On account of the disruption in education due to the corona pandemic, we're opening up our platform for teachers, free of cost. Know More →

JEE Main

Explore popular questions from Sequence and Series for JEE Main. This collection covers Sequence and Series previous year JEE Main questions hand picked by experienced teachers.

Select Subject

Physics

Chemistry

Mathematics

Sequence and Series

Correct Marks 4

Incorrectly Marks -1

Q 1. If {tex} ( 10 ) ^ { 9 } + 2 ( 11 ) ^ { 1 } ( 10 ) ^ { 8 } + 3 ( 11 ) ^ { 2 } ( 10 ) ^ { 7 } + \cdots + 10 ( 11 ) ^ { 9 } = k ( 10 ) ^ { 9 } , {/tex} then {tex} k {/tex} is equal to

100

B

110

C

{tex} \frac { 121 } { 10 } {/tex}

D

{tex} \frac { 441 } { 100 } {/tex}

Explanation




Correct Marks 4

Incorrectly Marks -1

Q 2. If the {tex} 2 ^ { \text { nd } } , 5 ^ { \text { th } } {/tex} and {tex} 9 ^ { \text { th } } {/tex} terms of a non-constant AP are in GP, then the common ratio of this GP is

A

{tex} \frac { 7 } { 4 } {/tex}

B

{tex} \frac { 8 } { 5 } {/tex}

{tex} \frac { 4 } { 3 } {/tex}

D

{tex} 1 {/tex}

Explanation




Correct Marks 4

Incorrectly Marks -1

Q 3. Let {tex} a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots , a _ { n } {/tex} be in AP. If {tex} a _ { 3 } + a _ { 7 } + a _ { 11 } + a _ { 15 } = 72 , {/tex} then the sum of its first {tex}17{/tex} terms is equal to

306

B

204

C

153

D

612

Explanation



Correct Marks 4

Incorrectly Marks -1

Q 4. If {tex} \tan n \theta = \tan m \theta , {/tex} then the different values of {tex} \theta {/tex} will be in

{tex} A P {/tex}

B

{tex} G P {/tex}

C

{tex} \mathrm { HP } {/tex}

D

None of these

Explanation



Correct Marks 4

Incorrectly Marks -1

Q 5. If the sum of {tex} n {/tex} terms of an AP is {tex} n A + n ^ { 2 } B , {/tex} where {tex} A , B {/tex} are constants, then its common difference will be

A

{tex} A - B {/tex}

B

{tex} A + B {/tex}

C

{tex}2 A {/tex}

{tex}2 B {/tex}

Explanation



Correct Marks 4

Incorrectly Marks -1

Q 6. The {tex} 9 ^ { \text { th } } {/tex} term of the series {tex} 27 + 9 + 5 \frac { 2 } { 5 } + 3 \frac { 6 } { 7 } + \cdots {/tex} will be

1{tex} \frac { 10 } { 17 } {/tex}

B

{tex} \frac { 10 } { 17 } {/tex}

C

{tex} \frac { 16 } { 27 } {/tex}

D

{tex} \frac { 17 } { 27 } {/tex}

Explanation



Correct Marks 4

Incorrectly Marks -1

Q 7. If {tex} \log _ { 3 } 2 , \log _ { 3 } \left( 2 ^ { x } - 5 \right) {/tex} and {tex} \log _ { 3 } \left( 2 ^ { x } - \frac { 7 } { 2 } \right) {/tex} are in AP, then {tex} x {/tex} is equal to

A

{tex} 1 , \frac { 1 } { 2 } {/tex}

B

{tex} 1 , \frac { 1 } { 3 } {/tex}

C

{tex} 1 , \frac { 3 } { 2 } {/tex}

None of these

Explanation


Correct Marks 4

Incorrectly Marks -1

Q 8. Let {tex} T _ { r } {/tex} be the {tex} r ^ { \text { th } } {/tex} term of an AP for {tex} r = 1,2,3 , \cdots . {/tex} If for some positive integers {tex} m , n , {/tex} we have {tex} T _ { m } = \frac { 1 } { n } {/tex} and {tex} T _ { n } = \frac { 1 } { m } , {/tex} then {tex} T _ { m n } {/tex} equals

A

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

B

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

1

D

0

Explanation


Correct Marks 4

Incorrectly Marks -1

Q 9. If the ratio of the sum of {tex} n {/tex} terms of two APs is {tex} ( 7 n + 1 ) : ( 4 n + 27 ) {/tex} , then the ratio of their {tex} 11 ^ { \text { th } } {/tex} terms will be

