JEE Main & Advanced Mathematics Sequence & Series Question Bank

done Geometric Progression Total Questions - 88

• question_answer1)
  If \[a,\,b,\,c\] are in G.P., then
  A)
  \[a({{b}^{2}}+{{a}^{2}})=c({{b}^{2}}+{{c}^{2}})\] done clear
  B)
  \[a({{b}^{2}}+{{c}^{2}})=c({{a}^{2}}+{{b}^{2}})\] done clear
  C)
  \[{{a}^{2}}(b+c)={{c}^{2}}(a+b)\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer2)
  \[{{7}^{th}}\] term of the sequence \[\sqrt{2},\ \sqrt{10},\ 5\sqrt{2},\ .......\]is
  A)
  \[125\sqrt{10}\] done clear
  B)
  \[25\sqrt{2}\] done clear
  C)
  125 done clear
  D)
  \[125\sqrt{2}\] done clear
  View Solution play_arrow

• question_answer3)
  If the \[{{4}^{th}},\ {{7}^{th}}\] and \[{{10}^{th}}\] terms of  a G.P. be \[a,\ b,\ c\] respectively, then the relation between \[a,\ b,\ c\] is [MNR 1995; Karnataka CET 1999]
  A)
  \[b=\frac{a+c}{2}\] done clear
  B)
  \[{{a}^{2}}=bc\] done clear
  C)
  \[{{b}^{2}}=ac\] done clear
  D)
  \[{{c}^{2}}=ab\] done clear
  View Solution play_arrow

• question_answer4)
  If the first  term of a G.P. be 5 and common ratio be \[-5\], then which term is 3125
  A)
  \[{{6}^{th}}\] done clear
  B)
  \[{{5}^{th}}\] done clear
  C)
  \[{{7}^{th}}\] done clear
  D)
  \[{{8}^{th}}\] done clear
  View Solution play_arrow

• question_answer5)
  The number which should be added to the numbers 2, 14, 62 so that the resulting numbers may be in G.P., is
  A)
  1 done clear
  B)
  2 done clear
  C)
  3 done clear
  D)
  4 done clear
  View Solution play_arrow

• question_answer6)
  If \[{{(p+q)}^{th}}\] term of a G.P. be \[m\] and \[{{(p-q)}^{th}}\]term be \[n\], then the \[{{p}^{th}}\] term will be    [RPET 1997; MP PET 1985, 99]
  A)
  \[m/n\] done clear
  B)
  \[\sqrt{mn}\] done clear
  C)
  \[mn\] done clear
  D)
  0 done clear
  View Solution play_arrow

• question_answer7)
  The terms of a G.P. are positive. If each term is equal to the sum of two terms that follow it, then the common ratio is
  A)
  \[\frac{\sqrt{5}-1}{2}\] done clear
  B)
  \[\frac{1-\sqrt{5}}{2}\] done clear
  C)
  1 done clear
  D)
  \[2\sqrt{5}\] done clear
  View Solution play_arrow

• question_answer8)
  If \[x,\,2x+2,\,3x+3,\]are in G.P., then the fourth term is [MNR 1981]
  A)
  27 done clear
  B)
  \[-27\] done clear
  C)
  13.5 done clear
  D)
  \[-13.5\] done clear
  View Solution play_arrow

• question_answer9)
  If the ratio of the sum of first three terms and the sum of first six terms of a G.P.  be 125 : 152, then the common ratio r is
  A)
  \[\frac{3}{5}\] done clear
  B)
  \[\frac{5}{3}\] done clear
  C)
  \[\frac{2}{3}\] done clear
  D)
  \[\frac{3}{2}\] done clear
  View Solution play_arrow

• question_answer10)
  If \[x,\ y,\ z\] are in G.P. and \[{{a}^{x}}={{b}^{y}}={{c}^{z}}\], then [IIT 1966, 68]
  A)
  \[{{\log }_{a}}c={{\log }_{b}}a\] done clear
  B)
  \[{{\log }_{b}}a={{\log }_{c}}b\] done clear
  C)
  \[{{\log }_{c}}b={{\log }_{a}}c\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer11)
  If the \[{{p}^{th}}\],\[{{q}^{th}}\] and \[{{r}^{th}}\]term of a G.P. are \[a,\ b,\ c\] respectively, then \[{{a}^{q-r}}.\ {{b}^{r-p}}.\ {{c}^{p-q}}\] is equal to [Roorkee 1955, 63, 73; Pb. CET 1991, 95]
  A)
  0 done clear
  B)
  1 done clear
  C)
  \[abc\] done clear
  D)
  \[pqr\] done clear
  View Solution play_arrow

