Q72.If m arithmetic means (A.Ms) and three geometric means (G.Ms) are inserted between 3 and 243 such that 4th A.M. is equal to 2nd G.M., then m is equal to:
What This Question Tests
This question tests the understanding of arithmetic and geometric means inserted between two numbers and the ability to find the common difference/ratio and specific terms, then equate them to solve for an unknown.
Concepts Tested
Formulas Used
An = a + n*d
Gn = a*r^(n-1)
d = (b-a)/(m+1)
r = (b/a)^(1/(n+1))
📚 NCERT Sections This Tests
12.7 — The Radius Of The Innermost Electron Orbit Of A Hydrogen Atom Is
Physics Class 12 · Chapter 12
12.7 The radius of the innermost electron orbit of a hydrogen atom is 5.3×10–11 m. What are the radii of the n = 2 and n =3 orbits?
13.4 — Obtain Approximately The Ratio Of The Nuclear Radii Of The Gold Isotope
Physics Class 12 · Chapter 13
13.4 Obtain approximately the ratio of the nuclear radii of the gold isotope 197 79 Au and the silver isotope 10747 Ag .
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.
📋 Question Details
- Chapter
- Sequences & Series
- Topic
- Arithmetic and Geometric Means
- Year
- 2020
- Shift
- 03 Sep Shift 2
- Q Number
- Q72
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 9: Sequences and Series
More from this Chapter
Q86.In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equals (1) 1 2 (1 −√5) (2) 21 √5 (3) √5 (4) 12 (√5 −1)
Q88.The sum of the series 2! 1 −13! + 4!1 −… upto infinity is (1) e−2 (2) e−1 (3) e−1/2 (4) e1/2
Q71.Statement - 1: For every natural number n ≥2, 1 + 1 + … + 1 > √n. Statement −2 : For every √1 √2 √n natural number n ≥2, √n(n + 1) < n + 1. (1) Statement −1 is false, Statement −2 is true (2) Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1 (3) Statement −1 is true, Statement −2 is true; (4) Statement −1 is true, Statement −2 is false. Statement −2 is not a correct explanation for Statement −1.
Q76.The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is (1) −4 (2) −12 (3) 12 (4) 4