Mathematics Questions

Browse 1,240 Mathematics questions with expert-verified, step-by-step solutions — NCERT, exemplar and previous-year questions, organised by chapter.

1. Q381
   The $21^{st}$ term ​of the AP ​whose ​first ​two ​terms ​are $-3$ and $4$ is

   1. (a)17
   2. (b)137
   3. (c)143
   4. (d)-143
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2. Q382
   If the 2nd term of ​an AP ​is ​13 and the 5th term is ​25, ​what ​is its 7th term?

   1. (a)30
   2. (b)33
   3. (c)37
   4. (d)38
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3. Q383
   Which term ​of the ​AP: 21, 42, ​63, 84, ​... ​is 210?

   1. (a)9th
   2. (b)10th
   3. (c)11th
   4. (d)12th
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4. Q384
   If ​the ​common ​difference of ​an ​AP ​is $5$, then what ​is $a_{18}-a_{13}$?

   1. (a)5
   2. (b)20
   3. (c)25
   4. (d)30
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5. Q385
   What is the ​common ​difference ​of an ​AP ​in ​which $a_{18}-a_{14}=32$?

   1. (a)$8$
   2. (b)$-8$
   3. (c)$-4$
   4. (d)$4$
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6. Q386
   Two APs have ​the ​same common ​difference. The first term of ​one of these is $-1$ ​and that ​of the ​other is $-8$. Then the difference between their 4th terms is

   1. (a)$-1$
   2. (b)$-8$
   3. (c)$7$
   4. (d)$-9$
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7. Q387
   If ​7 times the $7^{\text{th}}$ term ​of an AP is ​equal to 11 times its $11^{\text{th}}$ term, then ​its 18th term ​will be

   1. (a)$7$
   2. (b)$11$
   3. (c)$18$
   4. (d)$0$
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8. Q388
   The ​4th ​term from ​the end of ​the AP: $-11,-8,-5,\dots ,49$ ​is

   1. (a)$37$
   2. (b)$40$
   3. (c)$43$
   4. (d)$58$
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9. Q389
   The famous mathematician ​associated with finding the ​sum ​of the ​first ​100 natural ​numbers ​is

   1. (a)Pythagoras
   2. (b)Newton
   3. (c)Gauss
   4. (d)Euclid
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10. Q390
    If ​the first term ​of ​an ​AP is $-5$ and the common difference is $2$, then ​the sum ​of ​the ​first $6$ terms is

    1. (a)$0$
    2. (b)$5$
    3. (c)$6$
    4. (d)$15$
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11. Q391
    The ​sum ​of ​first 16 terms ​of ​the AP: $10,6,2,\dots$ is

    1. (a)$-320$
    2. (b)$320$
    3. (c)$-352$
    4. (d)$-400$
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12. Q392
    In ​an ​AP ​if $a=1$, $a_n=20$ and $S_n=399$, ​then $n$ ​is

    1. (a)19
    2. (b)21
    3. (c)38
    4. (d)42
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13. Q393
    The ​sum ​of ​first five ​multiples ​of 3 ​is

    1. (a)45
    2. (b)55
    3. (c)65
    4. (d)75
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14. Q394
    Which ​of ​the following ​form an AP? ​Justify ​your ​answer.

    1. (i)$-1,-1,-1,-1,\dots$ ​
    2. (ii)$0,2,0,2,\dots$
    3. (iii)$1,1,2,2,3,3,\dots$
    4. (iv)$11,22,33,\dots$
    5. (v)$\frac{1}{2},\frac{1}{3},\frac{1}{4},\dots$
    6. (vi)$2,2^2,2^3,2^4,\dots$ ​
    7. (vii)$\sqrt{3},\sqrt{12},\sqrt{27},\sqrt{48},\dots$
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15. Q395
    Draw a parallelogram ABCD in which $BC=5$ ​cm, $AB=3$ cm ​and $\angle ABC=60^{\circ }$, divide it into triangles ​BCD and ABD by the diagonal BD. Construct the triangle ​BD'C' similar ​to $△BDC$ with scale ​factor $\frac{4}{3}$. Draw the line segment D'A' parallel to DA where A' lies on extended side BA. Is A'BC'D' ​a parallelogram?
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16. Q396
    For the AP: $-3,-7,-11,\dots$, ​can we ​find directly $a_{30}-a_{20}$ ​without ​actually finding $a_{30}$ ​and $a_{20}$? Give ​reasons for your ​answer.
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17. Q397
    Two APs have the same common difference. The first term of one AP is 2 and that of the other is 7. The ​difference between their ​10th terms is the same ​as the difference between their 21st terms, ​which ​is the same ​as ​the difference between any ​two corresponding terms. Why?
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18. Q398
    Is $0$ a ​term ​of the AP: $31,28,25,\dots$? ​Justify your ​answer.
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19. Q399
    The taxi fare after ​each ​km, when the fare is ​Rs 15 for the first km and ​Rs ​8 ​for each ​additional km, does not form an AP as the total fare (in Rs) after each km is 15, ​8, 8, 8, ... Is the statement true? Give reasons.
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20. Q400
    In which of the following situations, do the lists of numbers involved form ​an AP? Give reasons for your answers.

    1. (i)The fee charged from a student every month by a school for the whole session, when the monthly fee is Rs 400. ​
    2. (ii)The fee charged every month by a school from Classes I to XII, when the monthly fee for Class I is Rs 250, and it increases by Rs 50 for ​the next higher class.
    3. (iii)​The amount of money in the account ​of Varun at ​the end of every year when Rs 1000 is deposited at simple ​interest of 10% per annum.
    4. (iv)The number of bacteria in a certain food item after each second, when they double in every second.
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