• question_answer12)
  If the third term of a G.P. is 4 then the product of its first 5 terms is [IIT 1982; RPET 1991]
  A)
  \[{{4}^{3}}\] done clear
  B)
  \[{{4}^{4}}\] done clear
  C)
  \[{{4}^{5}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer13)
  If the \[{{5}^{th}}\] term of a G.P. is \[\frac{1}{3}\] and \[{{9}^{th}}\] term is \[\frac{16}{243}\], then the \[{{4}^{th}}\] term will be [MP PET 1982]
  A)
  \[\frac{3}{4}\] done clear
  B)
  \[\frac{1}{2}\] done clear
  C)
  \[\frac{1}{3}\] done clear
  D)
  \[\frac{2}{5}\] done clear
  View Solution play_arrow

• question_answer14)
  The \[{{20}^{th}}\] term of the series \[2\times 4+4\times 6+6\times 8+.......\]will be [Pb. CET 1988]
  A)
  1600 done clear
  B)
  1680 done clear
  C)
  420 done clear
  D)
  840 done clear
  View Solution play_arrow

• question_answer15)
  If \[a,\ b,\ c\] are \[{{p}^{th}},\ {{q}^{th}}\] and \[{{r}^{th}}\]terms of a G.P., then \[{{\left( \frac{c}{b} \right)}^{p}}{{\left( \frac{b}{a} \right)}^{r}}{{\left( \frac{a}{c} \right)}^{q}}\] is equal to
  A)
  1 done clear
  B)
  \[{{a}^{P}}{{b}^{q}}{{c}^{r}}\] done clear
  C)
  \[{{a}^{q}}{{b}^{r}}{{c}^{p}}\] done clear
  D)
  \[{{a}^{r}}{{b}^{p}}{{c}^{q}}\] done clear
  View Solution play_arrow

• question_answer16)
  The first and last terms of a G.P. are \[a\] and \[l\] respectively; \[r\] being its common ratio; then the number of terms in this G.P. is
  A)
    \[\frac{\log l-\log a}{\log r}\] done clear
  B)
  \[1-\frac{\log l-\log a}{\log r}\] done clear
  C)
    \[\frac{\log a-\log l}{\log r}\] done clear
  D)
  \[1+\frac{\log l-\log a}{\log r}\] done clear
  View Solution play_arrow

• question_answer17)
  If \[{{\log }_{x}}a,\ {{a}^{x/2}}\] and \[{{\log }_{b}}x\] are in G.P., then \[x=\]
  A)
  \[-\log ({{\log }_{b}}a)\] done clear
  B)
  \[-{{\log }_{a}}({{\log }_{a}}b)\] done clear
  C)
   \[{{\log }_{a}}({{\log }_{e}}a)-{{\log }_{a}}({{\log }_{e}}b)\] done clear
  D)
    \[{{\log }_{a}}({{\log }_{e}}b)-{{\log }_{a}}({{\log }_{e}}a)\] done clear
  View Solution play_arrow

• question_answer18)
  If the roots of the cubic equation \[a{{x}^{3}}+b{{x}^{2}}+cx+d=0\] are in G.P., then
  A)
  \[{{c}^{3}}a={{b}^{3}}d\] done clear
  B)
  \[c{{a}^{3}}=b{{d}^{3}}\] done clear
  C)
  \[{{a}^{3}}b={{c}^{3}}d\] done clear
  D)
  \[a{{b}^{3}}=c{{d}^{3}}\] done clear
  View Solution play_arrow

• question_answer19)
  If the \[{{10}^{th}}\] term of a geometric progression is 9 and \[{{4}^{th}}\] term is 4, then its \[{{7}^{th}}\] term is [MP PET 1996]
  A)
  6 done clear
  B)
  36 done clear
  C)
  \[\frac{4}{9}\] done clear
  D)
  \[\frac{9}{4}\] done clear
  View Solution play_arrow

• question_answer20)
  The 6th term of a G.P. is 32 and its 8th term is 128, then the common ratio of the G.P. is [Pb. CET 1999]
  A)
  - 1 done clear
  B)
  2 done clear
  C)
  4 done clear
  D)
  - 4 done clear
  View Solution play_arrow

