Q64.Let A1 and A2 be two arithmetic means and G1, G2 and G3 be three geometric means of two distinct positive numbers. Then G41 + G42 + G43 + G21G23 is equal to (1) (A1 + A2)2G1G3 (2) 2(A1 + A2)G1G3 (3) (A1 + A2)G21G23 (4) 2(A1 + A2)G21G23
What This Question Tests
This question tests the understanding of inserting arithmetic and geometric means between two numbers and applying their properties to simplify the given expression. It requires basic algebraic manipulation of these definitions.
Concepts Tested
Formulas Used
If a, A1, A2, b are in AP, then A1 + A2 = a + b
If a, G1, G2, G3, b are in GP, then G1G3 = ab and G2 = sqrt(ab)
📚 NCERT Sections This Tests
5.11 — Draw All The Isomers (Geometrical And Optical) Of:
Chemistry Class 11 · Chapter 5
5.11 Draw all the isomers (geometrical and optical) of: (i) [CoCl2(en)2] + (ii) [Co(NH3)Cl(en)2] 2+ (iii) [Co(NH3)2Cl2(en)]+
9.19 — A Screen Is Placed 90Cm From An Object. The Image Of The Object On
Physics Class 12 · Chapter 9
9.19 A screen is placed 90cm from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by 20cm. Determine the focal length of the lens.
5.12 — Write All The Geometrical Isomers Of [Pt(Nh3)(Br)(Cl)(Py)] And How Many Of
Chemistry Class 11 · Chapter 5
5.12 Write all the geometrical isomers of [Pt(NH3)(Br)(Cl)(py)] and how many of these will exhibit optical isomers?
📋 Question Details
- Chapter
- Sequences & Series
- Topic
- Arithmetic Mean (AM) and Geometric Mean (GM)
- Year
- 2023
- Shift
- 15 Apr Shift 1
- Q Number
- Q64
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 9: Sequences & Series
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