Q65.If gcd(m, n) = 1 and 12 −22 + 32 −42+. . . . +(2021)2 −(2022)2 + (2023)2 = 1012m2n then m2 −n2 is equal to (1) 240 (2) 200 (3) 220 (4) 180
What This Question Tests
This question tests the ability to simplify a series involving squares using the difference of squares formula and then sum the resulting arithmetic series.
Concepts Tested
Formulas Used
a² - b² = (a-b)(a+b)
Σn = n(n+1)/2
📚 NCERT Sections This Tests
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.
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.
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
- 2023
- Shift
- 06 Apr Shift 2
- Q Number
- Q65
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 9: Sequences and Series
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