11th Class Mathematics Sequence and Series Question Bank

done Sequence and Series Total Questions - 40

• question_answer1)
  Which among the following is an Arithmetic progression?
  A)
  \[\frac{1}{2},\frac{7}{10},\frac{9}{10},1,....\]     done clear
  B)
         \[\sqrt{3},\sqrt{27},\sqrt{75},\sqrt{147},...\] done clear
  C)
  \[{{2}^{3}},{{2}^{6}},{{2}^{9}},{{2}^{12}},...\]       done clear
  D)
  \[-\,2,\text{ }0,\,-2,\text{ }0,\,-2,\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer2)
  If \[\mathbf{1}{{\mathbf{8}}^{\mathbf{th}}}\mathbf{term}\text{ }\mathbf{of}\text{ }\mathbf{an}\text{ }\mathbf{A}.\mathbf{P}.\text{ }\mathbf{is}\text{ }\mathbf{26}\text{ }\mathbf{and}\text{ }\mathbf{3}{{\mathbf{2}}^{\mathbf{th}}}\]of an A.P. is - 16, of the A.P. is______
  A)
  \[-\]51                done clear
  B)
  51           done clear
  C)
  \[-\]27                            done clear
  D)
   77 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer3)
  Find the sum of n terms of the series whose \[{{n}^{th}}\] term is 3n - 2.
  A)
  \[\frac{n}{2}(3n-1)\]     done clear
  B)
  \[\frac{n}{2}(3n+1)\]     done clear
  C)
  \[\frac{n}{2}(3n-3)\]       done clear
  D)
  \[\frac{n}{2}(2n-1)\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer4)
  If \[{{\mathbf{S}}_{\mathbf{n}}}\]of a series is \[\frac{\mathbf{35n}}{\mathbf{2}}\mathbf{-}\frac{\mathbf{7}{{\mathbf{n}}^{\mathbf{2}}}}{\mathbf{2}}\] then find its 7th term.
  A)
  -21                     done clear
  B)
  35           done clear
  C)
  18                                 done clear
  D)
  -28 done clear
  E)
  None of these done clear
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• question_answer5)
  The sum of the first three terms \[\mathbf{(}{{\mathbf{S}}_{\mathbf{3}}}\mathbf{)}\] of on A.P. is 108 and if it is given that \[{{\mathbf{a}}_{\mathbf{1}}}{{\mathbf{a}}_{\mathbf{2}}}+\text{ }{{\mathbf{S}}_{\mathbf{3}}}\]= 0 then find the value of its seventh term where \[{{a}_{1}},\text{ }{{a}_{2}}\] are first and second term of the A.P.
  A)
  225                   done clear
  B)
  231      done clear
  C)
  216                               done clear
  D)
  229 done clear
  E)
  None of these done clear
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• question_answer6)
  The trees of a row of a garden are numbered consecutively from 1 to 49. There is a value of p such that the sum of the numbers of trees preceding the tree numbered p is equal to the sum of the numbers of the houses following it, then value of p is:  
  A)
  25                                                                     done clear
  B)
  35     done clear
  C)
  28                                                                     done clear
  D)
  22 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer7)
  Find the sum of all three-digit numbers which are divisible by 3.
  A)
  165150  done clear
  B)
   195240       done clear
  C)
   199950             done clear
  D)
         201750 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer8)
  The sum of the 7th and 9th term of an A.P. is 82 and the 10th term is 56. The first term of this A.P. is _______
  A)
  7.5                                                                    done clear
  B)
  \[-\]7.5          done clear
  C)
  \[-\]11.5   done clear
  D)
  15 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer9)
  Split 312 into three distinct parts such that these are in A.P. and the product of its smeller parts is 9880. Find the value of its largest part.