A

{tex} 2 : 3 {/tex}

B

{tex} 3 : 4 {/tex}

{tex} 4 : 3 {/tex}

D

{tex} 5 : 6 {/tex}

Explanation




Correct Marks 4

Incorrectly Marks -1

Q 10. The sum of the series {tex} \frac { 1 } { 2 } + \frac { 1 } { 3 } + \frac { 1 } { 6 } + \dots {/tex} to 9 terms is

A

{tex} - \frac { 5 } { 6 } {/tex}

B

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

C

1

{tex} - \frac { 3 } { 2 } {/tex}

Explanation


Correct Marks 4

Incorrectly Marks -1

Q 11. If {tex} a _ { 1 } , a _ { 2 } , \ldots , a _ { n } {/tex} are in AP with common difference {tex} d , {/tex} then the sum of the following series is{tex} \sin d \left( \cosec a _ { 1 } \cosec a _ { 2 } + \cosec a _ { 2 } \cosec a _ { 3 } + \cdots + \cosec a _ { n - 1 } \right. {/tex} {tex} \cosec a _ { n } ) {/tex}

A

{tex} \sec a _ { 1 } - \sec a _ { n } {/tex}

{tex} \cot a _ { 1 } - \cot a _ { n } {/tex}

C

{tex} \tan a _ { 1 } - \tan a _ { n } {/tex}

D

{tex} \cosec a _ { 1 } - \cosec a _ { n } {/tex}

Explanation


Correct Marks 4

Incorrectly Marks -1

Q 12. The sum of the integers from 1 to 100 which are not divisible by 3 or 5 is

A

2489

B

4735

C

2317

2632

Explanation




Correct Marks 4

Incorrectly Marks -1

Q 13. The sum of numbers from 250 to 1000 which are divisible by 3 is

A

135657

B

136557

C

161575

156375

Explanation


Correct Marks 4

Incorrectly Marks -1

Q 14. The number of terms of the {tex} A P\,\, 3,7,11,15 , \ldots {/tex} to be taken so that the sum is 406 is

A

5

B

10

C

12

14

Explanation



Correct Marks 4

Incorrectly Marks -1

Q 15. If {tex} a , b , c , d , e , f {/tex} are in AP, then the value of {tex} e - c {/tex} will be

A

2{tex} ( c - a ) {/tex}

B

2{tex} ( f - d ) {/tex}

2{tex} ( d - c ) {/tex}

D

{tex} d - c {/tex}

Explanation

Correct Marks 4

Incorrectly Marks -1

Q 16. If the sum of three numbers of an arithmetic sequence is {tex}15{/tex} and the sum of their squares is {tex} 83 , {/tex} then the numbers are

A

{tex} 4,5,6 {/tex}

{tex} 3,5,7 {/tex}

C

{tex} 1,5,9 {/tex}

D

{tex} 2,5,8 {/tex}

Explanation



Correct Marks 4

Incorrectly Marks -1

Q 17. If the sum of three consecutive terms of an AP is {tex}51{/tex} and the product of last and first terms is {tex} 273 , {/tex} then the numbers are

{tex} 21,17,13 {/tex}

B

{tex} 20,16,12 {/tex}

C

{tex} 22,18,14 {/tex}

D

{tex} 24,20,16 {/tex}

Explanation


Correct Marks 4

Incorrectly Marks -1

Q 18. If {tex} a , b , c {/tex} are in {tex} A P , {/tex} then {tex} ( a + 2 b - c ) ( 2 b + c - a ) ( c + a - b ) {/tex} equals

A

{tex} \frac { 1 } { 2 } a b c {/tex}

B

{tex} a b c {/tex}

C

2{tex} a b c {/tex}

4{tex} a b c {/tex}

Explanation

Correct Marks 4

Incorrectly Marks -1

Q 19. If twice the {tex} 11 ^ { \text { th } } {/tex} term of an AP is equal to 7 times of its {tex} 21 ^ { \text { st } } {/tex} term, then its {tex} 25 ^ { \text { th } } {/tex} term is equal to

A

24

B

120

0

D

None of these

Explanation


Correct Marks 4

Incorrectly Marks -1

Q 20. If {tex} x , y , z {/tex} are in {tex} G P {/tex} and {tex} a ^ { x } = b ^ { y } = c ^ { z } , {/tex} then

A

{tex} \log _ { a } c = \log _ { b } a {/tex}

{tex} \log _ { b } a = \log _ { c } b {/tex}

C

{tex} \log _ { c } b = \log _ { a } c {/tex}

D

None of these

Explanation