For a R (the set of all real numbers), a # 1, lim Then a = (A) 5 (C) (1 + 2 +...+n) (n+1) [(na+1)+(na+2)+...+(na+n)] 60 -15 2 (B) 7 (D) -17 2 Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length 27 on y-axis is (are) (A) x + y - 6x + 8y + 9 = 0 (C) x + y - 6x-8y+9=0 (B) x + y - 6x + 7y+9=0 (D) x + y - 6x - 7y+9=0 Two lines L : x = 5, (A) 1 (C) 3 y 3- -2 and L : x = a, y -1 2-a (B) 2 (D) 4 are coplanar. Then a can take value(s) 1 In a triangle PQR, P is the largest angle and cos P = Further the incircle of the triangle touches the sides 3 PQ, QR and RP at N, L and M respectively, such that the lengths of PN, QL and RM are consecutive even integers. Then possible length(s) of the side(s) of the triangle is (are) (A) 16 (C) 24 (B) 18 (D) 22 Let w = (A) 1/2 (C) BIN M 3+i 2 2 and P = {w n = 1, 2, 3, {z C:Rez 1 } E 2 and H If 3* = 4*-1, then x = (A) 2log3 2 2log32-1 1 1-log4 3 (C) (B) (D) 2 2-log 3 2 log2 3 2log2 3-1