  A)
  102  done clear
  B)
                                                                     109        done clear
  C)
  113       done clear
  D)
                                                        108 done clear
  E)
  None of these done clear
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• question_answer10)
  If \[\mathbf{1}{{\mathbf{2}}^{\mathbf{th}}}\]term of an A.P. is zero then its \[\mathbf{2}{{\mathbf{2}}^{\mathbf{nd}}}\] term is one third of its ________
  A)
  \[{{45}^{th}}\] term  done clear
  B)
                                 \[{{36}^{th}}term\]     done clear
  C)
  \[{{44}^{th}}term\]    done clear
  D)
                                             \[{{42}^{nd}}term\] done clear
  E)
  None of these done clear
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• question_answer11)
  Find the sum of those numbers, which lie between 400 and 900 (including both) and leave a remainder 4 on dividing by 7.
  A)
  41302    done clear
  B)
      46609    done clear
  C)
    46908       done clear
  D)
                     48708 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer12)
  If\[\frac{{{\mathbf{p}}^{\mathbf{n-1}}}\mathbf{+}{{\mathbf{q}}^{\mathbf{n-1}}}}{{{\mathbf{p}}^{\mathbf{n-2}}}\mathbf{+}{{\mathbf{q}}^{\mathbf{n-2}}}}\]is the arithmetic mean between p and q then find the value of n.
  A)
  0    done clear
  B)
                                                                     1     done clear
  C)
        2          done clear
  D)
                                 3 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer13)
  The sum of first eight terms of an A.P. is 66 and the ratio of its \[\mathbf{1}{{\mathbf{3}}^{\mathbf{th}}}\]term to its \[\mathbf{2}{{\mathbf{1}}^{\mathbf{st}}}\]term is 7:11. Find the sum of first 31 terms of this A.P.
  A)
  885       done clear
  B)
                                                         765   done clear
  C)
       668          done clear
  D)
         826 done clear
  E)
  None of these done clear
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• question_answer14)
  If the \[{{\mathbf{p}}^{\mathbf{th}}}\]term of an A.P. is \[\frac{\mathbf{1}}{\mathbf{q}}\] and \[{{\mathbf{q}}^{\mathbf{th}}}\]term is \[\frac{\mathbf{1}}{\mathbf{p}}\] then sum of its pq terms is
  A)
  \[\frac{1}{2}(p+q)\]        done clear
  B)
   \[\frac{1}{2}(pq+1)\] done clear
  C)
  \[\frac{1}{2}pq\] done clear
  D)
                                                                     \[\frac{1}{2}q\] done clear
  E)
  None of these done clear
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• question_answer15)
  If the ratio of the sums of \[{{\mathbf{m}}^{\mathbf{2}}}\] and \[{{\mathbf{n}}^{\mathbf{2}}}\] of an AP is \[{{\mathbf{m}}^{\mathbf{3}}}:\text{ }{{\mathbf{n}}^{\mathbf{3}}}\], the of its \[{{\mathbf{m}}^{\mathbf{2}}}\] and \[{{\mathbf{n}}^{\mathbf{2}}}\] terms is ______
  A)
  \[\frac{2{{m}^{2}}+mn}{2{{n}^{2}}+mn}\]    done clear
  B)
                                 \[\frac{2{{m}^{2}}+mn-1}{2{{n}^{2}}+mn-1}\] done clear
  C)
  \[\frac{{{m}^{2}}+mn-2}{{{n}^{2}}+mn-2}\]     done clear
  D)
         \[\frac{2{{m}^{2}}+mn+1}{2{{n}^{2}}+mn+1}\] done clear
  E)
  None of these done clear
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• question_answer16)
  If there are (2n - 1) terms in an A.P., the of the of its terms to its even terms is _____
  A)
  \[\frac{n+1}{n}\]           done clear
  B)
  \[\frac{n-1}{n}\]        done clear
  C)
  \[\frac{n}{n-1}\]       done clear
  D)
         \[\frac{n}{n+1}\] done clear
  E)
  None of these done clear
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• question_answer17)
  315 workers were engaged to finish a piece of work in a fixed number of days. Four workers were dropped the second day, four more workers were dropped the third day and so on. Thus, it took 8 more days to complete the work. Find the number of days in which the work was completed.
  A)
  33      done clear
  B)
                                                         42      done clear
  C)
     36      done clear
  D)
                                             39 done clear
  E)
  None of these done clear
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• question_answer18)
  The ratio of the sum of n terms of two arithmetic progressions is (5n + 1): (2n + 15). Find the ratio of their \[{{\mathbf{m}}^{\mathbf{th}}}\]terms.
