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Recent questions tagged ch9
Questions
Sum of 20 terms of the series 1+2+3+4+5+8+7+16+9+....... is
jeemain
math
class11
ch9
sequences-and-series
medium
sum-of-n-terms-of-special-series
q134
asked
Jan 21, 2014
by
yamini.v
1
answer
The sum $1+\frac{3}{x}+\frac{9}{x^2}+\frac{27}{x^3}+....\infty$, ($x\neq\;0$) is finite if
jeemain
math
class11
ch9
sequences-and-series
medium
sum-of-n-terms-of-special-series
q133
asked
Jan 21, 2014
by
yamini.v
1
answer
If the numbers $\;1,x^2,6-x^2\;$ are in GP , then value of $x$ is :
jeemain
math
class11
ch9
sequences-and-series
medium
geometric-progression
q132
asked
Jan 21, 2014
by
yamini.v
1
answer
If 20 is divided into four parts which are in AP such that ratio of product of first and fourth part and product of second and third part is 2:3, then the largest part is
jeemain
math
class11
ch9
sequences-and-series
medium
arithmetic-progression
q131
asked
Jan 21, 2014
by
yamini.v
1
answer
$\displaystyle\sum_{r=1}^{n}\;\frac{r}{(r+1)!}=$
jeemain
math
class11
ch9
sequences-and-series
medium
sum-of-n-terms-of-special-series
q130
asked
Jan 21, 2014
by
yamini.v
1
answer
Sum of $\;\frac{1}{1.2.3.4}+\frac{1}{2.3.4.5}+\frac{1}{3.4.5.6}+\;.....\;upto\;\infty\;is$
jeemain
math
class11
ch9
sequences-and-series
medium
sum-of-n-terms-of-special-series
q129
asked
Jan 21, 2014
by
yamini.v
1
answer
If $j,k,l$ are in AP $p,q,r$ in HP and $jp,kq,lr$ in $GP$ , then $\;\frac{p}{r}+\frac{r}{p}\;is\;equal\;to:$
jeemain
math
class11
ch9
sequences-and-series
medium
relationship-between-ap-and-gm
q128
asked
Jan 21, 2014
by
yamini.v
1
answer
Let $\;a_{r}=\int\limits_{0}^{\frac{\pi}{4}}\;tan^{r}\;x\;dx$ , then $\;a_{1}+a_{3}\;,a_{2}+a_{4}\;,a_{3}+a_{5}\;$ are in
jeemain
math
class11
ch9
sequences-and-series
medium
relationship-between-ap-and-gm
q127
asked
Jan 21, 2014
by
yamini.v
1
answer
$(1-2y)\;(1+3x+9x^2+27x^3+81x^4+243x^5+729x^6)$ = $(1-64y^6)$, $(y\;\neq\;1)$, then $\frac{x}{y}$ is
jeemain
math
class11
ch9
sequences-and-series
medium
sum-of-n-terms-of-special-series
q126
asked
Jan 21, 2014
by
yamini.v
1
answer
Let $a_{1}+a_{2}+a_{3}+\;......$ be terms of an AP. If $\;\frac{S_{p}}{S_{q}}=\frac{p^2}{q^2}\;then\;\frac{a_{7}}{a_{14}} =$
jeemain
math
class11
ch9
sequences-and-series
easy
arithmetic-progression
q125
asked
Jan 21, 2014
by
yamini.v
1
answer
If $l,m,n$ are $\;x^{th}\;,y^{th}\;and\;z^{th}$ term of a GP then , $\begin{vmatrix}\log l& x & 1\\\log m &y &1\\\log n &z &1\end{vmatrix}=$
jeemain
math
class11
ch9
sequences-and-series
easy
geometric-progression
q124
asked
Jan 21, 2014
by
yamini.v
1
answer
If first and last term of an AP are $a$ & $l$ and sum of all terms is $s$, then common difference is
jeemain
math
class11
ch9
sequences-and-series
easy
arithmetic-progression
q123
asked
Jan 21, 2014
by
yamini.v
1
answer
Sum of $n$ terms of AP is $6n^2+5n$ while $a_{m}=164$, the value of $m$ is
jeemain
math
class11
ch9
sequences-and-series
easy
sum-of-n-terms-of-special-series
q122
asked
Jan 21, 2014
by
yamini.v
1
answer
Let $S=\frac{3}{19}+\frac{33}{(19)^2}+\frac{333}{(19)^3}+$......$\infty$. Find $S$.
