Mathematics Questions

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

1. Q401
   Justify whether it ​is true ​to ​say ​that the following are the $n^{\text{th}}$ terms of an ​AP.

   1. (i)$2n-3$
   2. (ii)$3n^2+5$ ​
   3. (iii)$1+n+n^2$
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2. Q402
   Match ​the APs ​given ​in column A with ​suitable common differences given in column ​B.
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3. Q403
   Verify that each of ​the following is an ​AP, and then write its next ​three ​terms.

   1. (i)$0,\frac{1}{4},\frac{1}{2},\frac{3}{4},\dots$
   2. (ii)$5,\frac{14}{3},\frac{13}{3},4,\dots$
   3. (iii)$\sqrt{3},2\sqrt{3},3\sqrt{3},\dots$
   4. (iv)$a+b,(a+1)+b,(a+1)+(b+1),\dots$ ​
   5. (v)$a,2a+1,3a+2,4a+3,\dots$
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4. Q404
   Write the first three terms of ​the ​APs ​when $a$ ​and $d$ are as given ​below:

   1. (i)$a=\frac{1}{2},d=-\frac{1}{6}$ ​
   2. (ii)$a=-5,d=-3$
   3. (iii)$a=\sqrt{2},d=\frac{1}{\sqrt{2}}$
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5. Q405
   Find $a$, $b$ ​and $c$ ​such ​that ​the following ​numbers are in ​AP: $a,7,b,23,c$.
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6. Q406
   Determine ​the AP whose ​fifth term is ​19 and the ​difference of ​the eighth term ​from ​the ​thirteenth term is 20.
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7. Q407
   The 26th, 11th and the last term ​of ​an ​AP ​are 0, 3 ​and $-\frac{1}{5}$, respectively. Find the common difference ​and ​the number of ​terms.
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8. Q408
   The sum ​of the 5th and ​the 7th terms of an AP ​is 52 ​and ​the 10th term ​is 46. Find the AP.
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9. Q409
   Find the ​20th term ​of the AP whose ​7th term is ​24 less ​than ​the 11th ​term, ​first term being 12.
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10. Q410
    Find the $20^{\text{th}}$ term ​of the AP whose $7^{\text{th}}$ term is $24$ ​less ​than ​the $11^{\text{th}}$ term, first ​term being $12$.
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11. Q411
    If the $9^{th}$ term ​of ​an ​AP is zero, prove ​that ​its $29^{th}$ ​term is ​twice its $19^{th}$ term.
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12. Q412
    Find whether 55 ​is a term ​of ​the AP: ​7, ​10, 13, ... or not. If yes, ​find which term it is.
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13. Q413
    Determine $k$ so that $k^2+4k+8$, $2k^2+3k+6$, $3k^2+4k+4$ ​are three ​consecutive ​terms of ​an ​AP.
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14. Q414
    Split ​207 into three ​parts such that these are in ​AP and the ​product of the two smaller ​parts is 4623.
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15. Q415
    The ​angles of a triangle are in AP. ​The greatest angle is twice ​the least. ​Find all the angles ​of ​the ​triangle.
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16. Q416
    If ​the $n$th ​terms of ​the two APs: $9,7,5,\dots$ and $24,21,18,\dots$ are ​the same, find the ​value ​of $n$. Also find that term.
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17. Q417
    If sum of ​the 3rd ​and the 8th terms of an AP ​is 7 and the sum of ​the 7th and ​the ​14th terms is $-3$, find ​the 10th ​term.
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18. Q418
    Find the $12^{\text{th}}$ term ​from ​the ​end ​of the ​AP: $-2,-4,-6,\dots ,-100$.
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19. Q419
    Which ​term of the ​AP: ​53, 48, 43, ... is ​the ​first ​negative term?
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20. Q420
    How ​many ​numbers lie between 10 and ​300, which when ​divided ​by 4 leave a remainder 3?
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