10th Class Mathematics Arithmetic Progressions Question Bank

done Arithmetic Progressions Total Questions - 25

• question_answer1)
  If 9th term of an A.P. is zero, then its 29th; term is _____ its 19th term.           
  A)
  Thrice of          done clear
  B)
  Twice of      done clear
  C)
         Half of          done clear
  D)
          Equal to                      done clear
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• question_answer2)
  Find the sum of first 20 terms of an A.P. whose nth term is given by \[{{T}_{n}}=(7-3n).\];
  A)
  382                  done clear
  B)
         \[-490\]            done clear
  C)
  420                  done clear
  D)
         \[-382\]            done clear
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• question_answer3)
  In an A.P., the sum of first n terms is \[\frac{3{{n}^{2}}}{2}+\frac{13n}{2}.\]Find its 25th term.             
  A)
  80                    done clear
  B)
         120      done clear
  C)
  60                    done clear
  D)
          78       done clear
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• question_answer4)
  Which term of the A.P. \[5,2,-1,\]....... is\[-22\]?                              
  A)
  9                      done clear
  B)
         11        done clear
  C)
  10                    done clear
  D)
          7         done clear
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• question_answer5)
  The sum of all terms of the arithmetic progression having ten terms except for the first term, is 99, and except for the sixth term, is 89. Find the 8th term of the progression if the sum of the first and the fifth term is equal to 10.                
  A)
  15                    done clear
  B)
  25        done clear
  C)
  18                    done clear
  D)
          10       done clear
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• question_answer6)
  The 2nd, 31st and the last term of an AP are \[7\frac{3}{4},\frac{1}{2}\]and \[-6\frac{1}{2},\]respectively. Find the number of terms.                   
  A)
  60                    done clear
  B)
  59        done clear
  C)
                     65                    done clear
  D)
          45 done clear
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• question_answer7)
  In an A.P., if the \[{{p}^{th}}\] term is 'q' and the \[{{q}^{th}}\] term is 'p', then its \[{{n}^{th}}\] term is _____.
  A)
  \[p+q-n\]         done clear
  B)
  \[p+q+n\]       done clear
  C)
         \[p-q+n\]       done clear
  D)
         \[p-q-n\]           done clear
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• question_answer8)
  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 is equal to _____.
  A)
  \[\frac{1}{2}{{p}^{3}}\]                 done clear
  B)
  \[mnp\] done clear
  C)
         \[{{p}^{3}}\]                        done clear
  D)
          \[(m+n){{p}^{2}}\]            done clear
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• question_answer9)
  An A.P. consists of 21 terms. The sum of the three terms in the middle is 129 and of the last three is 237. Find the A.P.                
  A)
  4, 8, 12, 16     done clear
  B)
  3, 6, 9, 12        done clear
  C)
         4, 7, 10, 13     done clear
  D)
         3, 7, 11, 15      done clear
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• question_answer10)
  If \[x\ne y\] and the sequences x, \[{{a}_{1}},{{a}_{2}},y\] and x, \[{{b}_{1}},{{b}_{2}},\]y each are in A.P., then \[\left( \frac{{{a}_{2}}-{{a}_{1}}}{{{b}_{2}}-{{b}_{1}}} \right)\] is _____.
  A)
  \[\frac{2}{3}\]                         done clear
  B)
  \[\frac{3}{2}\]             done clear
  C)
  1                      done clear
  D)
          \[\frac{3}{4}\]            done clear
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• question_answer11)
  The ratio of the sum of m and n terms of an A.P. is m2: n2, then find the ratio of \[{{m}^{th}}\]and \[{{n}^{th}}\] terms.
  A)
  \[2m+1:2n+1\]           done clear
  B)
  \[2m-1:2n-1\]   done clear
  C)
  \[2m:n\]            done clear
  D)
          \[m:n\] done clear
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• question_answer12)
              Four numbers are inserted between the numbers 4 and 39 such that an A.P. results. Find the biggest of these four numbers.
  A)
  33                                done clear
  B)
  31                    done clear
  C)
         32                    done clear
  D)
          30                   done clear
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• question_answer13)
  If the \[{{m}^{th}}\] term of an A.P. is \[\frac{1}{n}\] and \[{{n}^{th}}\] term is \[\frac{1}{m}\], then the sum of first mn terms is ___.
  A)
  \[mn+1\]        done clear
  B)
  \[\frac{mn+1}{2}\]    done clear
  C)
  \[\frac{mn-1}{2}\]        done clear
  D)
   \[\frac{mn-1}{3}\]                 done clear
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• question_answer14)
  If 'a' is the A.M. of 3 numbers and 'b' is the A.M. of their squares, then the A.M. of their pair-wise products In terms of a and b is _____.
  A)
  \[\frac{3{{a}^{2}}+b}{2}\]            done clear
  B)
  \[\frac{3{{a}^{2}}-b}{2}\]  done clear
  C)
  \[\frac{b-3{{a}^{2}}}{2}\]              done clear
  D)
          \[\frac{{{b}^{2}}-3{{a}^{2}}}{2}\]       done clear