  A)
  \[\frac{10m-4}{4m+13}\]           done clear
  B)
                     \[\frac{5m+3}{7m+11}\]     done clear
  C)
  \[\frac{7m-3}{5m+13}\]             done clear
  D)
                     \[\frac{4m-5}{3n+11}\] done clear
  E)
  None of these done clear
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• question_answer19)
  In an A.P., the sum of its first n terms is \[\frac{\mathbf{5}{{\mathbf{n}}^{\mathbf{2}}}}{\mathbf{3}}\mathbf{+}\frac{\mathbf{13n}}{\mathbf{5}}\]. Find its \[{{\mathbf{n}}^{\mathbf{th}}}\]terms.
  A)
  \[\frac{50n-14}{15}\]      done clear
  B)
  \[\frac{50n+14}{15}\]    done clear
  C)
  \[\frac{64(2n-1)}{15}\]                done clear
  D)
                     \[\frac{64(2n+1)}{15}\] done clear
  E)
  None of these done clear
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• question_answer20)
  If the sum of m, 2m, 3m terms of an A.P. are \[{{\mathbf{S}}_{\mathbf{1}}},{{\mathbf{S}}_{\mathbf{2}}},{{\mathbf{S}}_{\mathbf{3}}}\] respectively, then (\[{{\mathbf{S}}_{\mathbf{2}}}-{{\mathbf{S}}_{\mathbf{1}}}\]) equals to __
  A)
  2\[{{S}_{3}}\]           done clear
  B)
                                                         3\[{{S}_{3}}\]       done clear
  C)
    \[\frac{{{s}_{3}}}{2}\]           done clear
  D)
                                 \[\frac{{{s}_{3}}}{3}\] done clear
  E)
  None of these done clear
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• question_answer21)
  If the sum of the first m, n, r terms of an A.P. are a, b, c respectively, then\[\frac{\mathbf{a}}{\mathbf{3}}\mathbf{(n-r)+}\frac{\mathbf{b}}{\mathbf{n}}\mathbf{(r-m)+}\frac{\mathbf{c}}{\mathbf{r}}\mathbf{(m-n)}\] equals to ________
  A)
  0    done clear
  B)
                                                                     1 done clear
  C)
  m + n + r        done clear
  D)
                                             2 done clear
  E)
  None of these done clear
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• question_answer22)
  If sum of first p terms of an A.P. is equal to q and the sum of first q terms of it is equal to p, then find the sum of (p + q) terms of this A.P.
  A)
  \[p+q\]      done clear
  B)
                                                         \[-\left( p\text{ }+\text{ }q \right)\] done clear
  C)
  \[\text{ }p+q\]              done clear
  D)
                                             1 done clear
  E)
  None of these done clear
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• question_answer23)
  If \[\mathbf{1}{{\mathbf{9}}^{\mathbf{th}}}\] term of an A.P. is 544 and \[\mathbf{54}{{\mathbf{4}}^{\mathbf{th}}}\] term is 19 then find the term which is equal to zero?