jeemain
math
class11
ch9
sequences-and-series
easy
sum-of-n-terms-of-special-series
q121
asked
Jan 21, 2014
by
yamini.v
1
answer
Harmonic mean of roots of equation $(5+\sqrt{2})\;x^2$ - $(4+\sqrt{2})\;x$ + $8$ + $2\;\sqrt{2}$ will be
jeemain
math
class11
ch9
sequences-and-series
easy
harmonic-progression
q120
asked
Jan 21, 2014
by
yamini.v
1
answer
Natural numbers are divided into groups $\;(1)\;,\;(2,3,4)\;,\;(5,6,7,8,9)\;.....$ Sum of first and last term of $n^{th}\;$ group will be :
jeemain
math
class11
ch9
sequences-and-series
easy
sum-of-n-terms-of-special-series
q119
asked
Jan 21, 2014
by
yamini.v
1
answer
If in an AP $m$ times $\;m^{th}\;$ term equals $n$ times $\;n^{th}$ term , then $\;(m+n)^{th}$ term will be
jeemain
math
class11
ch9
sequences-and-series
easy
arithmetic-progression
q118
asked
Jan 21, 2014
by
yamini.v
1
answer
Let $a_{n}\;$ be $\;n^{th}$ term of AP. If $\;\displaystyle\sum_{r=1}^{50}\;a_{2r}=p\;and \;\displaystyle\sum_{r=1}^{50}\;a_{2r-1}=q\;$ the common difference is :
jeemain
math
class11
ch9
sequences-and-series
easy
sum-of-n-terms-of-special-series
q117
asked
Jan 21, 2014
by
yamini.v
1
answer
If $\;x=\sqrt{2+\sqrt{2+\sqrt{2+------\;\infty}}}\;and\;y=\sqrt{2\;\sqrt{2\;\sqrt{2\;\sqrt{2\;----\;\infty}}}}$ then $xy$ equals
jeemain
math
class11
ch9
sequences-and-series
easy
sum-of-n-terms-of-special-series
q116
asked
Jan 20, 2014
by
yamini.v
1
answer
Sum of series $\;S=\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\;....\;+\frac{1}{100\sqrt{99}+99\sqrt{100}} \;is$
jeemain
math
class11
ch9
sequences-and-series
easy
sum-of-n-terms-of-special-series
q115
asked
Jan 20, 2014
by
yamini.v
1
answer
If $1^4+2^4+3^4+.....n^4$ = $an^5+bn^4+cn^3+dn^2+en+f$, find $a$
jeemain
math
class11
ch9
sequences-and-series
easy
sum-of-n-terms-of-special-series
q114
asked
Jan 20, 2014
by
yamini.v
1
answer
Sum of series $(n)(n)$ + $(n-1)(n+1)$ + $(n-2)(n+2)$ +....+ $1\;(2n-1)$ is
jeemain
math
class11
ch9
sequences-and-series
easy
sum-of-n-terms-of-special-series
q113
asked
Jan 20, 2014
by
yamini.v
1
answer
Sum of series $\;\sum_{r=1}^{n}\;r\;log\;\frac{r+1}{r}$ is :
jeemain
math
class11
ch9
sequences-and-series
easy
sum-of-n-terms-of-special-series
q112
asked
Jan 20, 2014
by
yamini.v
1
answer
If $a_{1},a_{2},...a_{n}$ are in HP. , Then $\;a_{1}a_{2}+a_{2}a_{3}+.....+a_{n}\;a_{n-1}$ is equal to
jeemain
math
class11
ch9
sequences-and-series
easy
relationship-between-ap-and-gm
q111
asked
Jan 20, 2014
by
yamini.v
1
answer
Sum of $n$ terms of series $S$ = $1$ + $2 \;(1+\frac{1}{n})$ + $3(1+\frac{1}{n})^2$ + ....is given by
jeemain
math
class11
ch9
sequences-and-series
easy
sum-of-n-terms-of-special-series
q110
asked
Jan 20, 2014
by
yamini.v
1
answer
For $0\;<\;x\;<\;\pi$, the values of x which satisfies $1+|cos\;x|+|cos\;x|^2+|cos\;x|^3+$....$\infty$ = $2^4$ are
jeemain
math
class11
ch9
sequences-and-series
easy
sum-of-n-terms-of-special-series
