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Arithmetic Progressions MATHS - Arithmetic Progressions

Rajasthan Board (RBSE) - STD 11 Science - MATHS (Rajasthan - English Medium). 214 questions in this chapter.

Question types

Arithmetic Progressions question types

214 questions across 4 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

214
Questions
4
Question groups
5
Question types
Sample Questions

Arithmetic Progressions questions

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

Q 31 Marks Question1 Mark
The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by $\frac{\text{l}^2-\text{a}^2}{\text{k}-(\text{l}+\text{a})},$ then $\text{k}=$
  1. S
  2. 2S
  3. 3S
  4. None of these
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Q 51 Marks Question1 Mark
In the arithmetic progression whose common difference is non-zero, the sum of first 3n terms is equal to the sum of next n terms. Then the ratio of the sum of the first 2n terms to the next 2n terms is:

  1. $\frac{1}{5}$

  2. $\frac{2}{3}$

  3. $\frac{3}{4}$

  4. None of these

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Q 72 Marks Questions2 Marks

The 4th term of an A.P. is three times the first and the 7th term exceeds twice the third term by 1. Find the first term and the common difference.

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Q 102 Marks Questions2 Marks
A sequence is defined by $\text{a}_\text{n}=\text{n}^3-6\text{n}^2-11\text{n}-6,\text{n}\in\text{N.}$ show that the first three terms of the sequence are zero and all other terms are positive.
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Q 123 Marks Question3 Marks
If in $\text{a}\triangle\text{ABC},\tan\text{B}+\tan\text{C}=6,$ then $\cot\text{A}\cot\text{B}\cot\text{C}=$
  1. $6$
  2. $1$
  3. $\frac16$
  4. None of these
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Q 133 Marks Question3 Marks
If $\tan\theta_1\tan\theta_2=\text{k},$ then $\frac{\cos(\theta_1-\theta_2)}{\cos(\theta_1+\theta_2)}=$
  1. $\frac{1+\text{k}}{1-\text{k}}$
  2. $\frac{1-\text{k}}{1+\text{k}}$
  3. $\frac{\text{k}+1}{\text{k}-1}$
  4. $\frac{\text{k}-1}{\text{k}+1}$
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Q 165 Marks Questions5 Marks
In a potato race 20 potatoes are placed in a line at intervals of 4 meters with the first potato 24 metres from the starting point. A contestant is required to bring the potatoes back to the starting place one at a time. How far would he run in bringing back all the potatoes?
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Q 175 Marks Questions5 Marks
A man arranges to pay off a debt of ₹ 3600 by 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one-third of the debt unpaid, find the value of the first instalment.
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Q 185 Marks Questions5 Marks
A man starts repaying a loan as first instalment of ₹ 100 = 00. If he increases the instalments by ₹ 5 every month, what amount he will pay in the 30th instalment?
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Q 195 Marks Questions5 Marks
A man starts repaying a loan as first instalment of ₹ 100 = 00. If he increases the instalments by ₹ 5 every month, what amount he will pay in the 30th instalment?
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Q 205 Marks Questions5 Marks
Show that $\text{x}^2+\text{xy}+\text{y}^2,\ \text{z}^2+\text{zx}+\text{x}^2$ and $\text{y}^2+\text{yz}+\text{z}^2$ are consecutive terms of an A.P., if x, y and z are in A.P.
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