Q64.Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series 12 + 2 ⋅22 + 32 + 2 ⋅42 + 52 + 2 ⋅62 + … If B −2A = 100λ, then λ is equal to : (1) 496 (2) 232 (3) 248 (4) 464
What This Question Tests
This problem tests the ability to analyze a non-standard series, break it down into summations of terms based on their index parity, and apply standard sum formulas efficiently.
Concepts Tested
Formulas Used
Σk^2 = n(n+1)(2n+1)/6
Σk = n(n+1)/2
📚 NCERT Sections This Tests
12.5 — A Hydrogen Atom Initially In The Ground Level Absorbs A Photon,
Physics Class 12 · Chapter 12
12.5 A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.
12.8 — A 12.5 Ev Electron Beam Is Used To Bombard Gaseous Hydrogen At
Physics Class 12 · Chapter 12
12.8 A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted?
13.5 — The Q Value Of A Nuclear Reaction A + B ® C + D Is Defined By
Physics Class 12 · Chapter 13
13.5 The Q value of a nuclear reaction A + b ® C + d is defined by Q = [ mA + mb – mC – md]c2 where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic. (i) 11 H+13 H →12 H+12 H (ii) 126 C+126 C →1020 Ne+ 24 He Atomic masses are given to be m ( 12 H ) = 2.014102 u m ( 13 H) = 3.016049 u m ( 126 C ) = 12.000000 u m ( 1020 Ne ) = 19.992439 u
📋 Question Details
- Chapter
- Sequences & Series
- Topic
- Sum of series
- Year
- 2018
- Shift
- 08 Apr
- Q Number
- Q64
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 9: Sequences and Series
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