  A)
  525           done clear
  B)
                                 563       done clear
  C)
  562         done clear
  D)
                                                         544 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer24)
  Sum of n terms of the series \[\sqrt{\mathbf{80}}\mathbf{,}\sqrt{\mathbf{45}}\mathbf{,}\sqrt{\mathbf{20}}\mathbf{,}.......\] is ______
  A)
  \[\frac{\sqrt{5n}}{2}(9-n)\]          done clear
  B)
  \[4\sqrt{5}(9-n)\] done clear
  C)
  \[2\sqrt{5}(9-n)\]   done clear
  D)
                                                         \[3\sqrt{5}(3-n)\] done clear
  E)
  None of these done clear
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• question_answer25)
  If p, q, r are in A.P., then q + r, r + p and p + q are in __
  A)
  arithmetic progression     done clear
  B)
  geometric progression done clear
  C)
  harmonic progression           done clear
  D)
  arithmetic-geometric progression done clear
  E)
  None of these done clear
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• question_answer26)
  If \[{{\mathbf{a}}^{\mathbf{th}}},\text{ }{{\mathbf{b}}^{\mathbf{th}}}\mathbf{and}\text{ }{{\mathbf{c}}^{\mathbf{th}}}\]terms of an H.P. are p, q and r respectively, the value of \[\mathbf{qr}\,\,\left( \mathbf{b}-\mathbf{c} \right)+\mathbf{pr}\,\,\left( \mathbf{c}-\mathbf{a} \right)+\mathbf{pq}\text{ }\left( \mathbf{a}-\mathbf{b} \right)\]
  A)
  -1                                                                     done clear
  B)
  1             done clear
  C)
   0            done clear
  D)
  2q done clear
  E)
  None of these done clear
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• question_answer27)
  If (a + 1), (b + 1), (c + 1), (d + 1) are in G.P., then \[{{\left( \mathbf{b}+\mathbf{c}+\mathbf{2} \right)}^{\mathbf{2}}}=\]_________
  A)
  (a + b + 2) (b + c + 2)          done clear
  B)
  \[\left( a\text{ }+\text{ }b\text{ }+\text{ }1 \right)\text{ }{{\left( c\text{ }+\text{ }d\text{ }+\text{ }1 \right)}^{2}}\] done clear
  C)
  (a+b+2) (b+c+2)                                              done clear
  D)
  (a + b + 1) (b + c + 1) done clear
  E)
  None of these done clear
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• question_answer28)
  Find the value of P, if P = 1+ (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4) +..... + (1 + 2+3+.....+25)
  A)
  2715                                                                 done clear
  B)
   2925         done clear
  C)
  3055                                                                 done clear
  D)
  2655 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer29)
  Find the sum to n terms of the following series. 3 + 33 + 333 + .........
  A)
  \[\frac{10}{27}({{10}^{n}}-1)\]                                                            done clear
  B)
  \[\frac{50}{81}({{10}^{n}}-1)-\frac{5n}{9}\] done clear
  C)
  \[\frac{10}{27}({{10}^{n}}-1)-\frac{n}{3}\]  done clear
  D)
  \[\frac{50}{81}({{10}^{n}}-1)\] done clear
  E)
  None of these done clear
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• question_answer30)
  If the first and 10th terms of a G.P. are \[\frac{{{\mathbf{q}}^{\mathbf{6}}}}{{{\mathbf{q}}^{\mathbf{5}}}}\] and  \[\frac{{{\mathbf{p}}^{\mathbf{4}}}}{{{\mathbf{q}}^{\mathbf{3}}}}\] , then find the ratio between its 6th to 7th term.
  A)
  \[\frac{{{q}^{2}}}{{{p}^{3}}}\]                                                        done clear
  B)
  \[\frac{q}{{{p}^{2}}}\]           done clear
  C)
   \[\frac{q}{p}\]           done clear
  D)
                     \[\frac{{{p}^{2}}}{q}\] done clear
  E)
  None of these done clear
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• question_answer31)
  If \[\mathbf{A=5+}\frac{\mathbf{5}}{\mathbf{B}}\mathbf{+}\frac{\mathbf{5}}{{{\mathbf{B}}^{\mathbf{2}}}}\mathbf{+}\frac{\mathbf{5}}{{{\mathbf{B}}^{\mathbf{3}}}}\mathbf{+}.....\infty \]then the value of B is________
  A)
  \[\frac{-A}{A-5}\]                                                           done clear
  B)
  \[\frac{A}{A-5}\]        done clear
  C)
  \[\frac{A}{A+5}\]                                                          done clear
  D)
  \[\frac{-A}{A+5}\] done clear
  E)
   None of these done clear
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• question_answer32)
  If \[\mathbf{Q=}\frac{\mathbf{3}}{\sqrt{\mathbf{3}}}\mathbf{+1+}\frac{\mathbf{1}}{\sqrt{\mathbf{3}}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{3}}\mathbf{+}......\]\[\infty \]then find the value of \[\mathbf{Q}-\frac{\mathbf{1}}{\mathbf{Q}}\]
  A)
  \[\frac{3\sqrt{3}-1}{6}\]                                                             done clear
  B)
   \[\frac{7\sqrt{3}+11}{6}\] done clear
  C)
  \[\frac{3\sqrt{3}+1}{6}\]                                                            done clear
  D)
   \[\frac{7\sqrt{3}-11}{6}\] done clear
  E)
  None of these done clear
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• question_answer33)
  Find the value of x (where \[\mathbf{o}{}^\circ <\mathbf{x}<\mathbf{90}{}^\circ )\]if \[\mathbf{3}{{\mathbf{2}}^{\mathbf{1}+\,\,\mathbf{sinx}\,+\,\,\mathbf{s}i{{\mathbf{n}}^{\mathbf{2}}}\mathbf{x}\,+\,\,......\infty }}\] =1024
  A)
  \[30{}^\circ \]   done clear
  B)
  \[45{}^\circ \]           done clear
  C)
  \[60{}^\circ \]                                                               done clear
  D)
  \[15{}^\circ \] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer34)
  Find the value of 7th term of the series.
