Q73.Let the positive numbers a1, a2, a3, a4 and a5 be in a G.P. Let their mean and variance be 1031 and mn respectively, where m and n are co-prime. If the mean of their reciprocals is 31 and a3 + a4 + a5 = 14, then 10 m + n is equal to ____________.
What This Question Tests
This question is a multi-concept problem combining properties of Geometric Progressions, arithmetic mean, and variance, requiring careful algebraic manipulation and equation solving.
Concepts Tested
Formulas Used
Mean = ฮฃai/N
Variance = (ฮฃai^2/N) - (Mean)^2
Terms of G.P. a, ar, ar^2, ...
Sum of G.P. = a(r^n-1)/(r-1)
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๐ Question Details
- Chapter
- Sequences & Series
- Topic
- Geometric Progression
- Year
- 2023
- Shift
- 12 Apr Shift 1
- Q Number
- Q73
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 9: Sequences & Series; Class 11 Mathematics Ch 15: Statistics
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