if `A_1,A_2,A_3,....A_100 `are set of `A_1 sub A_2 sub A_3 sub A_4.....sub A_100` `n(A_i)=i+2` , `nn_(i=3)^100A_i` =

If A_1,A_2, A_3,.. are sets such that n(A_i)=101-i , A_1 sup A_2 sup A_3 sup ...supA_100 and A=nn_(i=5)^100 A_i then n(A) is equal to

Find the number of ways of arranging 15 students A_1,A_2,........A_15 in a row such that (i) A_2 , must be seated after A_1 and A_3 , must come after A_2 (ii) neither A_2 nor A_3 seated brfore A_1

If A, A_1,A_2,A_3 are the areas of the inscribed and escribed circles of a DeltaABC, then

Let a_1 , a_2 , a_3,.... be terms of an A.P. if (a_1 + a_2 +....+ a_p)/(a_1 + a_2 +...+ a_q) = p^2/q^2. p ne q then a_6/a_21 equals

If A_1 , A_2 , A_3 are mutually exclusive and exhaustive, then P(A_1) + P(A_2) + P(A_3) equal______

Let vec r_1, vec r_2, vec r_3, .....vec r_n be the position vectors of points P_1,P_2, P_3 ,......P_n relative to the origin O . If the vector equation a_1 vec r_1+a_2 vec r_2+.....a_n vec r_n=0 hold, then a similar equation will also hold w.r.t. to any other origin provided a) a_1+a_2+......a_n=n b) a_1+a_2+....a_n=1 c) a_1+a_2+....a_n=0 d) a_1=a_2=a_3+a_n=0

If a_1. a_2 ....... a_n are positive and (n - 1) s = a_1 + a_2 +.....+a_n then prove that (a_1 + a_2 +....+a_n)^n ge (n^2 - n)^n (s - a_1) (s - a_2)........(s - a_n)

Statement 1: if A={2,4,6,},B{1,5,3}w h e r eAa n dB are the events of numbers occurring on a dice, then P(A)+P(B)=1. Statement 2: A_1, A_2, A_3,...... , A_n are all mutually exclusive events, then P(A_1)+P(A_2)+.......+P(A_n)=1.

Suppose A_1 , A_2 ..... A_30 are thirty sets each with five elements and B_1,B_2....B_n are n sets each with three elements such that cap_(i=1)^30 A_i = cap_(j=1)^n B_j = S . If each elements of S belongs to exactly ten of the A_i s and exactly nine of the B_j's then the value of n is

If the sequence a_1, a_2, a_3,....... a_n ,dot forms an A.P., then prove that a_1^2-a_2^2+a_3^2-a_4^2+.......+ a_(2n-1)^2 - a_(2n)^2=n/(2n-1)(a_1^2-a_(2n)^2)