• question_answer21)
  If the nth term of geometric progression \[5,-\frac{5}{2},\frac{5}{4},-\frac{5}{8},...\] is \[\frac{5}{1024}\], then the value of n is [Kerala (Engg.) 2002]
  A)
  11 done clear
  B)
  10 done clear
  C)
  9 done clear
  D)
  4 done clear
  View Solution play_arrow

• question_answer22)
  The third term of a G.P. is the square of first term. If the second term is 8, then the \[{{6}^{th}}\] term is [MP PET 1997]
  A)
  120 done clear
  B)
  124 done clear
  C)
  128 done clear
  D)
  132 done clear
  View Solution play_arrow

• question_answer23)
  Fifth term of a G.P. is 2, then the product of its 9 terms is    [Pb. CET 1990, 94; AIEEE 2002]
  A)
  256 done clear
  B)
  512 done clear
  C)
  1024 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer24)
  If the sum of an infinite G.P. be 9 and the sum of first two terms be 5, then the common ratio is
  A)
  1/3 done clear
  B)
  3/2 done clear
  C)
  3/4 done clear
  D)
  2/3 done clear
  View Solution play_arrow

• question_answer25)
  The sum of the first five terms of the series \[3+4\frac{1}{2}+6\frac{3}{4}+......\] will be
  A)
  \[39\frac{9}{16}\] done clear
  B)
  \[18\frac{3}{16}\] done clear
  C)
  \[39\frac{7}{16}\] done clear
  D)
  \[13\frac{9}{16}\] done clear
  View Solution play_arrow

• question_answer26)
  The sum of 100 terms of the series \[.9+.09+.009.........\]will be
  A)
  \[1-{{\left( \frac{1}{10} \right)}^{100}}\] done clear
  B)
  \[1+{{\left( \frac{1}{10} \right)}^{100}}\] done clear
  C)
  \[\]\[1-{{\left( \frac{1}{10} \right)}^{106}}\] done clear
  D)
  \[1+{{\left( \frac{1}{10} \right)}^{100}}\] done clear
  View Solution play_arrow

• question_answer27)
  The value of \[0.\overset{\,\,\,\,\,\,\bullet \,\,\,\,\bullet \,\,\,}{\mathop{234}}\,\] is   [MNR 1986; UPSEAT 2000]
  A)
  \[\frac{232}{990}\] done clear
  B)
  \[\frac{232}{9990}\] done clear
  C)
  \[\frac{232}{990}\] done clear
  D)
  \[\frac{232}{9909}\] done clear
  View Solution play_arrow

• question_answer28)
  If the sum of three terms of G.P. is 19 and product is 216, then the common ratio of the series is  [Roorkee 1972]
  A)
  \[-\frac{3}{2}\] done clear
  B)
  \[\frac{3}{2}\] done clear
  C)
  2 done clear
  D)
  3 done clear
  View Solution play_arrow

• question_answer29)
  The sum of the series \[6+66+666+..........\]upto \[n\] terms is [IIT 1974]
  A)
  \[({{10}^{n-1}}-9n+10)/81\] done clear
  B)
  \[2({{10}^{n+1}}-9n-10)/27\] done clear
  C)
  \[2({{10}^{n}}-9n-10)/27\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer30)
  If every term of a G.P. with positive terms is the sum of its two previous terms, then the common ratio of the series is [RPET 1986]
  A)
  1 done clear
  B)
  \[\frac{2}{\sqrt{5}}\] done clear
  C)
  \[\frac{\sqrt{5}-1}{2}\] done clear
  D)
  \[\frac{\sqrt{5}+1}{2}\] done clear
  View Solution play_arrow

• question_answer31)
  The sum of first two terms of a G.P. is 1 and every term of this series is twice of its previous term, then the first term will be [RPET 1988]
  A)
  1/4 done clear
  B)
  1/3 done clear
  C)
  2/3 done clear
  D)
  3/4 done clear
  View Solution play_arrow

