Solutions for Sequence Series. Advanced Level

SEQUENCE & SERIES SECTION-1: STRAIGHT OBJECTIVE TYPE 17.1 a, b, c are positive integers forming an increasing G.P. whose common ratio is a natural number, b- a is cube of a natural number and log, a + log, b + log, c = 6, then a+b+c= (A) 100 (D) 189 (B) 111 (C) 122 17.2 If S, P and R are the sum, product and sum of the reciprocals of n terms of an increasing G.P. and SR". P, then k is equal to (A) 1 (B) 2 (C) 3 17.3 Sum of first hundred numbers common to the two A.P.'s 12, 15, 18, and 17, 21, 25. is (A) 56100 (B) 65100 (C) 61500 (D) none of these (D) none of these 17.4 If 11 A.M.s are inserted between 28 and 10, then number of integral A.M's is (A) 5 (B) 6 (C) 7 (D) 8 1 1 17.5 If a, b, c are in HP, then is equal to b-a b-c 2 (B) (A) (C) B+C (D) none of these 17.6 100 r=1 Let a, be the n term of an A.P. If a = a and 2 a, then the common difference of the r=1 A.P. is is: 17.7 If a, b, c, d are in G.P., then (a² + b²+c²) (b²+c² + d²) equals to: 17.8 If aaaaa, are in H.P.. then a, a, a, a, a, a, a, a, is equal to: 100 (A) a-B (B) Ba α-β (C) 2 (D) none of these (A) ab+bc+cd (C) (ab+bc+cd) (B) (ab+bc+cd) (D) none of these (A) 2a, a (B) 3a,a, (C) 4 a, a, (D)-4 35 is where x < 1, then 'x' equals to: 17.9 If the sum to infinity of the series, 1+4x+7x²+10x³ + (B) 1/5 (A) 19/7 (C) 1/4 (D) none of these 17.10 If a, b, c and d are four positive real numbers such that abcd 1, the minimum value of (1+a) (1+b) (1+c) (1+d) is: (A) 4 (B) 1 (C) 16 (D) 18 SEQUENCE & SERIES SECTION-1: STRAIGHT OBJECTIVE TYPE 17.1 a, b, c are positive integers forming an increasing G.P. whose common ratio is a natural number, b- a is cube of a natural number and log, a + log, b + log, c = 6, then a+b+c= (A) 100 (D) 189 (B) 111 (C) 122 17.2 If S, P and R are the sum, product and sum of the reciprocals of n terms of an increasing G.P. and SR". P, then k is equal to (A) 1 (B) 2 (C) 3 17.3 Sum of first hundred numbers common to the two A.P.'s 12, 15, 18, and 17, 21, 25. is (A) 56100 (B) 65100 (C) 61500 (D) none of these (D) none of these 17.4 If 11 A.M.s are inserted between 28 and 10, then number of integral A.M's is (A) 5 (B) 6 (C) 7 (D) 8 1 1 17.5 If a, b, c are in HP, then is equal to b-a b-c 2 (B) (A) (C) B+C (D) none of these 17.6 100 r=1 Let a, be the n term of an A.P. If a = a and 2 a, then the common difference of the r=1 A.P. is is: 17.7 If a, b, c, d are in G.P., then (a² + b²+c²) (b²+c² + d²) equals to: 17.8 If aaaaa, are in H.P.. then a, a, a, a, a, a, a, a, is equal to: 100 (A) a-B (B) Ba α-β (C) 2 (D) none of these (A) ab+bc+cd (C) (ab+bc+cd) (B) (ab+bc+cd) (D) none of these (A) 2a, a (B) 3a,a, (C) 4 a, a, (D)-4 35 is where x < 1, then 'x' equals to: 17.9 If the sum to infinity of the series, 1+4x+7x²+10x³ + (B) 1/5 (A) 19/7 (C) 1/4 (D) none of these 17.10 If a, b, c and d are four positive real numbers such that abcd 1, the minimum value of (1+a) (1+b) (1+c) (1+d) is: (A) 4 (B) 1 (C) 16 (D) 18 17.16 For the series S = 1+ ( 1 1 1+3) (1+2)+(1+3+5) 1 (1+2+3)+(1+3+5+7) (A) 7 term is 16 (B) 7th term is 18 (1+2+3+4+.... (C) sum of first ten terms is 505 4 (D) sum of first ten term is 405 17.17 If r(+1) = (n+a)(n+b)(n+c) 3 where a < b < c. then (A) 2b = c (B) a8b²+c² = Babc (C) c is prime number (D) (a + b) = 0 17.18 In a GP. the ratio of the sum of the first eleven terms to the sum of the last eleven terms is 1 and the ratio of the sum of all the terms without the first nine to the sum of all the terms without the last nine is 2. Then the number of terms of the G.P is less than.. (A) 15 (B) 43 (C) 38 (D) 56 17.19 Let a = (111.....1) n times then (A) a is not prime (B) a, is not prime (C) a is not prime (D) a,, is not prime SECTION - III: ASSERTION AND REASON TYPE 17.20 STATEMENT-1: If a, b, c are non zero real numbers such that 3(a²+b²+c²+1)=2(a+b+c+ab+bc+ca), then a, b, c are in A.P. as well as in G.P. STATEMENT-2: A series is in A.P. as well as in GP. if all the terms in the series are equal and non zero. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True 17.21 STATEMENT-1: Equations x²-4x+1=0 and x-ax+b = 0, where a, b are rational numbers, have atleast one common root, then a = 4 and b = 1 STATEMENT-2: If two equations ax + bx + c = 0 and ax + bx + c = 0, where a, b, c, a, b, c, are non-zero rational numbers, have common irrational root, then (A) Statement-1 is True, Statement-2 is True: Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True 17.22 STATEMENT-1: Let a, b, c be positive integers, then aabi babic.caibic (a+b+c) STATEMENT-2: Let a,, a a, be positive numbers in A.P. If A & G are the arithmetic and the geometric means of a, and a respectively then, Gaaa Show description