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Geometric Progressions MATHS - Geometric Progressions

Rajasthan Board (RBSE) - STD 11 Science - MATHS (Rajasthan - English Medium). 181 questions in this chapter.

Question types

Geometric Progressions question types

181 questions across 5 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

181
Questions
5
Question groups
5
Question types
Sample Questions

Geometric Progressions questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
If in an infinite G.P., first term is equal to 10 times the sum of all successive terms, the its common ratio is:
  1. $\frac{1}{10}$
  2. $\frac{1}{11}$
  3. $\frac{1}{9}$
  4. $\frac{1}{20}$
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Q 3M.C.Q (1 Marks)1 Mark
If a, b, c are in G.P. and $\text{a}^{\frac{1}{\text{x}}}=\text{b}^{\frac{1}{\text{y}}}=\text{c}^{\frac{1}{\text{z}}},$ then xyz are in:
  1. AP
  2. GP
  3. HP
  4. None of these.
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Q 4M.C.Q (1 Marks)1 Mark
The sum of an infinite G.P. is 4 and the sum of the cubes of its terms is 92. The common ratio of original G.P. is:
  1. $\frac12$
  2. $\frac{2}{3}$
  3. $\frac13$
  4. $\frac{-1}{2}.$
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Q 173 Marks Question3 Marks
If Sp denotes the sum of the series $1+\text{r}^{\text{p}}+\text{r}^{2\text{r}}+\ \dots\text{ to }\infty$ and Sp the sum of the series $1-\text{r}^{\text{p}}+\text{r}^{\text{2p}}-\ \dots\text{ to }\infty,$ prove that $\text{S}_\text{p} + \text{S}_\text{p} = 2 \text{S}_{2\text{p}}.$
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Q 183 Marks Question3 Marks
If a, b, c are in G.P., prove that:
$\frac{(\text{a}+\text{b}+\text{c})^2}{\text{a}^2+\text{b}^2+\text{c}^2}=\frac{\text{a}+\text{b}+\text{c}}{\text{a}-\text{b}+\text{c}}$
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Q 215 Marks Questions5 Marks
One side of equilateral triangle is 18 cm. The mid-points of its sides are joined to from another triangle whose mind-points, in turn, are joined to from still another triangle. the process is continued indefinitely. Find the sum of the (i) Perimeters of all the triangles. (ii) Areas of all triangles.
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Q 235 Marks Questions5 Marks
If one A.M., A and two geometric means G1 and G2 inserted between any two positive number, show that $\frac{\text{G}^2_1}{\text{G}_2}+\frac{\text{G}^2_2}{\text{G}_1}=2\text{A}.$
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