• question_answer32)
  If the sum of \[n\] terms of a G.P. is 255 and \[{{n}^{th}}\]terms is 128 and common ratio is 2, then first term will be  [RPET 1990]
  A)
  1 done clear
  B)
  3 done clear
  C)
  7 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer33)
  The sum of \[n\] terms of the following series \[1+(1+x)+(1+x+{{x}^{2}})+..........\]will be [IIT 1962]
  A)
  \[\frac{1-{{x}^{n}}}{1-x}\] done clear
  B)
  \[\frac{x(1-{{x}^{n}})}{1-x}\] done clear
  C)
  \[\frac{n(1-x)-x(1-{{x}^{n}})}{{{(1-x)}^{2}}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer34)
  If the sum of first  6 term is 9 times to the sum of first 3 terms of the same G.P., then the common ratio of the series will be [RPET 1985]
  A)
  \[-2\] done clear
  B)
  2 done clear
  C)
  1 done clear
  D)
  1/2 done clear
  View Solution play_arrow

• question_answer35)
  The number \[111..............1\] (91 times) is a
  A)
  Even number done clear
  B)
  Prime number done clear
  C)
  Not prime done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer36)
  For a sequence \[<{{a}_{n}}>,\ {{a}_{1}}=2\] and \[\frac{{{a}_{n+1}}}{{{a}_{n}}}=\frac{1}{3}\]. Then \[\sum\limits_{r=1}^{20}{{{a}_{r}}}\] is
  A)
  \[\frac{20}{2}[4+19\times 3]\] done clear
  B)
  \[3\left( 1-\frac{1}{{{3}^{20}}} \right)\] done clear
  C)
  \[2(1-{{3}^{20}})\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer37)
  The solution of the equation \[1+a+{{a}^{2}}+{{a}^{3}}+.......+{{a}^{x}}\] \[=(1+a)(1+{{a}^{2}})(1+{{a}^{4}})\] is given by \[x\] is equal to
  A)
  3 done clear
  B)
  5 done clear
  C)
  7 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer38)
  If in a geometric progression \[\left\{ {{a}_{n}} \right\},\ {{a}_{1}}=3,\ {{a}_{n}}=96\] and \[{{S}_{n}}=189\] then the value of \[n\] is
  A)
  5 done clear
  B)
  6 done clear
  C)
  7 done clear
  D)
  8 done clear
  View Solution play_arrow

• question_answer39)
  The sum of few terms of any ratio series is 728, if common ratio is 3 and last term is 486, then first term of series will be [UPSEAT 1999]
  A)
  2 done clear
  B)
  1 done clear
  C)
  3 done clear
  D)
  4 done clear
  View Solution play_arrow

• question_answer40)
  The product of \[n\] positive numbers is unity. Their sum is  [MP PET 2000]
  A)
  A positive integer done clear
  B)
  Equal to \[n+\frac{1}{n}\] done clear
  C)
  Divisible by \[n\] done clear
  D)
  Never less than done clear
  View Solution play_arrow

• question_answer41)
  Three numbers are in G.P. such that their sum is 38 and their product is 1728. The greatest number among them is [UPSEAT 2004]
  A)
  18 done clear
  B)
  16 done clear
  C)
  14 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer42)
  The sum of the series \[3+33+333+...+n\] terms is [RPET 2000]
  A)
  \[\frac{1}{27}({{10}^{n+1}}+9n-28)\] done clear
  B)
  \[\frac{1}{27}({{10}^{n+1}}-9n-10)\] done clear
  C)
  \[\frac{1}{27}({{10}^{n+1}}+10n-9)\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer43)
  The first term of a G.P. is 7, the last term is 448 and sum of all terms is 889, then the common ratio is  [MP PET 2003]
  A)
  5 done clear
  B)
  4 done clear
  C)
  3 done clear
  D)
  2 done clear
  View Solution play_arrow

• question_answer44)
  The sum of a G.P. with common ratio 3 is 364, and last term is 243, then the number of terms is [MP PET 2003]
  A)
  6 done clear
  B)
  5 done clear
  C)
  4 done clear
  D)
  10 done clear
  View Solution play_arrow

• question_answer45)
  If \[n\] geometric means be inserted between \[a\] and \[b\]then the \[{{n}^{th}}\] geometric mean will be
  A)
  \[a\,{{\left( \frac{b}{a} \right)}^{\frac{n}{n-1}}}\] done clear
  B)
    \[a\,{{\left( \frac{b}{a} \right)}^{\frac{n-1}{n}}}\] done clear
  C)
  \[a\,{{\left( \frac{b}{a} \right)}^{\frac{n}{n+1}}}\] done clear
  D)
  \[a\,{{\left( \frac{b}{a} \right)}^{\frac{1}{n}}}\] done clear
  View Solution play_arrow

