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RD Sharma - Mathematics

20. Geometric Progressions

1. Sets
2. Relations
3. Functions
4. Measurement of Angles
5. Trigonometric Functions
6. Graphs of Trigonometric Functions
7. Values of Trigonometric Functions at Sum of Difference of Angles
8. Transformation Formulae
9. Values of Trigonometric Functions at Multiples and Submultiple of an Angles
10. Sine and Cosine Formulae and their Applications
11. Trigonometric Equations
12. Mathematical Induction
13. Complex Numbers
14. Quadratic Equations
15. Linear Inequations
16. Permutations
17. Combinations
18. Binomial Theorem
19. Arithmetic Progressions
20. Geometric Progressions
21. Some Special Series
22. Brief Review of Cartesian System of Rectangular Co-ordinates
23. The Straight Lines
24. The Circle
25. Parabola
26. Ellipse
27. Hyperbola
28. Introduction to 3-D Coordinate Geometry
29. Limits
30. Derivatives
31. Mathematical Reasoning
32. Statistics
33. Probability

Exercise 20.1

1 2 3 A 3 B 3 C 3 D 3 E 3 F 4 5 6 A 6 B 6 C 6 D 7 8 9 10 11 12 13 14 15 16 17

Exercise 20.2

1 2 3 4 5 6 7 8 9

Exercise 20.3

1 A 1 B 1 C 1 D 1 E 2 A 2 B 2 C 2 D 2 E 2 F 2 G 2 H 2 I 3 A 3 B 3 C 4 A 4 B 4 C 4 D 4 E 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Exercise 20.4

1 A 1 B 1 C 1 D 1 E 2 3 4 5 6 7 8 A 8 B 8 C 8 D 9 10 11 12 13

Exercise 20.5

1 2 3 4 5 6 7 8 A 8 B 8 C 8 D 8 E 9 A 9 B 9 C 10 A 10 B 10 C 11 A 11 B 11 C 11 D 12 13 14 15 16 17 18 19 20 21 22 23

Exercise 20.6

1 2 3 4 5 6 7 8 9 10 11 12 13

Very Short Answer

1 2 3 4 5 6 7 8 9 10

MCQ

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Q. 23.7( 3 Votes )

Mark the correct A. − 2/5

B. − 3/5

C. 2/5

D. none of these

Class 11th RD Sharma - Mathematics 20. Geometric Progressions

Answer :

Given GP has first term unity

∴ a₁ = 1.

Hence the GP will become

⇒ 1,r,r²,…

As given 4a₂+5a₃ is least

∴ 4r + 5r² is least

We can say f(r) = 4r + 5r²

Now the given function will be least if df(r)/dr =0

∴

⇒ 8+10r=0

⇒ 8=-10r

⇒

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