q109
asked
Jan 20, 2014
by
yamini.v
1
answer
If $f\;(x)$ is a two degree polynomial such that $f\;(3)=f\;(-3)$ and $a, b, c$ are in $AP$, then $f'(a)$, $f'(b)$ and $f'(c)$ are in
jeemain
math
class11
ch9
sequences-and-series
easy
arithmetic-progression
q108
asked
Jan 20, 2014
by
yamini.v
1
answer
If $\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+$......upto $\infty$ = $\frac{\phi^2}{g}$, then $\frac{1}{1^2}+\frac{1}{3^2}+\frac{1}{5^2}+$.....upto $\infty$ will be
jeemain
math
class11
ch9
sequences-and-series
easy
sum-of-n-terms-of-special-series
q107
asked
Jan 20, 2014
by
yamini.v
1
answer
If $S_{n}=\frac{1}{6}\;n\;(2n^2+9n+13)\;$, then $\sum_{r=1}^n\;\sqrt{a_{r}}\;$ equals.
jeemain
math
class11
ch9
sequences-and-series
easy
sum-of-n-terms-of-special-series
q106
asked
Jan 20, 2014
by
yamini.v
1
answer
Sum of series $\;\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+.....\;is:$
jeemain
math
class11
ch9
sequences-and-series
easy
sum-of-n-terms-of-special-series
q105
asked
Jan 20, 2014
by
yamini.v
1
answer
If $f\;(xy)=f\;(x+y)\;\forall\;x,y\;\in\;R$ and $\;f\;(2009)=2009$, then $f\;(-2009)$ equals
jeemain
math
class11
ch9
sequences-and-series
easy
sum-of-n-terms-of-special-series
q104
asked
Jan 20, 2014
by
yamini.v
1
answer
Sum of n terms of series $\;\frac{1}{1^3}\;+\frac{1+2}{1^3+2^3}\;+\frac{1+2+3}{1^3+2^3+3^3}\;+....\;is$
jeemain
math
class11
ch9
sequences-and-series
easy
sum-of-n-terms-of-special-series
q103
asked
Jan 20, 2014
by
yamini.v
1
answer
If x, y, z > 1 are in GP, then $\frac{1}{1+lnx}$, $\frac{1}{lny}$, $\frac{1}{lnz}$ are in
jeemain
math
class11
ch9
sequences-and-series
easy
geometric-progression
q102
asked
Jan 20, 2014
by
yamini.v
1
answer
If in an AP , $\;m^{th}$ term is $\;\frac{1}{n}$ and $\;n^{th}\;term\;is\frac{1}{m}$ , then $\;mn^{th}$ term is :
jeemain
math
class11
ch9
sequences-and-series
easy
arithmetic-progression
q101
asked
Jan 20, 2014
by
yamini.v
1
answer
Let $S_{1}, S_{2}$....be the squares such that for each $n\geq\;1$, the length of side of $S_{n}$ = length of diagonal of $S_{n+1}$. If side of $S_{1}$ is 20 cm, the smallest value of n such that area of $S_{n}\;<\;2$ is
jeemain
math
class11
ch9
sequences-and-series
easy
sum-of-n-terms-of-special-series
q100
asked
Jan 20, 2014
by
yamini.v
1
answer
If $a, b, c$ are in AP and $a^2$, $b^2$, $c^2$ in GP, and $a+b+c=\frac{3}{2}$, then value of $c$ is
jeemain
math
class11
ch9
sequences-and-series
easy
relationship-between-ap-and-gm
q99
asked
Jan 20, 2014
by
yamini.v
1
answer
If $(1+3+5+....+p)$+$(1+3+5+....+q)$ = the smallest value of $p+q+r, (p>6)$ is
jeemain
math
class11
ch9
sequences-and-series
easy
sum-of-n-terms-of-special-series
q98
asked
Jan 20, 2014
by
yamini.v
1
answer
Sum of series $S$ = $\frac{1}{2}$+$\frac{1}{3}\;(1+2)$+$\frac{1}{4}\;(1+2+3)$+$\frac{1}{5}\;(1+2+3+4)$+......upto 20 terms is
jeemain
math
class11
ch9