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• question_answer15)
  A circle with area \[{{A}_{1}}\] is contained in the interior of a larger circle with area \[{{A}_{1}}+{{A}_{2}}.\] If the radius of the larger circle is 3 units and \[{{A}_{1}},{{A}_{2}},{{A}_{1}}+{{A}_{2}}\]are in A.P., then the radius of the smaller circle is ___.
  A)
  \[\sqrt{2}\] units     done clear
  B)
         1 unit   done clear
  C)
  2 units          done clear
  D)
  \[\sqrt{3}\] units done clear
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• question_answer16)
  The production of TV in a factory increases uniformly by a fixed number every year. It produced 8000 sets in 6th year and 11300 in 9th year. Find the production in the 6 years.
  A)
  40500              done clear
  B)
  20000              done clear
  C)
         20500         done clear
  D)
         31500                          done clear
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• question_answer17)
  Deepak repays his total loan of Rs.1,18,000 by paying every month starting with the first instalment of Rs.1000. If he increases the instalment by Rs.100 every month, what amount will be paid as the last instalment of loan?
  A)
  Rs.4900          done clear
  B)
  Rs.5400       done clear
  C)
                     Rs.3500          done clear
  D)
         Rs.4500           done clear
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• question_answer18)
  A manufacturer of laptop produced 6000 units in 3rd year and 7000 units in the 7th year. Assuming that production increases uniformly by a fixed number every year, find the production in the 5th year.       
  A)
  6500 units        done clear
  B)
  5000 units        done clear
  C)
  6000 units    done clear
  D)
   8000 units done clear
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• question_answer19)
  Raghav buys a shop for Rs. 120000. He pays half of the amount in cash and agrees to pay the balance in 12 annual instalments of Rs. 5000 each. If the rate of interest Is 12% and he pays the interest due on the unpaid amount with the instalment. Find the total cost of the shop.
  A)
  Rs.156800                   done clear
  B)
  Rs.156700       done clear
  C)
         Rs.165200        done clear
  D)
          Rs.166800                  done clear
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• question_answer20)
  There are 25 trees at equal distances of 5 metres in a line with a well, the distance of the well from the nearest tree being 10 metres. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. Find the total distance the gardner will cover in order to water all the trees.
  A)
  3000 m            done clear
  B)
  3500 m            done clear
  C)
  3800 m        done clear
  D)
          4000 m           done clear
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• question_answer21)
  Which of the following statements is INCORRECT? (a) Sum of n terms of the list of numbers \[\sqrt{2},\sqrt{8},\sqrt{18},\sqrt{32},....\]is \[\frac{n(n+1)}{\sqrt{2}}\] (b) The common difference of the A.P. given by is 3. (c) The sum of the A.P. \[(-5),(-8),(-11),......(-230)\] is\[-\text{ }8930\].
  A)
  Only (a)           done clear
  B)
  Only (b)      done clear
  C)
                     Both (a) and (b)           done clear
  D)
   (a), (b) and (c) done clear
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• question_answer22)
  If there are \[(2n+1)\]terms in A. P., then find the ratio of the sum of odd terms and the sum of even terms.                    
  A)
  \[n:(n+1)\]                   done clear
  B)
  \[(n+1):n\]       done clear
  C)
         \[n:(n+2)\]       done clear
  D)
          \[(n+2):n\]                  done clear
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• question_answer23)
  If \[\frac{{{a}^{n+1}}+{{b}^{n+1}}}{{{a}^{n}}+{{b}^{n}}}\]is the A.M. between a and b, then find the value of n.             
  A)
  0                                  done clear
  B)
  1                      done clear
  C)
  2                      done clear
  D)
          3   done clear
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• question_answer24)
  The sum of the third and seventh terms; of an A.P. is 6 and their product is 8.  Find the sum of first sixteen terms of the A. P.            
  A)
  86            done clear
  B)
  90 done clear
  C)
  Both (A) and (B) done clear
  D)
   None of these done clear
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• question_answer25)
  Fill in the blanks.

  (i)  If the ratio of sum of n terms of two A.P is \[(7n+1)\,:\,(4n+27),\] then ratio of their \[{{m}^{th}}\] terms is P.

  (ii) Sum of n odd natural numbers is Q

  (iii) If sum of n terms of three A.P. are

  \[{{S}_{1}},{{S}_{2}},{{S}_{3}}\]. The first term of each is 1 and common difference are 1, 2 and 3 respectively, then \[\frac{{{S}_{1}}+{{S}_{3}}}{{{S}_{2}}}=\underline{R}\]
  A)

  P	Q	R
  \[\frac{14m-6}{8m+23}\]	\[{{n}^{2}}\]	2

                  done clear
  B)

  \[\frac{13m+6}{7m+9}\]

  \[{{n}^{2}}\]

  5

                  done clear
  C)

  \[\frac{14m+6}{8m+23}\]

  \[2n+1\]

  1

                  done clear
  D)

  \[\frac{7m+1}{4m+27}\]

  \[2n-1\]

  3

  done clear
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