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

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

If A_1,A_2,A_3,........A_1006 be independent events such that P(A)=1/(2i)(i=1,2,3,.....1006) and probability that none of the events occur be (alpha!)/(2^alpha(beta!)^2). then

If A_1,A_2,A_3,........A_1006 be independent events such that P(A)=1/(2i)(i=1,2,3,.....1006) and probability that none of the events occur be (alpha!)/(2^alpha(beta!)^2). then

If A_1, A_2, …, A_n are n independent events, such that P(A_i)=(1)/(i+1), i=1, 2,…, n , then the probability that none of A_1, A_2, …, A_n occur, is

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_2 , must come after A_2 (ii) neither A_2 nor A_3 seated brfore A_1

Let A be the set of 4-digit numbers a_1 a_2 a_3 a_4 where a_1 > a_2 > a_3 > a_4 , then n(A) is equal to

Let A be the set of 4-digit numbers a_1 a_2 a_3 a_4 where a_1 > a_2 > a_3 > a_4 , then n(A) is equal to

For any three sets A_1,A_2, A_3 , let B_1=A_1, B_2 = A_2-A_1 and B_3 = A_3-(A_1uuA_2) , then which one of the following statement is always true

If a_1,a_2,a_3,... are in A.P. and a_i>0 for each i, then sum_(i=1)^n n/(a_(i+1)^(2/3)+a_(i+1)^(1/3)a_i^(1/3)+a_i^(2/3)) is equal to (a) (n)/(a_(n)^(2//3)+a_(n)^(1//3)+a_(1)^(2//3)) (b) (n(n+1))/(a_(n)^(2//3)+a_(n)^(1//3)+a_(1)^(2//3)) (c) (n(n-1))/(a_(n)^(2//3)+a_(n)^(1//3)*a_(1)^(1//3)+a_(1)^(2//3)) (d) None of these

Let a_1,a_2,a_3,...... be an A.P. such that [a_1+a_2+......+a_p]/[a_1+a_2+a_3+......+a_q]=p^3/q^3 ; p!=q .Then a_6/a_[21] is equal to: