11th Class Mathematics Sequence and Series Question Bank

done Sequence and Series (A.P., G.P. and H.P.) Total Questions - 30

• question_answer1)
  In which of the following situations, does the list of numbers involved does not make an arithmetic progression?

  (i) The taxi fare after each km when the fare is Rs. 20 for the first km and Rs. 11 for each additional km.

  (ii) The amount of air present in a cylinder when a vacuum pump removes \[\frac{1}{4}\]of the air remaining in the cylinder at a time.

  (iii) The cost of digging a well after every metre of digging, when it cost Rs. 250 for the metre and rises by Rs. 40 for each subsequent metre.

  (iv) The amount of money in the account every year, when Rs. 8000 is deposited at compound interest at 10% per annum.

  A)
   (i) & (ii)                        done clear
  B)
   (ii) & (iv)    done clear
  C)
   (iii) & (i)                        done clear
  D)
   (i) & (iv) done clear
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• question_answer2)
  Which of the following are APs?

  (i) \[\sqrt{2},\sqrt{8},\sqrt{18},\sqrt{32},....\]

  (ii) \[\sqrt{3},\sqrt{6},\sqrt{9},\sqrt{12},....\]

  (iii) \[{{1}^{2}},{{3}^{2}},{{5}^{2}},{{7}^{2}},.....\]

  (iv) \[{{1}^{2}},{{5}^{2}},{{7}^{2}},73,.....\]

  A)
   (i) & (ii)                        done clear
  B)
   (i) & (iii)             done clear
  C)
   (i) & (iv)       done clear
  D)
   (ii) & (iv) done clear
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• question_answer3)
  Choose the correct choice in the following 11th term of the\[AP-3,-\frac{1}{2},2,\]....... is
  A)
   28                                done clear
  B)
   22    done clear
  C)
   - 38                             done clear
  D)
   \[-48\frac{1}{2}\] done clear
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• question_answer4)
  Which term of the AP 3, 8, 13, 18,..........is 78?
  A)
   10th                              done clear
  B)
   12th                 done clear
  C)
   14th                              done clear
  D)
   16th done clear
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• question_answer5)
  Find the number of terms in the following AP: \[18,15\frac{1}{2},13,......-47\]
  A)
   21                                done clear
  B)
   25               done clear
  C)
   31                                done clear
  D)
   27 done clear
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• question_answer6)
  150 is a term of the AP 11, 8, 5, 2,.........
  A)
   yes                               done clear
  B)
   no done clear
  C)
   - 148 is not a term of this A.P.            done clear
  D)
   - 149 is a term of this AP. done clear
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• question_answer7)
  If the 3rd and 9th terms of an AP are 4 and - 8 respectively, which term of this AP is zero?
  A)
   4th                                done clear
  B)
   5th      done clear
  C)
   6th                                done clear
  D)
   7th done clear
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• question_answer8)
  Which term of the AP 3, 15, 27, 39,......will be 132 more than its 54th  term?
  A)
   55th                              done clear
  B)
   60th                 done clear
  C)
   65th        done clear
  D)
   70th done clear
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• question_answer9)
  Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?
  A)
   100          done clear
  B)
   1000              done clear
  C)
   1200               done clear
  D)
   10000 done clear
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• question_answer10)
  How many three digit numbers are divisible by 7?
  A)
   102                              done clear
  B)
   114              done clear
  C)
   126                  done clear
  D)
   128 done clear
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• question_answer11)
  For what value of n, are the nth terms of the APs 63, 65, 67,... and 3, 10, 17 equal?
  A)
   n = 6                           done clear
  B)
   n = 12             done clear
  C)
   n = 13    done clear
  D)
   n = 16 done clear
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• question_answer12)
  Find the 20th term from the last term of the AP 3, 8, 13,.?. 253.
  A)
   196                              done clear
  B)
   158   done clear
  C)
   148                  done clear
  D)
   138 done clear
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• question_answer13)
  The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
  A)
   - 13, - 8, - 3                done clear
  B)
   - 24, - 18, -12 done clear
  C)
   6, 12, 18                      done clear
  D)
   0, 2, 4 done clear
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• question_answer14)
  Given \[a=3,d=10,{{S}_{n}}=168\] find n and \[{{a}_{6}}\].
  A)
   6, 53         done clear
  B)
   7, 54              done clear
  C)
   8, 86               done clear
  D)
   9, 90 done clear
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• question_answer15)
  In the series, \[{{T}_{n}}=2n+5\], find \[{{S}_{4}}\].
  A)
   20                                done clear
  B)
   40    done clear
  C)
   60                                done clear
  D)
   80 done clear
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• question_answer16)
  Find the 21st term of an AP whose first term is 4 and the common difference is 3.
  A)
   57                                done clear
  B)
   60                done clear
  C)
   66                    done clear
  D)
   64 done clear
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• question_answer17)
  Find the sum of 100 terms of the series \[1\left( 3 \right)+3\left( 5 \right)+5\left( 7 \right)+.....\]
  A)
   1353300      done clear
  B)
   1253300           done clear
  C)
   1453300                       done clear
  D)
   1753300 done clear
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• question_answer18)
  Divide 124 into four parts in such way that they are in AP and the product of the first and the 4th part is 128 less than the product of the 2nd and the 3rd parts, the parts are:
  A)
   27, 35, 45, 17               done clear
  B)
   19, 27, 35, 43   done clear
  C)
   21, 29, 33, 41               done clear
  D)
   13, 33, 37, 41 done clear
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• question_answer19)
  If \[\left| x \right|<1\], then find the sum of the series \[1+2x+3{{x}^{2}}+4{{x}^{3}}+\] ....... up to \[\infty \]
  A)
   \[\frac{2}{1-{{x}^{2}}}\]                    done clear
  B)
   \[\frac{3}{{{(1-x)}^{2}}}\] done clear
  C)
   \[\frac{x}{1-{{x}^{2}}}\]                    done clear
  D)
   \[\frac{x}{{{(1-x)}^{2}}}\] done clear
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• question_answer20)
  If \[\frac{5+9+13+....to\,\,n\,\,terms}{7+9+11+.....to\,\,(n+1)terms}=\frac{17}{16}\] then n =
  A)
   7            done clear
  B)
   9                done clear
  C)
   11                    done clear
  D)
   13            done clear
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• question_answer21)
  Find the 20th term of the HP \[-2,6,\frac{6}{5},\frac{2}{3},.....\]
  A)
   \[\frac{3}{13}\]                         done clear
  B)
   \[\frac{6}{73}\] done clear
  C)
   \[\frac{3}{87}\]                         done clear
  D)
   \[\frac{6}{97}\] done clear
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• question_answer22)
  For a sequence in AP, the sum of n terms of the sequence is \[3n-{{n}^{2}}\], then find the 101st term of the sequence,                                                               
  A)
   201                              done clear
  B)
   - 201               done clear
  C)
   - 198    done clear
  D)
   + 198          done clear
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• question_answer23)
  Find the three numbers which are in GP such that their is 31 and their product is 125. The three numbers are:
  A)
   (1, 5, 25) done clear
  B)
   (6, 32, 128)         done clear
  C)
   (4, 10, 17)                    done clear
  D)
   (2, 8, 21) done clear
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• question_answer24)
  There is a sequence of slumbers such that they are m GP and sum to infinite of the numbers of terms of the sequence is 6 and the sum of their squares up to infinite terms is 18. The first term of the sequence is given by:
  A)
   16                                done clear
  B)
   4    done clear
  C)
   6                                 done clear
  D)
   1/3 done clear
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• question_answer25)
  If the three terms p, q, t are the\[{{\text{m}}^{\text{th}}}\],\[{{\text{n}}^{\text{th}}}\] and \[~{{\text{s}}^{\text{th}}}\]terms of GP. Then, the value of \[{{p}^{n-s}}.{{q}^{s-m}}.{{r}^{m-n}}\]
  A)
   1        done clear
  B)
   2                 done clear
  C)
   4                                 done clear
  D)
   0 done clear
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• question_answer26)
  The harmonic mean between two numbers is \[9\frac{8}{13}\] and geometric mean is 25. The two numbers are:
  A)
   (6 and 16)         done clear
  B)
   (6 and 60)          done clear
  C)
   (5 and 125)     done clear
  D)
   (8 and 216) done clear
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• question_answer27)
  If\[{{\text{p}}^{\text{th}}}\]  term of HP is equal to q and the \[{{\text{q}}^{\text{th}}}\]term of HP is equal to p, then \[{{\left( p+q \right)}^{th}}\] term of the series is
  A)
   \[\frac{pq}{p+q}\] done clear
  B)
   \[\frac{{{p}^{2}}-{{q}^{2}}}{p+q}\] done clear
  C)
   \[\frac{{{p}^{2}}-{{q}^{2}}}{p-q}\]              done clear
  D)
   \[\frac{{{p}^{2}}-{{q}^{2}}}{{{p}^{3}}-{{q}^{3}}}\] done clear
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• question_answer28)
  If in an A.P., \[{{S}_{n}}={{n}^{2}}p\] and \[{{S}_{m}}={{m}^{2}}p\], where \[{{S}_{r}}\] denotes the sum of r terms of the A.P.,  then \[{{S}_{p}}\] is equal to
  A)
   \[(m-n){{p}^{2}}\]                  done clear
  B)
   \[{{p}^{3}}\] done clear
  C)
   \[{{p}^{2}}m\]                                   done clear
  D)
   \[\frac{1}{8}{{p}^{3}}\] done clear
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• question_answer29)
  A number of bricks are arranged in a compete pyramid on a square base of side 13 cm. when each brick is a cube of 1 cm, then total number of bricks used, is given by
  A)
   1027                            done clear
  B)
   819         done clear
  C)
   313                 done clear
  D)
   727 done clear
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• question_answer30)
  Insert two harmonic means between \[\frac{1}{20}\] and \[\frac{1}{32}\]
  A)
   \[\frac{1}{24},\frac{1}{26}\]                 done clear
  B)
   \[\frac{1}{24},\frac{1}{28}\] done clear
  C)
   \[\frac{1}{26},\frac{1}{30}\]                 done clear
  D)
   \[\frac{1}{30},\frac{1}{31}\] done clear
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