# Numbers & Algebra - Numbers and Algebra MCQ

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revise 40. What is the sum to infinity of the series, 3 + 6x2 + 9x4 + 12x6 + ... given lxl < 1?

 A. 3 / (1+x²) B. 3 / (1-x²)² C. 3 / (1+x²)² D. 3 / (1-x²) Answer Report Discuss Option: C Explanation : Let s = 3 + 6x² + 9xâ�´ + 12xâ�¶ +…….. * x²s = 3x² + 6xâ�´ + 9xâ�¶ +12xâ�¶+…….. => s - x²s=3+3x²+3xâ�´+3xâ�¶+…….. => s(1-x)²=3[1+x²+x+xâ�¶+…..…] => s(1-x)²=3[1/(1-x²][.:â”‚xâ”‚<1] .: s = 3 / (1-x²)² Click on Discuss to view users comments. Write your comments here:
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revise 38. What is the ratio of common differences d1 and d2 of two arithmetic progressions if respective nth terms are in the ratio of 2n + 3 : n -11?

 A. 1 : 2 B. 2 : 3 C. 2 : 1 D. 1 : 3 Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. Write your comments here:
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A group of four numbers has only one prime number amongst them. Which of the following must be true about the group?
I. HCF of the four numbers of the group is .either 1 or equal to that prime number.
II. LCM of the four numbers of the group is same as product of the prime number and LCM of the remaining three numbers.
III. Product of four numbers is equal to product of the prime number * HCF of the group * LCM of the group.

 A. I only B. II only C. I and II only D. All of these Answer Report Discuss Option: A Explanation : I. In case all the remaining three numbers are multiples of the prime number, HCF of the group is equal to that prime number. otherwise HCF of the group is 1. Thus, I is true. II. Case 1: Let numbers be 2, 4, 6 and 8, where 2 is only prime number, then LCM = 24. But LCM of 4, 6 and 8 = 24. Case 2 : Let numbers be 2, 9, 81 and 27 Then LCM = 162 and LCM of 9, 81 and 27 = 81. Thus, LCM = 81 * 2 = 162 Hence II is not always true. III. Let numbers be 2, 4, 6 and 8 LCM =24 and HCF = 2 Product of four numbers = 2 *4 * 6 * 8= 384 Also, 384 ≠ 24 * 2 * 2. Thus, III is not true. Click on Discuss to view users comments. Write your comments here: