x, y) | x, y are real numbers and x = wy for some rational number w}; S={(m/n , p/q)"m , n , p and q are integers such that n ,q"!="0 and q m = p n"} . Then (1) neither R nor S is an equivalence relation (2) S is an equivalence relation but R is not an equivalence relation (3) R and S both are equivalence relations (4) R is an equivalence relation but S is not an equivalence relation

A straight line through the vertex P of a triangle P Q R intersects the side Q R at the points S and the cicumcircle of the triangle P Q R at the point Tdot If S is not the center of the circumcircle, then 1/(P S)+1/(S T) 2/(sqrt(Q SxxS R)) 1/(P S)+1/(S T) 4/(Q R)