• question_answer46)
  If the geometric mean between \[a\] and \[b\] is \[\frac{{{a}^{n+1}}+{{b}^{n+1}}}{{{a}^{n}}+{{b}^{n}}}\],  then the value of n is
  A)
  1 done clear
  B)
  -1/2 done clear
  C)
  1/2 done clear
  D)
  2 done clear
  View Solution play_arrow

• question_answer47)
  If \[G\] be the geometric mean of \[x\] and \[y\], then \[\frac{1}{{{G}^{2}}-{{x}^{2}}}+\frac{1}{{{G}^{2}}-{{y}^{2}}}=\]
  A)
  \[{{G}^{2}}\] done clear
  B)
  \[\frac{1}{{{G}^{2}}}\] done clear
  C)
  \[\frac{2}{{{G}^{2}}}\] done clear
  D)
  \[3{{G}^{2}}\] done clear
  View Solution play_arrow

• question_answer48)
  If three geometric means be inserted between 2 and 32, then the third geometric mean will be
  A)
  8 done clear
  B)
  4 done clear
  C)
  16 done clear
  D)
  12 done clear
  View Solution play_arrow

• question_answer49)
   If five G.M.?s are inserted between 486 and 2/3 then fourth G.M. will be   [RPET 1999]
  A)
  4 done clear
  B)
  6 done clear
  C)
  12 done clear
  D)
  - 6 done clear
  View Solution play_arrow

• question_answer50)
  The G.M. of roots of the equation \[{{x}^{2}}-18x+9=0\] is [RPET 1997]
  A)
  3 done clear
  B)
  4 done clear
  C)
  2 done clear
  D)
  1 done clear
  View Solution play_arrow

• question_answer51)
  The G.M. of the numbers \[3,\,{{3}^{2}},\,{{3}^{3}},....,\,{{3}^{n}}\] is  [DCE 2002]
  A)
  \[{{3}^{\frac{2}{n}}}\] done clear
  B)
  \[{{3}^{\frac{n+1}{2}}}\] done clear
  C)
  \[{{3}^{\frac{n}{2}}}\] done clear
  D)
  \[{{3}^{\frac{n-1}{2}}}\] done clear
  View Solution play_arrow

• question_answer52)
  The product of three geometric means between 4 and \[\frac{1}{4}\] will be
  A)
  4 done clear
  B)
  2 done clear
  C)
  \[-1\] done clear
  D)
  1 done clear
  View Solution play_arrow

• question_answer53)
  The two geometric means between the number 1 and 64 are [Kerala (Engg.) 2002]
  A)
  1 and 64 done clear
  B)
  4 and 16 done clear
  C)
  2 and 16 done clear
  D)
  8 and 16 done clear
  View Solution play_arrow

• question_answer54)
  If \[a,\ b,\ c\] are in G.P., then [RPET 1995]
  A)
  \[{{a}^{2}},\ {{b}^{2}},\ {{c}^{2}}\] are in G.P. done clear
  B)
  \[{{a}^{2}}(b+c),\ {{c}^{2}}(a+b),\ {{b}^{2}}(a+c)\] are in G.P. done clear
  C)
    \[\frac{a}{b+c},\ \frac{b}{c+a},\ \frac{c}{a+b}\] are in G.P. done clear
  D)
  None of the above done clear
  View Solution play_arrow

• question_answer55)
  If x, \[{{G}_{1}}{{,}_{\ }}{{G}_{2}},\ y\]be the consecutive terms of a G.P., then the value of \[{{G}_{1}}\,{{G}_{2}}\]will be
  A)
  \[\frac{y}{x}\] done clear
  B)
  \[\frac{x}{y}\] done clear
  C)
  \[xy\] done clear
  D)
  \[\sqrt{xy}\] done clear
  View Solution play_arrow

• question_answer56)
  The sum of 3 numbers in geometric progression is 38 and their product is 1728. The middle number is [MP PET 1994]
  A)
  12 done clear
  B)
  8 done clear
  C)
  18 done clear
  D)
  6 done clear
  View Solution play_arrow

