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JEE Advanced

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

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Sequence and Series

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Q 1. The third term of a geometric progression is {tex} 4 . {/tex} The product of the first five terms is

A

{tex} 4 ^ { 3 } {/tex}

{tex} 4 ^ { 5 } {/tex}

C

{tex} 4 ^ { 4 } {/tex}

D

none of these

Explanation

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

A

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

B

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

C

{tex} a , b , c {/tex} are in G.P.

{tex} a , b , c {/tex} are in H.P.

Explanation

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Q 3. Let {tex} a _ { 1 } , a _ { 2 } , \ldots . a _ { 10 } {/tex} be in {tex} A , P , {/tex} and {tex} h _ { 1 } , h _ { 2 } , \ldots h _ { 10 } {/tex} be in H.P. If {tex} a _ { 1 } = h _ { 1 } = 2 {/tex} and {tex} a _ { 10 } = h _ { 10 } = 3 , {/tex} then {tex} a _ { 4 } h _ { 7 } {/tex} is

A

2

B

3

C

5

6

Explanation

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Q 4. Consider an infinite geometric series with first term a and common ratio {tex} r . {/tex} If its sum is 4 and the second term is {tex} 3 / 4 , {/tex} then

A

{tex} a = \frac { 4 } { 7 } , r = \frac { 3 } { 7 } {/tex}

B

{tex} a = 2 , r = \frac { 3 } { 8 } {/tex}

C

{tex} a = \frac { 3 } { 2 } , r = \frac { 1 } { 2 } {/tex}

{tex} a = 3 , r = \frac { 1 } { 4 } {/tex}

Explanation

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Q 5. Suppose {tex} a , b , c {/tex} are in A.P. and {tex} a ^ { 2 } , b ^ { 2 } , c ^ { 2 } {/tex} are in G.P. if {tex} a < b < c {/tex} and {tex} a + b + c = \frac { 3 } { 2 } , {/tex} then the value of {tex} a {/tex} is

A

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

B

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

C

{tex} \frac { 1 } { 2 } - \frac { 1 } { \sqrt { 3 } } {/tex}

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

Explanation


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Q 6. An infinite G.P. has first term '{tex} x {/tex}'and sum '5', then {tex} x {/tex} belongs to

A

{tex} x < - 10 {/tex}

B

{tex} - 10 < x < 0 {/tex}

{tex} 0 < x < 10 {/tex}

D

{tex} x > 10 {/tex}

Explanation

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Q 7. In the sum of first {tex} n {/tex} terms of an A.P. is {tex} c n ^ { 2 } {/tex}, the sum of squares of these {tex} n {/tex} terms is

A

{tex} \frac { n \left( 4 n ^ { 2 } - 1 \right) c ^ { 2 } } { 6 } {/tex}

B

{tex} \frac { n \left( 4 n ^ { 2 } + 1 \right) c ^ { 2 } } { 3 } {/tex}

{tex} \frac { n \left( 4 n ^ { 2 } - 1 \right) c ^ { 2 } } { 3 } {/tex}

D

{tex} \frac { n \left( 4 n ^ { 2 } + 1 \right) c ^ { 2 } } { 6 } {/tex}

Explanation


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Q 8. Let {tex} b _ { i } > 1 {/tex} for {tex} i = 1,2 , \ldots , 101. {/tex} Suppose {tex}\mathrm {log_e}{/tex} {tex} b _ { 1 } , \log _ { e } b _ { 2 } , \ldots , \log _ { e } {/tex} {tex} b _ { 101 } {/tex} are in Arithmetic Progression (A.P.) with the common difference {tex}\mathrm {log_e} {tex} 2 . {/tex} Suppose {tex} a _ { 1 } , a _ { 2 } , \ldots , a _ { 101 } {/tex} are in A.P. such that {tex} a _ { 1 } = b _ { 1 } {/tex} and {tex} a _ { 51 } = b _ { 51 } {/tex}. If {tex} t = b _ { 1 } + b _ { 2 } + \ldots . + b _ { 51 } {/tex} and {tex} s = a _ { 1 } + a _ { 2 } + \ldots . + {/tex} {tex} a 5 _ { 3 } , {/tex} then

A

{tex} \mathrm { s } > \mathrm { t } {/tex} and {tex} \mathrm { a } _ { 101 } > \mathrm { b } _ { 100 } {/tex}

{tex} \mathrm { s } > \mathrm { t } {/tex} and {tex} \mathrm { a } _ { 101 } < \mathrm { b } _ { 101 } {/tex}

C

{tex} \mathrm { s } < \mathrm { t } {/tex} and {tex} \mathrm { a } _ { 101 } > \mathrm { b } _ { 101 } {/tex}

D

{tex} \mathrm { s } < \mathrm { t } {/tex} and {tex} \mathrm { a } _ { 101 } < \mathrm { b } _ { 101 } {/tex}

Explanation