sequences-and-series
easy
sum-of-n-terms-of-special-series
q97
asked
Jan 20, 2014
by
yamini.v
1
answer
Sum of series $1^2$-$2^2$+$3^2$-$4^2$+$5^2$+.....+$1001^2$ is
jeemain
math
class11
ch9
sequences-and-series
easy
sum-of-n-terms-of-special-series
q96
asked
Jan 20, 2014
by
yamini.v
1
answer
If the $\;10^{th}\;$ term of a $GP$ is $9$ and the $\;4^{th}\;$ term is $4$, then the $\;7^{th} \;$term is
jeemain
math
class11
ch9
sequences-and-series
easy
geometric-progression
q95
asked
Jan 19, 2014
by
yamini.v
1
answer
In an AP, the $\; 4^{th}\;$ term is $36$. The$\; 21^{st}\;$ term is $108$ more than the $\;9^{th}\;$ term. What is the first term a and the common difference $d$?
jeemain
math
class11
ch9
sequences-and-series
easy
arithmetic-progression
q94
asked
Jan 19, 2014
by
yamini.v
1
answer
The sum of 0.2, 0.22, 0.222, 0.2222.....till n terms is given by
jeemain
math
class11
ch9
sequences-and-series
easy
sum-of-n-terms-of-special-series
q93
asked
Jan 18, 2014
by
yamini.v
2
answers
The sum of $n$ terms of an arithmetic progression is $\;n\;(2n-1)$. What is the $m^{th}$ term of the series?
jeemain
math
class11
ch9
sequences-and-series
easy
arithmetic-progression
q92
asked
Jan 18, 2014
by
yamini.v
1
answer
If a, g and h are the AM, GM and HM respectively of two positive numbers x and y, then identify the correct statement.
jeemain
math
class11
ch9
sequences-and-series
easy
relationship-between-ap-and-gm
q91
asked
Jan 18, 2014
by
yamini.v
1
answer
The sum of n terms of two APs is in the ratio$\; 5n + 1: 4n+10$. Find the ratio of their $\;5^{th}$ terms.
jeemain
math
class11
ch9
sequences-and-series
easy
sum-of-n-terms-of-special-series
q90
asked
Jan 18, 2014
by
yamini.v
1
answer
The number of terms in the AP a, b,....c is
jeemain
math
class11
ch9
sequences-and-series
easy
arithmetic-progression
q89
asked
Jan 17, 2014
by
yamini.v
1
answer
A train travels from A to B at speed of x km/hour and from B to A at speed of y km/hour. The average speed of the train from A to B and back to A, would be calculated by the
jeemain
math
class11
ch9
sequences-and-series
easy
arithmetic-progression
q88
asked
Jan 17, 2014
by
yamini.v
1
answer
If three numbers are in GP, then their logarithms will be in
jeemain
math
class11
ch9
sequences-and-series
easy
relationship-between-ap-and-gm
q87
asked
Jan 17, 2014
by
yamini.v
1
answer
The sum of three decreasing numbers in AP is 27. If -1, -1, and 3 are added to them respectively the resulting series is in GP. The numbers are
jeemain
math
class11
ch9
sequences-and-series
easy
relationship-between-ap-and-gm
q86
asked
Jan 17, 2014
by
yamini.v
1
answer
The $n^{th}$ term of series is $\frac{1}{1}$, $\frac{(1+2)}{2}$, $\frac{(1+2+3)}{3}$......is
jeemain
math
class11
ch9
sequences-and-series
easy
sum-of-n-terms-of-special-series
q85
asked
Jan 17, 2014
by
yamini.v
1
answer
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