Thenumber of subsets o the set `{1,2,…………….,m}` havig least element r and greatest element `k, 1lerltklem` is (A) `2^(m-1)` (B) `2^(k-r-1)` (C) `2^(k-1)` (D) none of these

Let 1 le m lt n le p . The number of subsets o the set A={1,2,3, . . .P} having m, n as the least and the greatest elements respectively, is

Find sum of sum_(r=1)^n r . C (2n,r) (a) n*2^(2n-1) (b) 2^(2n-1) (c) 2^(n-1)+1 (d) None of these

sum_(k=1)^m(k^2+1)k=2009xx2010!, then m= (A) 2009 (B) 2010 (C) 2011 (D) none of these

Number of non-empty subsets {1,2,3,4,5,6,7,8} having exactly k elements and do not contain the element k for some k = 1,2"….."8 is

If int_0^1 xe^(x^2) dx=k int_0^1 e^(x^2) dx , then (A) kgt1 (B) 0ltklt1 (C) k=1 (D) none of these

If k in R_o then det{adj(k I_n)} is equal to (A) K^(n-1) (B) K^((n-1)n) (C) K^n (D) k

A is a set containing n elements. A subset P_1 is chosen and A is reconstructed by replacing the elements of P_1 . The same process is repeated for subsets P_1,P_2,....,P_m with m>1 . The number of ways of choosing P_1,P_2,....,P_m so that P_1 cup P_2 cup....cup P_m=A is (a) (2^m-1)^(mn) (b) (2^n-1)^m (c) (m+n)C_m (d) none of these

If tan 69^(@) + tan 66^(@) - tan 69^(@)tan 66^(@) = 2k then k = (a) -(1)/(2) (b) (1)/(2) (c) -1 (d)None of these

Consider the following statements : 1. Nuu(BnnZ)=(NuuB)nnZ for any subset B of R , where N is the set of positive integers, Z is the set of integers, R is the set of real numbers. 2. Let A={n in N : 1 ge n ge 24, n "is a multiple of" 3} . There exists no subsets B of N such that the number of elements in A is equal to the number of elements in B . Which of the above statemetns is/are correct ? (A) 1 only (B) 2 only (C) Both 1 and 2 (D) Neither 1 nor 2

Lt_(nrarroo) sum_(r=1)^n (2r)^k/n^(k+1),k!=-1 , is equal to (A) 2^k/(k-1) (B) 2^k/k (C) 1/(k+1) (D) 2^k/(k+1)