  A)
  \[\frac{-12}{11}\]  done clear
  B)
  \[-\]24          done clear
  C)
   \[-\]16                                                               done clear
  D)
  \[\frac{-12}{7}\] done clear
  E)
  None of these done clear
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• question_answer35)
  If p, q and r are in Harmanic Progression, then, \[\frac{\mathbf{p}}{\mathbf{q+r}}\mathbf{,}\frac{\mathbf{q}}{\mathbf{p+r}}\] and \[\frac{\mathbf{r}}{\mathbf{p+q}}\] are in ______
  A)
  arithmetic progression                              done clear
  B)
  geometric progression  done clear
  C)
  harmonic progression        done clear
  D)
  arithmetic-geometric progression done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer36)
  If A, G and H are respectively arithmetic, geometric and harmonic means between two distinct positive real numbers p and q, then which one of the following is incorrect?
  A)
  \[{{G}^{2}}=AH\]                                                       done clear
  B)
  \[A-G>0\] done clear
  C)
  \[G-H>0\]                                                          done clear
  D)
  \[A<G<H\] done clear
  E)
  None of these done clear
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• question_answer37)
  If p, q and r are the \[{{\mathbf{a}}^{\mathbf{th}}},\text{ }{{\mathbf{b}}^{\mathbf{th}}}\mathbf{and}\text{ }{{\mathbf{c}}^{\mathbf{th}}}\] terms respectively of an A.P. as well as G.P., then the value of \[{{\mathbf{p}}^{\mathbf{q}-\mathbf{r}}},\text{ }{{\mathbf{q}}^{\mathbf{r}-\mathbf{p}}},\text{ }{{\mathbf{r}}^{\mathbf{p}-\mathbf{q}}}\] equals to ______
  A)
  0                                                                      done clear
  B)
  1            done clear
  C)
  \[-\,1\]                                                               done clear
  D)
  2 done clear
  E)
  None of these done clear
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• question_answer38)
  On inserting 5 Arithmetic means between 3 and 27, the sum of these five terms is equal to ______
  A)
  six times the A.M. between 3 and 27                     done clear
  B)
  five times the A.M. between 3 and 27 done clear
  C)
   105                                                                  done clear
  D)
   72 done clear
  E)
   None of these done clear
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• question_answer39)
  The Arithmetic Mean of two numbers is 5 more than geometric Mean and 9.8 more than harmonic mean. Find the numbers.
  A)
  20, 80                                                               done clear
  B)
  30, 120 done clear
  C)
   90, 160             done clear
  D)
  160, 250 done clear
  E)
  None of these done clear
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• question_answer40)
  If third and eighth terms of a Geometric progression are\[\frac{\mathbf{3}}{\mathbf{16}}\] and 6 respectively, then find the \[\mathbf{1}{{\mathbf{0}}^{\mathbf{th}}}\] term of the series.
  A)
  16                                                                     done clear
  B)
  \[\frac{1}{8}\]            done clear
  C)
  \[\frac{1}{12}\]                                      done clear
  D)
  24 done clear
  E)
  None of these done clear
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