• question_answer57)
  If the product of three consecutive terms of G.P. is 216 and the sum of product of pair-wise is 156, then the numbers will be [MNR 1978]
  A)
  1, 3, 9 done clear
  B)
  2, 6, 18 done clear
  C)
  3, 9, 27 done clear
  D)
  2, 4, 8 done clear
  View Solution play_arrow

• question_answer58)
  The sum of infinity of a geometric progression is \[\frac{4}{3}\] and the first term is \[\frac{3}{4}\]. The common ratio is  [MP PET 1994]
  A)
  7/16 done clear
  B)
  9/16 done clear
  C)
  1/9 done clear
  D)
  7/9 done clear
  View Solution play_arrow

• question_answer59)
  If \[3+3\alpha +3{{\alpha }^{2}}+.........\infty =\frac{45}{8}\], then the value of \[\alpha \] will be [Pb. CET 1989]
  A)
  15/23 done clear
  B)
  7/15 done clear
  C)
  7/8 done clear
  D)
  15/7 done clear
  View Solution play_arrow

• question_answer60)
  The sum can be found of a infinite G.P. whose common ratio is \[r\] [AMU 1982]
  A)
  For all values of \[r\] done clear
  B)
  For only positive value of \[r\] done clear
  C)
  Only for \[0<r<1\] done clear
  D)
  Only for \[-1<r<1(r\ne 0)\] done clear
  View Solution play_arrow

• question_answer61)
  If \[A=1+{{r}^{z}}+{{r}^{2z}}+{{r}^{3z}}+.......\infty \], then the value of r will be
  A)
  \[A{{(1-A)}^{z}}\] done clear
  B)
  \[{{\left( \frac{A-1}{A} \right)}^{1/z}}\] done clear
  C)
  \[{{\left( \frac{1}{A}-1 \right)}^{1/z}}\] done clear
  D)
  \[A{{(1-A)}^{1/z}}\] done clear
  View Solution play_arrow

• question_answer62)
  \[x=1+a+{{a}^{2}}+....\infty \,(a<1)\]\[y=1+b+{{b}^{2}}.......\infty \,(b<1)\]Then the value of \[1+ab+{{a}^{2}}{{b}^{2}}+..........\infty \] is [MNR 1980; MP PET 1985]
  A)
  \[\frac{xy}{x+y-1}\] done clear
  B)
  \[\frac{xy}{x+y+1}\] done clear
  C)
  \[\frac{xy}{x-y-1}\] done clear
  D)
  \[\frac{xy}{x-y+1}\] done clear
  View Solution play_arrow

• question_answer63)
  The first term of a G.P. whose second term is 2 and sum to infinity is 8, will be                   [MNR 1979; RPET 1992, 95]
  A)
  6 done clear
  B)
  3 done clear
  C)
  4 done clear
  D)
  1 done clear
  View Solution play_arrow

• question_answer64)
  \[0.\overset{\,\,\,\,\bullet \,\,\,\bullet \,}{\mathop{423}}\,=\]       [Roorkee 1961; IIT 1973]
  A)
  \[\frac{419}{990}\] done clear
  B)
  \[\frac{419}{999}\] done clear
  C)
  \[\frac{417}{990}\] done clear
  D)
  \[\frac{417}{999}\] done clear
  View Solution play_arrow

• question_answer65)
  If \[y=x-{{x}^{2}}+{{x}^{3}}-{{x}^{4}}+......\infty \], then value of  x will be [MNR 1975; RPET 1988; MP PET 2002]
  A)
  \[y+\frac{1}{y}\] done clear
  B)
  \[\frac{y}{1+y}\] done clear
  C)
  \[y-\frac{1}{y}\] done clear
  D)
  \[\frac{y}{1-y}\] done clear
  View Solution play_arrow

• question_answer66)
  If \[x=\sum\limits_{n=0}^{\infty }{{{a}^{n}}},\ y=\sum\limits_{n=0}^{\infty }{{{b}^{n}},\ z=\sum\limits_{n=0}^{\infty }{{{(ab)}^{n}}}}\], where, then
  A)
  \[xyz=x+y+z\] done clear
  B)
  \[xz+yz=xy+z\] done clear
  C)
  \[xy+yz=xz+y\] done clear
  D)
  \[xy+xz=yz+x\] done clear
  View Solution play_arrow

