JEE Main Algebra — Combinatorics & Series – Topic Test

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Difficulty: 15 medium · 15 hard

Algebra — Combinatorics & Series MCQ questions with answers

The first 3 of 30 questions. Unlock the series for the rest, each with a solution.

1. Q1. The value of Σ (from r = 1 to 10) of (2r − 1) is:

   Σ (r = 1 से 10 तक) (2r − 1) का मान है:

   • A. 100
   • B. 110
   • C. 121
   • D. 90
   Solution

   This is the sum of the first 10 odd numbers, which equals 10² = 100.

   यह प्रथम 10 विषम संख्याओं का योग है, जो 10² = 100 के बराबर है।

2. Q2. The arithmetic mean and geometric mean of two positive numbers are 10 and 8 respectively. The harmonic mean of the same two numbers is:

   दो धनात्मक संख्याओं का समांतर माध्य और गुणोत्तर माध्य क्रमशः 10 और 8 हैं। इन्हीं दो संख्याओं का हरात्मक माध्य है:

   • A. 32/5
   • B. 25/4
   • C. 16/3
   • D. 40/7
   Solution

   For two positive numbers, GM² = AM × HM, so HM = GM²/AM = 64/10 = 32/5.

   दो धनात्मक संख्याओं के लिए, GM² = AM × HM, अतः HM = GM²/AM = 64/10 = 32/5।

3. Q3. Eight delegates are to be seated around a circular table. The number of seating arrangements in which two particular delegates never sit next to each other is:

   आठ प्रतिनिधियों को एक वृत्ताकार मेज़ के चारों ओर बिठाना है। ऐसे बैठने के विन्यासों की संख्या, जिनमें दो विशेष प्रतिनिधि कभी भी एक-दूसरे के बगल में नहीं बैठते, है:

   • A. 4320
   • B. 1440
   • C. 3600
   • D. 5040
   Solution

   Total circular arrangements are (8−1)! = 5040, and arrangements with the two particular delegates together are 2! × 6! = 1440 (treating them as one unit). Hence the required number is 5040 − 1440 = 3600.

   कुल वृत्तीय विन्यास (8−1)! = 5040 हैं, और दोनों विशेष प्रतिनिधियों के एक साथ बैठने वाले विन्यास 2! × 6! = 1440 हैं (उन्हें एक इकाई मानकर)। अतः अभीष्ट संख्या 5040 − 1440 = 3600 है।

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