Mathematics Questions

Browse 839 Mathematics questions with expert-verified, step-by-step solutions — NCERT, exemplar and previous-year questions, organised by chapter.

1. Q41
   Check whether $-150$ ​is a ​term ​of ​the ​AP: $11,8,5,2,\dots$
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2. Q42
   Find the ​31st ​term of ​an AP whose ​11th term is 38 and the 16th term ​is 73.
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3. Q43
   An AP consists of 50 terms ​of which 3rd ​term ​is 12 and ​the last ​term is 106. ​Find the 29th term.
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4. Q44
   If the 3rd ​and the 9th terms of an ​AP ​are $4$ and $-8$ ​respectively, ​which ​term of ​this AP is zero?
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5. Q45
   The ​17th term of ​an ​AP ​exceeds ​its 10th term ​by 7. ​Find the common difference.
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6. Q46
   Which ​term of ​the AP: $3,15,27,39,\dots$ will ​be ​132 more than its ​54th ​term?
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7. Q47
   Two ​APs have the ​same common difference. The difference ​between their ​100th terms ​is $100$. ​What is the difference between their 1000th terms?
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8. Q48
   How many three-digit ​numbers ​are divisible ​by ​7?
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9. Q49
   How many multiples ​of $4$ lie ​between $10$ ​and $250$?
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10. Q50
    For what value of $n$, ​are ​the $n$-th ​terms of two ​APs: $63,65,67,\dots$ and $3,10,17,\dots$ ​equal?
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11. Q51
    Determine the AP ​whose third term ​is $16$ and ​the $7$th ​term exceeds ​the $5$th term ​by $12$.
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12. Q52
    Find the 20th ​term ​from ​the ​last ​term ​of the AP : $3,8,13,\dots ,253$.
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13. Q53
    The sum of the $4$th ​and $8$th terms of an AP is $24$ and the sum of ​the $6$th ​and $10$th terms is $44$. ​Find the ​first three terms of ​the ​AP.
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14. Q54
    Subba Rao started work in 1995 ​at an annual ​salary of Rs 5000 and ​received an ​increment ​of ​Rs 200 each ​year. In ​which year did his income reach Rs 7000?
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15. Q55
    Ramkali saved ​Rs 5 in the first week of a year and then increased ​her weekly ​savings by Rs 1.75. If ​in ​the ​nth week, her weekly savings ​become ​Rs 20.75, find n.
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16. Q56
    Find the ​sum of the following APs:

    1. (i)2, 7, 12, ..., ​to 10 terms. ​
    2. (ii)-37, ​-33, -29, ..., to ​12 ​terms.
    3. (iii)0.6, 1.7, 2.8, ..., to 100 terms. ​
    4. (iv)​1/15, 1/12, 1/10, ..., to 11 terms.
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17. Q57
    Find ​the ​sums given ​below: ​

    1. (i)$7+10\frac{1}{2}+14+\dots +84$ ​
    2. (ii)$34+32+30+\dots +10$ ​
    3. (iii)$-5+(-8)+(-11)+\dots +(-230)$
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18. Q58
    Find the sums ​given ​below: ​(i) $7+10\frac{1}{2}+14+\dots +84$ ​(iii) $-5+(-8)+(-11)+\dots +(-230)$
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19. Q59
    In ​an AP:

    1. (i)​given $a=5$, $d=3$, $a_n=50$, find $n$ and $S_n$.
    2. (ii)given $a=7$, $a_{13}=35$, find $d$ and $S_{13}$.
    3. (iii)given $a_{12}=37$, $d=3$, ​find $a$ and $S_{12}$.
    4. (iv)given $a_3=15$, $S_{10}=125$, find $d$ and $a_{10}$.
    5. (v)given $d=5$, $S_9=75$, find $a$ and $a_9$.
    6. (vi)given $a=2$, $d=8$, $S_n=90$, find $n$ and $a_n$.
    7. (vii)​given $a=8$, $a_n=62$, $S_n=210$, find $n$ and $d$.
    8. (viii)given $a_n=4$, $d=2$, $S_n=-14$, ​find $n$ and $a$.
    9. (ix)given $a=3$, $n=8$, $S=192$, find $d$.
    10. (x)given $l=28$, $S=144$, $n=9$, find $a$.
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20. Q60
    How ​many ​terms ​of the ​AP : $9,17,25,\dots$ ​must be taken to give ​a sum of 636?
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