• question_answer67)
  The sum of infinite terms of a G.P. is  and on squaring the each term of it, the sum will be , then the common ratio of this series is [RPET 1988]
  A)
  \[\frac{{{x}^{2}}-{{y}^{2}}}{{{x}^{2}}+{{y}^{2}}}\] done clear
  B)
  \[\frac{{{x}^{2}}+{{y}^{2}}}{{{x}^{2}}-{{y}^{2}}}\] done clear
  C)
  \[\frac{{{x}^{2}}-y}{{{x}^{2}}+y}\] done clear
  D)
  \[\frac{{{x}^{2}}+y}{{{x}^{2}}-y}\] done clear
  View Solution play_arrow

• question_answer68)
  If the sum of an infinite G.P. and the sum of square of its terms is 3, then the common ratio of the first series is [Roorkee 1972]
  A)
  1 done clear
  B)
  \[\frac{1}{2}\] done clear
  C)
  \[\frac{2}{3}\] done clear
  D)
  \[\frac{3}{2}\] done clear
  View Solution play_arrow

• question_answer69)
  If \[S\] is the sum to infinity of a G.P., whose first term is \[a\], then the sum of the first \[n\] terms is [UPSEAT 2002]
  A)
    \[S{{\left( 1-\frac{a}{S} \right)}^{n}}\] done clear
  B)
  \[S\left[ 1-{{\left( 1-\frac{a}{S} \right)}^{n}} \right]\] done clear
  C)
  \[a\left[ 1-{{\left( 1-\frac{a}{S} \right)}^{n}} \right]\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer70)
  0.14189189189?. can be expressed as a rational number [AMU 2000]
  A)
  \[\frac{7}{3700}\] done clear
  B)
  \[\frac{7}{50}\] done clear
  C)
  \[\frac{525}{111}\] done clear
  D)
  \[\frac{21}{148}\] done clear
  View Solution play_arrow

• question_answer71)
  The sum of the series \[5.05+1.212+0.29088+...\,\infty \] is   [AMU 2000]
  A)
  6.93378 done clear
  B)
  6.87342 done clear
  C)
  6.74384 done clear
  D)
  6.64474 done clear
  View Solution play_arrow

• question_answer72)
  The sum of an infinite geometric series is 3. A series, which is formed by squares of its terms, have the sum also 3. First series will be [UPSEAT 1999]
  A)
  \[\frac{3}{2},\frac{3}{4},\frac{3}{8},\frac{3}{16},.....\] done clear
  B)
  \[\frac{1}{2},\frac{1}{4},\frac{1}{8},\frac{1}{16},.....\] done clear
  C)
  \[\frac{1}{3},\frac{1}{9},\frac{1}{27},\frac{1}{81},.....\] done clear
  D)
  \[1,-\frac{1}{3},\,\frac{1}{{{3}^{2}}},-\frac{1}{{{3}^{3}}},.....\] done clear
  View Solution play_arrow

• question_answer73)
  Consider an infinite G.P. with first term a and common ratio r, its sum is 4 and the second term is 3/4, then [IIT Screening 2000; DCE 2001]
  A)
  \[a=\frac{7}{4},\,r=\frac{3}{7}\] done clear
  B)
  \[a=\frac{3}{2},\,r=\frac{1}{2}\] done clear
  C)
  \[a=2,\,r=\frac{3}{8}\] done clear
  D)
  \[a=3,\,r=\frac{1}{4}\] done clear
  View Solution play_arrow

• question_answer74)
  The value of\[{{a}^{{{\log }_{b}}x}}\], where \[a=0.2,\ b=\sqrt{5},\ x=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+.........\]to \[\infty \] is
  A)
  1 done clear
  B)
  2 done clear
  C)
  \[\frac{1}{2}\] done clear
  D)
  4 done clear
  View Solution play_arrow

• question_answer75)
  The value of \[{{4}^{1/3}}{{.4}^{1/9}}{{.4}^{1/27}}...........\infty \] is [RPET 2003]
  A)
  2 done clear
  B)
  3 done clear
  C)
  4 done clear
  D)
  9 done clear
  View Solution play_arrow

