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Class 10

Explore popular questions from Arithmetic Progressions for Class 10. This collection covers Arithmetic Progressions previous year Class 10 questions hand picked by experienced teachers.

Arithmetic Progressions

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Q 1. If arithmetic mean of a and b is {tex} \frac { a ^ { n } + b ^ { n } } { a ^ { n - 1 } + b ^ { n - 1 } } {/tex} then the value of {tex} n {/tex} is

A

-1

B

0

1

D

None

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Q 2. {tex} \left. \frac { S _ { n } } { S _ { m } } = \frac { n ^ { 4 } } { m ^ { 4 } } \text { (where } \mathrm { S } _ { \mathrm { k } } \text { is the sum of first } \mathrm { k } \text { terms of an } \mathrm { AP } \mathrm { a } _ { 1 } \mathrm { a } _ { 2 } \mathrm { a } _ { 3 } \ldots \ldots \infty \right) {/tex} then the value of {tex} \frac { a _ { m + 1 } } { a _ { n + 1 } } {/tex} in terms of {tex} \mathrm { m } {/tex} and {tex} \mathrm { n } {/tex} will be

{tex} \left( \frac { 2 m + 1 } { 2 n + 1 } \right) ^ { 3 } {/tex}

B

{tex} \left( \frac { 2 n + 1 } { 2 m + 1 } \right) ^ { 3 } {/tex}

C

{tex} \left( \frac { 2 m - 1 } { 2 n + 1 } \right) ^ { 3 } {/tex}

D

{tex} \left( \frac { 2 m + 1 } { 2 n - 1 } \right) ^ { 3 } {/tex}

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Q 3. The sum of all 2 digit odd numbers is

2475

B

2530

C

4905

D

5049

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Q 4. If {tex} \frac { 1 } { b + c } , \frac { 1 } { c + a } , \frac { 1 } { a + b } {/tex} are in AP then

A

{tex} a , b , c {/tex} are in {tex} \mathrm{A P} {/tex}

{tex} a ^ { 2 } , b ^ { 2 } , c ^ { 2 } {/tex} are in {tex} \mathrm{A P} {/tex}

C

{tex} \frac { 1 } { a } + \frac { 1 } { b } + \frac { 1 } { a } {/tex} are in {tex} \mathrm { AP } {/tex}

D

None of these

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Q 5. The sum of two numbers is {tex} 2 \frac { 1 } { 6 } . {/tex} If an even number of arithmetic means are inserted between them and their sum exceeds their number by {tex}1{/tex}, then number of means inserted is

12

B

18

C

6

D

None of these

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Q 6. If the first term of a series in AP is {tex} 17 , {/tex} the last term is {tex} - 12 \frac { 3 } { 8 } {/tex} and the sum is {tex} 25 \frac { 7 } { 16 } , {/tex} then find the common difference.

A

{tex} - \frac { 43 } { 18 } {/tex}

B

{tex} - \frac { 45 } { 17 } {/tex}

{tex} - \frac { 47 } { 16 } {/tex}

D

{tex} \frac { 47 } { 16 } {/tex}

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Q 7. If three positive real numbers {tex}a, b, c{/tex} are in AP such that {tex}abc = 4 , {/tex} then the minimum value of {tex} b {/tex} is

A

{tex} 2 ^ { 1 / 3 } {/tex}

{tex} 2 ^ { 2 / 3 } {/tex}

C

{tex} 2 ^ { 1 / 2 } {/tex}

D

{tex} 2 ^ { 3 / 2 } {/tex}

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Q 8. Match the following (one to one)
Column-I and column-II contains four entries each. Entries of column-I are to be matched with some entries of column-II. Only One entries of column-I may have the matching with the some entries of column-II and one entry of column-II Only one matching with entries of column-I

{tex}(\mathrm A) - (\mathrm Q ) {/tex}

B

{tex} ( \mathrm { B } ) - ( \mathrm { P } ) {/tex}

C

{tex} ( \mathrm { C } ) - ( \mathrm { R } ) {/tex}

D

{tex} (\mathrm D ) - (\mathrm S ) {/tex}

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Q 9. If the sum of the first {tex} 2 \mathrm { n } {/tex} terms of the AP {tex} 2,5,8 \ldots \ldots {/tex} is equal to the sum of the first {tex} n {/tex} terms of the AP {tex} 57 , 59,61 , \ldots , {/tex} then {tex} \mathrm { n } {/tex} is equal to

A

10

B

12

11

D

13

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Q 10. Let {tex} T _ { r } {/tex} be the rth term of an AP, for {tex} r = 1,2,3 \ldots \ldots \ldots . {/tex} for some positive integers {tex} m , n . {/tex} We have {tex} T _ { m } = 1 / n {/tex} and {tex} T _ { n } = 1 / m {/tex} then {tex} T _ { m n } {/tex} equals

A

{tex} \frac { 1 } { m n } {/tex}

B

{tex} \frac { 1 } { m } + \frac { 1 } { n } {/tex}

1

D

0

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Q 11. A body falls {tex}16{/tex} metres in the first second of its motion, {tex} 48 \mathrm { m } {/tex} in the second, {tex} 80 \mathrm { m } {/tex} in the third, {tex} 112 \mathrm { m } {/tex} in the fourth and so on. How for does it fall during the {tex} 11 \mathrm { th } {/tex} second of its motion?

