### Mathematics - Sequences & Series

#### Question - 1

If the sum of the first 2n terms of the A.P. 2, 5, 8, .... is equal to the sum of the first n terms of the A.P. 57, 59, 61, ..... then n equal equals

• A 10
• B 12
• C 11
• D 13

#### Question - 2

If x, y, z (x>1, y>1, z>1) are three positive numbers in G.P. then ${1\over {1+1n\ x}}$${1\over {1+1n\ y}}$${1\over {1+1n\ z}}$ are in

• A A.P.
• B G.P.
• C H.P.
• D NONE OF THESE

#### Question - 3

Let an be the nth terms of a G.P. of positive integers. Let $\overset { 100 }{ \underset { n=1 }{ \sum { { a }_{ 2n } } } } \quad =\quad \alpha \quad and\quad \overset { 100 }{ \underset { n=1 }{ \sum { { a }_{ 2n } } } } +1\quad =\quad \beta$ such that $\alpha \quad \neq \quad \beta$ Thus common ratio of the G.P. is

• A $\frac { \alpha }{ \beta }$
• B $\frac { \beta }{ \alpha }$
• C ${ \left( \frac { \alpha }{ \beta } \right) }^{ 1/2 }$
• D ${ \left( \frac { \beta }{ \alpha } \right) }^{ 1/2 }$

#### Question - 4

Let T be the rth term of an A.P. for r = 1, 2, 3 .... If for some positive integers m, n ${ T }_{ m }\quad =\quad \frac { 1 }{ n } ,\quad { T }_{ n }\quad =\quad \frac { 1 }{ m }$then Tmn equals

• A $1\over mn$
• B ${1\over m}+{1\over n}$
• C 1
• D 0

#### Question - 5

Let the positive numbers a, b, c, d be in A.P. Then abc, abd, bcd are

• A not in A.P./G.P./H.P.
• B in A.P.
• C in G.P.
• D in H.P.

#### Question - 6

Consider an infinite series with first term a and common ratio r. If its sum is 4 and the second term is $3\over 4$then

• A $a\quad =\quad \frac { 7 }{ 4 } ,\quad r\quad =\quad \frac { 3 }{ 7 }$
• B $a\quad =\quad 2,\quad r\quad =\quad \frac { 3 }{ 8 }$
• C $a\quad =\quad \frac { 3 }{ 2 } ,\quad r\quad =\quad \frac { 1 }{ 2 }$
• D $a\quad =\quad 3,\quad r\quad =\quad \frac { 1 }{ 4 }$

#### Question - 7

If a, b , c are positive numbers, the least value of $\frac { a+b }{ c } +\frac { b+c }{ a } +\frac { c+a }{ b }$is

• A 6
• B 4
• C 3
• D NONE OF THESE

#### Question - 8

If a, b, c are positive numbers then value of $(a+b+c)\left( \frac { 1 }{ a } +\frac { 1 }{ b } +\frac { 1 }{ c } \right)$is

• A $\ge 10$
• B $\ge 9$
• C $\ge 12$
• D NONE OF THESE

#### Question - 9

If the 9th term of A.P. is zero, then ratio of 29th term to 19th term is

• A 2 : 1
• B 3 : 1
• C 9 : 1
• D NONE OF THESE

#### Question - 10

The sum of the first m terms of an A.P. is the same as the sum of the n terms, where $m\quad \neq \quad n$Then the sum of the first (m+n) terms is

• A m
• B n
• C 0
• D NONE OF THESE