Q65.The sum of the series 12 + 2.22 + 32 + 2.42 + 52 + 2.62 + … . . +2(2m)2 is (1) m(2m + 1)2 (2) m2(m + 2) (3) m2(2m + 1) (4) m(m + 2)2
What This Question Tests
The problem asks for the sum of a mixed series. It requires reorganizing the terms into a sum of squares of all natural numbers up to 2m and then a sum of squares of even numbers, applying the standard summation formula.
Concepts Tested
Formulas Used
Σk² = n(n+1)(2n+1)/6
📚 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?
2.2 — A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its
Physics Class 11 · Chapter 2
2.2 A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.
📋 Question Details
- Chapter
- Sequences & Series
- Topic
- Summation of series
- Year
- 2012
- Shift
- 07 May Online
- Q Number
- Q65
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 9: Sequences and Series
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