Arithmetic Progressions - Uttarakhand Board (UBSE) STD 11 Science Maths Questions

Q 11 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 $\text{k}=$

A
$S$
✓
$2S$
C
$3S$
D
None of these

Answer: B.

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Q 21 Marks Question1 Mark

If the sum of $p$ terms of an $A.P.$ is $q$ and the sum of $q$ terms is $p$, then the sum of $p + q$ terms will be:

A
$0$
B
$p - q$
C
$p + q$
✓
$-(p + q)$

Answer: D.

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Q 31 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:

✓
$\frac{1}{5}$
B
$\frac{2}{3}$
C
$\frac{3}{4}$
D
None of these

Answer: A.

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Q 41 Marks Question1 Mark

Write the sum of first n even natural numbers.

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Q 51 Marks Question1 Mark

If $n$ arithmetic means are inserted between $1$ and $31$ such that the ratio of the first mean and $n^{th}$ mean is $3 : 29,$ then the value of $n$ is:

A
$10$
B
$12$
C
$13$
✓
$14$

Answer: D.

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Q 62 Marks Questions2 Marks

Show thet the followiong sequences is an A.P. Also, find the common difference and write 3 more terms in each case.
$9,\ 7,\ 5,\ 3,\ ...$

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Q 72 Marks Questions2 Marks

Find the sum of the following series:
$101 + 99 + 97 + ... + 47$

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Q 82 Marks Questions2 Marks

Show thet the followiong sequences is an A.P. Also, find the common difference and write 3 more terms in each case.
$-1,\frac{1}{4},\frac{3}{2},\frac{11}{4},...$

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Q 92 Marks Questions2 Marks

Find the second term and nth term of an A.P. whose 6th term is 12 and the 8th term is 22.

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Q 102 Marks Questions2 Marks

If the nth term of the A.P. $9, 7, 5, ...$ is same as the $n^{th}$ term of the A.P. $15, 12, 9, ..$ find $n.$

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Q 113 Marks Question3 Marks

If in $\text{a}\triangle\text{ABC},\tan\text{B}+\tan\text{C}=6,$ then $\cot\text{A}\cot\text{B}\cot\text{C}=$

A
$6$
B
$1$
✓
$\frac16$
D
None of these

Answer: C.

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Q 123 Marks Question3 Marks

If $\tan\theta_1\tan\theta_2=\text{k},$ then $\frac{\cos(\theta_1-\theta_2)}{\cos(\theta_1+\theta_2)}=$

✓
$\frac{1+\text{k}}{1-\text{k}}$
B
$\frac{1-\text{k}}{1+\text{k}}$
C
$\frac{\text{k}+1}{\text{k}-1}$
D
$\frac{\text{k}-1}{\text{k}+1}$

Answer: A.

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Q 133 Marks Question3 Marks

If $\text{A}-\text{B}=\frac\pi4,$ then $(1+\tan\text{A})(1-\tan\text{B})$ is equal to:

✓
$2$
B
$1$
C
$0$
D
$3$

Answer: A.

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Q 143 Marks Question3 Marks

The value of $\cos^2\Big(\frac{\pi}{6}+\text{x}\Big)-\sin^2\Big(\frac\pi6-\text{x}\Big)$ is:

✓
$\frac{1}{2}\cos2\text{x}$
B
$0$
C
$-\frac{1}{2}\cos2\text{x}$
D
$\frac12$

Answer: A.

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Q 153 Marks Question3 Marks

If $\tan69^\circ+\tan66^\circ-\tan69^\circ\tan66^\circ=2\text{k},$ then $k =$

A
$-1$
B
$\frac12$
✓
$\frac{-1}{2}$
D
none of these

Answer: C.

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Q 165 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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Q 175 Marks Questions5 Marks

A farmer buys a used tractor for ₹ 12000. He pays ₹ 6000 cash and agrees to pay the balance in annual instalments of ₹ 500 plus 12% interest on the unpaid amount. How much the tractor cost him?

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Q 185 Marks Questions5 Marks

If a, b, c are in A.P., prove that:
$\text{a}^2+\text{c}^2+4\text{ac}=2(\text{ab}+\text{bc}+\text{ca})$

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Q 195 Marks Questions5 Marks

The income of a person is ₹ 300,000 in the first year and he receives an increase of ₹ 10000 to his income per year for the next 19 years. Find the total amount, he received in 20 years.

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Q 205 Marks Questions5 Marks

Shamshad Ali buys a scooter for ₹ 22000. He pays ₹ 4000 cash and agrees to pay the balance in annual instalments of ₹ 1000 plus 10% interest on the unpaid amount. How much the scooter will cost him.

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Arithmetic Progressions question types

Arithmetic Progressions questions

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Arithmetic Progressions Maths - Arithmetic Progressions

Arithmetic Progressions question types

Arithmetic Progressions questions

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