A

{tex} 338 \mathrm { m } {/tex}

B

{tex} 340 \mathrm { m } {/tex}

C

{tex} 334 \mathrm { m } {/tex}

{tex} 336 \mathrm { m } {/tex}

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Q 12. If {tex} a , b , c , d , e , f {/tex} are arithmetic mean between {tex}2{/tex} and {tex} 12 , {/tex} then {tex} a + b + c + d + e + f {/tex} is equal to

A

14

42

C

84

D

None of these

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Q 13. {tex} 11 ^ { \text {th } } {/tex} term of the {tex} \mathrm { A } . \mathrm { P., }{/tex}:{tex} - 3 , - \frac { 1 } { 2 } , 2 , \ldots . {/tex} is :

A

{tex}28{/tex}

{tex}22{/tex}

C

{tex} - 38 {/tex}

D

{tex} - 48 \frac { 1 } { 2 } {/tex}

Explanation

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Q 14. In an A.P., if {tex} a = 3.5 , d = 0 , n = 101 , {/tex} then {tex} a _ { n } {/tex} will be

A

{tex}0{/tex}

{tex} 3.5 {/tex}

C

{tex}103.5{/tex}

D

{tex}104.5{/tex}

Explanation

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Q 15. The list of numbers {tex} - 10 , - 6 , - 2,2 , \ldots \ldots {/tex} is :

A

an {tex} \mathrm { A } . \mathrm { P., } {/tex} with {tex} d = - 16 {/tex}

an {tex}\mathrm {A.P}.,{/tex} with {tex} d = 4 {/tex}

C

an {tex}\mathrm {A.P}.,{/tex} with {tex} d = - 4 {/tex}

D

not an an {tex}\mathrm {A.P}.,{/tex}

Explanation

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Q 16. The first four terms of an A.P., whose first term is {tex} - 2 {/tex} and the common difference is {tex} - 2 , {/tex} are :

A

{tex} - 2,0,2,4 {/tex}

B

{tex} - 2,4 , - 8,16 {/tex}

{tex} - 2 , - 4 , - 6 , - 8 {/tex}

D

{tex} - 2 , - 4 , - 8 , - 16 {/tex}

Explanation

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Q 17. If the {tex} 2 ^ { \text {nd } } {/tex} term of an {tex} A . P {/tex}, is {tex}13{/tex} and the {tex}5{/tex} th term is {tex} 25 , {/tex} what is its {tex}7{/tex} th term?

A

30

33

C

37

D

38

Explanation

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Q 18. Which term of the A.P., {tex} : 21,42,63,84 , \dots {/tex} is {tex} 210 ? {/tex}

A

{tex} 9 \mathrm { th } {/tex}

{tex} 10 \mathrm { th } {/tex}

C

{tex} 11 \mathrm { th } {/tex}

D

{tex} 12 \mathrm { th } {/tex}

Explanation

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Q 19. If the common difference of an A.P., is {tex} 5 , {/tex} then what is {tex} a _ { 18 } - a _ { 13 } {/tex} ?

A

5

B

20

25

D

30

Explanation

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Q 20. What is the common difference of an A.P., in which {tex} a _ { 18 } - a _ { 14 } = 32 ? {/tex}

{tex}8{/tex}

B

{tex} - 8 {/tex}

C

{tex} - 4 {/tex}

D

{tex}4{/tex}

Explanation

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Q 21. The famous mathematician associated with finding the sum of the first 100 natural numbers is :

A

Pythagoras

B

Newton

Gauss

D

Euclid

Explanation

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Q 22. The sum of first {tex}16{/tex} terms of the A.P., {tex} : 10,6,2 , \ldots . . {/tex} is :

{tex} - 320 {/tex}

B

{tex}320{/tex}

C

{tex} - 352 {/tex}

D

{tex} - 400 {/tex}

Explanation

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Q 23. The sum of first five multiples of 3 is :

45

B

55

C

65

D

75

Explanation

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Q 24. If the first term of an AP is {tex} 17 , {/tex} the last term is {tex} - 12 \frac { 3 } { 8 } {/tex} and the sum is {tex} 25 \frac { 7 } { 16 } , {/tex} then find the common difference.

A

{tex} - \frac { 43 } { 18 } {/tex}

B

{tex} - \frac { 45 } { 17 } {/tex}

{tex} - \frac { 47 } { 16 } {/tex}

D

{tex} \frac { 47 } { 16 } {/tex}

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Q 25. If {tex} a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots \ldots a _ { n }{/tex} are in AP where {tex} a _ { i } > 0 {/tex} and for all {tex} i {/tex} then the value of {tex} \frac { 1 } { \sqrt { a _ { 1 } } + \sqrt { a _ { 2 } } } + \frac { 1 } { \sqrt { a _ { 2 } } + \sqrt { a _ { 3 } } } + \ldots \ldots + \frac { 1 } { \sqrt { a _ { n - 1 } } + \sqrt { a _ { n } } } {/tex}

A

{tex} \frac { 1 } { \sqrt { a _ { 1 } } + \sqrt { a _ { n } } } {/tex}

B

{tex} \frac { 1 } { \sqrt { a _ { 1 } } - \sqrt { a _ { n } } } {/tex}

C

{tex} \frac { n } { \sqrt { a _ { 1 } } - \sqrt { a _ { n } } } {/tex}

{tex} \frac { n - 1 } { \sqrt { a _ { 1 } } + \sqrt { a _ { n } } } {/tex}