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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:
  • A
    $\frac{1}{10}$
  • ✓
    $\frac{1}{11}$
  • C
    $\frac{1}{9}$
  • D
    $\frac{1}{20}$

Answer: B.

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Q 2M.C.Q (1 Marks)1 Mark
If $a, b, c$ are in $A.P.$ and $x, y, z$ are in $G.P.,$ then the value of $x^{b-c} y^{c-a} z^{a-b}$ is:
 
  • A
    $0$
  • ✓
    $1$
  • C
    $x y z$
  • D
    $x^a y^b z^c$

Answer: B.

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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:
  • ✓
    AP
  • B
    GP
  • C
    HP
  • D
    None of these.

Answer: A.

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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:
  • ✓
    $\frac12$
  • B
    $\frac{2}{3}$
  • C
    $\frac13$
  • D
    $\frac{-1}{2}.$

Answer: A.

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Q 5M.C.Q (1 Marks)1 Mark
The nth term of a $G.P$. is $128$ and the sum of its n terms is $225$. If its common ratio is $2$, then its first term is:
  • ✓
    $1$
  • B
    $3$
  • C
    $8$
  • D
    None of these.

Answer: A.

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Q 122 Marks Questions2 Marks
The sum of three numbers which are consecutive terms of an A.P. is $21.$ If the second number is reduced by $1$ and the third is increased by $1,$ we obtain three consecutive terms of a G.P. Find the numbers.
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Q 173 Marks Question3 Marks
If $\frac{\text{a}+\text{bx}}{\text{a}-\text{bx}}=\frac{\text{b}+\text{cx}}{\text{b}-\text{cx}}=\frac{\text{c}+\text{dx}}{\text{c}-\text{dx}}(\text{x}\neq0),$ then show that a, b, c and d are in G.P.
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Q 193 Marks Question3 Marks
If S denotes the sum of an infinite G.P. and $S_1$ denotes the sum of the squares of its terms, then prove that the first terms and common ratio are respectively $\frac{2\text{SS}_1}{\text{S}^2+\text{S}_1}\text{ and }\frac{\text{S}^2-\text{S}_1}{\text{S}^2+\text{S}_1}.$
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