• question_answer76)
  If \[y=x+{{x}^{2}}+{{x}^{3}}+.......\,\infty ,\,\text{then}\,\,x=\] [DCE 1999]
  A)
  \[\frac{y}{1+y}\] done clear
  B)
  \[\frac{1-y}{y}\] done clear
  C)
  \[\frac{y}{1-y}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer77)
  If sum of infinite terms of a G.P. is 3 and sum of squares of its terms is 3, then its first term and common ratio are  [RPET 1999]
  A)
  3/2, 1/2 done clear
  B)
  1, 1/2 done clear
  C)
  3/2, 2 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer78)
  The sum of infinite terms of the geometric progression \[\frac{\sqrt{2}+1}{\sqrt{2}-1},\frac{1}{2-\sqrt{2}},\frac{1}{2}.....\] is [Kerala (Engg.) 2002]
  A)
  \[\sqrt{2}{{(\sqrt{2}+1)}^{2}}\] done clear
  B)
  \[{{(\sqrt{2}+1)}^{2}}\] done clear
  C)
  \[5\sqrt{2}\] done clear
  D)
  \[3\sqrt{2}+\sqrt{5}\] done clear
  View Solution play_arrow

• question_answer79)
  Sum of infinite number of terms in G.P. is 20 and sum of their square is 100. The common ratio of G.P. is   [AIEEE 2002]
  A)
  5 done clear
  B)
  3/5 done clear
  C)
  8/5 done clear
  D)
  1/5 done clear
  View Solution play_arrow

• question_answer80)
  If in an infinite G.P. first term is equal to the twice of the sum of the remaining terms, then its common ratio is [RPET 2002]
  A)
  1 done clear
  B)
  2 done clear
  C)
  1/3 done clear
  D)
  - 1/3 done clear
  View Solution play_arrow

• question_answer81)
  If the sum of the series \[1+\frac{2}{x}+\frac{4}{{{x}^{2}}}+\frac{8}{{{x}^{3}}}+....\infty \] is a  finite number, then [UPSEAT 2002]
  A)
  \[x>2\] done clear
  B)
  \[x>-2\] done clear
  C)
  \[x>\frac{1}{2}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer82)
   \[0.5737373......=\] [Karnataka CET 2004]
  A)
  \[\frac{284}{497}\] done clear
  B)
  \[\frac{284}{495}\] done clear
  C)
  \[\frac{568}{990}\] done clear
  D)
  \[\frac{567}{990}\] done clear
  View Solution play_arrow

• question_answer83)
  The value of \[\overline{0.037}\] where, \[\overline{.037}\] stands for the number 0.037037037........ is [MP PET 2004]
  A)
  \[\frac{37}{1000}\] done clear
  B)
  \[\frac{1}{27}\] done clear
  C)
  \[\frac{1}{37}\] done clear
  D)
  \[\frac{37}{999}\] done clear
  View Solution play_arrow

• question_answer84)
  If \[x\] is added to each of numbers 3, 9, 21 so that the resulting numbers may be in G.P., then the value of \[x\] will be [MP PET 1986]
  A)
  3 done clear
  B)
  \[\frac{1}{2}\] done clear
  C)
  2 done clear
  D)
  \[\frac{1}{3}\] done clear
  View Solution play_arrow

• question_answer85)
  If s is the sum of an infinite G.P., the first term a then the common ratio r given by [J & K 2005]
  A)
  \[\frac{a-s}{s}\] done clear
  B)
  \[\frac{s-a}{s}\] done clear
  C)
  \[\frac{a}{1-s}\] done clear
  D)
  \[\frac{s-a}{a}\] done clear
  View Solution play_arrow

• question_answer86)
  The sum to infinity of the progression \[9-3+1-\frac{1}{3}+.....\] is  [Karnataka CET 2005]
  A)
  9 done clear
  B)
  9/2 done clear
  C)
  27/4 done clear
  D)
  15/2 done clear
  View Solution play_arrow

• question_answer87)
  If \[{{a}^{2}}+a{{b}^{2}}+16{{c}^{2}}=2(3ab+6bc+4ac)\], where \[a,b,c\] are non-zero numbers. Then \[a,b,c\]are in [AMU 2005]
  A)
   A.P done clear
  B)
  G.P done clear
  C)
  H.P done clear
  D)
    None of these done clear
  View Solution play_arrow

• question_answer88)
  The product (32)(32) 1/6(32)1/36 ...... to \[\infty \] is  [Kerala (Engg.) 2005]
  A)
  16 done clear
  B)
    32 done clear
  C)
  64 done clear
  D)
  0 done clear
  E)
  62 done clear
  View Solution play_arrow