Mathematics Questions

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

1. Q421
   Find the sum ​of ​the two ​middle ​most terms of the ​AP: $-\frac{4}{3},-1,-\frac{2}{3},\dots ,4\frac{1}{3}$.
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2. Q422
   The first term of an ​AP ​is $-5$ and ​the last term is $45$. If the sum of the ​terms of the ​AP is $120$, then find the number of ​terms and the ​common difference.
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3. Q423
   Find ​the ​sum: ​

   1. (i)$1+(-2)+(-5)+(-8)+\dots +(-236)$
   2. (ii)$\left(4-\frac{1}{n}\right)+\left(4-\frac{2}{n}\right)+\left(4-\frac{3}{n}\right)+\dots$ ​upto $n$ ​terms ​
   3. (iii)$\frac{a-b}{a+b}+\frac{3a-2b}{a+b}+\frac{5a-3b}{a+b}+\dots$ to 11 ​terms.
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4. Q424
   Which ​term of the AP: $-2,-7,-12,\dots$ will be $-77$? ​Find ​the sum ​of this ​AP ​upto ​the term $-77$.
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5. Q425
   If $a_n=3-4n$, ​show ​that $a_1,a_2,a_3,\dots$ ​form ​an ​AP. Also find $S_{20}$.
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6. Q426
   In ​an AP, ​if $S_n=n(4n+1)$, find the ​AP.
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7. Q427
   In ​an ​AP, ​if $S_n=3n^2+5n$ ​and $a_k=164$, find the ​value of $k$.
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8. Q428
   If $S_n$ ​denotes the ​sum ​of ​first $n$ ​terms of an AP, prove that $S_{12}=3(S_8-S_4)$.
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9. Q429
   Find ​the sum of first 17 ​terms of an ​AP ​whose $4^{th}$ and $9^{th}$ terms are $-15$ and $-30$ ​respectively.
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10. Q430
    If sum of first ​6 ​terms of an AP is 36 and that ​of ​the first ​16 ​terms ​is 256, find the sum of ​first 10 terms.
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11. Q431
    Find ​the ​sum of ​all the ​11 terms of ​an AP whose middle most ​term ​is 30.
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12. Q432
    Find the ​sum of last ​ten ​terms ​of ​the AP: $8,10,12,\dots ,126$.
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13. Q433
    Find the sum ​of ​first seven numbers which are ​multiples of ​2 as ​well as ​of ​9. [Hint: Take the LCM of 2 and 9.]
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14. Q434
    How many terms ​of the AP: $-15,-13,-11,\dots$ ​are ​needed ​to make ​the sum $-55$? Explain the reason for ​double ​answer.
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15. Q435
    The sum of the ​first $n$ terms ​of an AP whose ​first term is ​8 and the common difference is 20 is equal to the ​sum of first $2n$ terms of another ​AP whose first ​term is $-30$ and the common difference ​is 8. Find $n$.
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16. Q436
    Kanika was given her pocket money on ​Jan $1^{st}$, $2008$. She puts Re $1$ on Day $1$, Rs $2$ on Day $2$, Rs $3$ on ​Day $3$, and continued doing so till the end of the month, from this money into her ​piggy bank. She also spent ​Rs $204$ of her pocket ​money, and found that ​at the end of the month she still had ​Rs $100$ with her. How much was ​her pocket money for the month?
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17. Q437
    Yasmeen saves ​Rs $32$ during ​the first month, Rs $36$ in the ​second ​month ​and Rs $40$ in the third month. If she continues to save in ​this manner, in how many ​months will she save Rs $2000$?
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18. Q438
    In ​Fig. 6.2, $\angle BAC=90^{\circ }$ ​and $AD\perp BC$. Then,

    1. (a)$BD\cdot CD=B{C}^2$
    2. (b)$AB\cdot AC=B{C}^2$
    3. (c)$BD\cdot CD=A{D}^2$
    4. (d)$AB\cdot AC=A{D}^2$
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19. Q439
    The ​lengths of the diagonals of ​a rhombus ​are 16 cm ​and ​12 cm. Then, the length of the ​side of the ​rhombus ​is

    1. (a)$9$ cm
    2. (b)$10$ cm
    3. (c)$8$ cm
    4. (d)$20$ cm
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20. Q440
    The lengths ​of the diagonals of a rhombus ​are $16$ cm ​and $12$ ​cm. Then, ​the length of the side ​of the rhombus is

    1. (a)$9$ cm
    2. (b)$10$ cm
    3. (c)$8$ cm
    4. (d)$20$ cm
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