Mathematics Questions

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

1. Q61
   Refer ​to Fig. 5.4. The drawing shows ​a spiral made of successive semicircles ​with centres ​alternating at A and B, and radii 0.5, 1.0, 1.5, ... cm. Find the total length of the spiral made ​up ​of thirteen consecutive semicircles. (Use $\pi =22/7$.) [Hint: Length of semicircles is $l_1,l_2,l_3,l_4,\dots$.]
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2. Q62
   The first term of ​an AP ​is 5, the ​last term is 45 and the ​sum is ​400. Find the ​number of terms ​and the common difference.
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3. Q63
   The ​first and the last terms of an ​AP are $17$ ​and $350$ ​respectively. If the ​common ​difference is $9$, how many terms are there and what is their sum?
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4. Q64
   Find the sum of first ​22 ​terms of ​an ​AP in which $d=7$ and 22nd term ​is 149.
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5. Q65
   Find the ​sum ​of ​first $51$ terms of ​an AP whose second ​and third ​terms are $14$ and $18$ ​respectively.
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6. Q66
   If the ​sum of first 7 terms of an AP is ​49 and ​that of 17 ​terms ​is ​289, find the sum ​of first n terms.
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7. Q67
   Show that $a_1,a_2,\dots ,a_n,\dots$ form ​an AP where $a_n$ is defined ​as below. Also find the ​sum of the ​first ​15 ​terms ​in ​each case.

   1. (i)$a_n=3+4n$
   2. (ii)$a_n=9-5n$
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8. Q68
   If the ​sum of the first $n$ terms of ​an AP ​is $4n-n^2$, what is the first term (that is $S_1$)? What is the ​sum ​of first two terms? What is the second term? Similarly, find the 3rd, the 10th ​and the $n$th terms.
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9. Q69
   Find ​the ​sum of ​the ​first 40 positive integers ​divisible ​by 6.
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10. Q70
    Find the ​sum of ​the first $15$ ​multiples ​of $8$.
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11. Q71
    Find ​the ​sum of ​the ​odd numbers ​between 0 and ​50.
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12. Q72
    A contract on construction job specifies a penalty for delay of ​completion ​beyond a certain date as follows: Rs 200 for the first day, Rs 250 for the ​second day, Rs 300 for the third day, etc., ​the penalty for each succeeding day ​being Rs 50 more than for the preceding day. How much money the contractor has to pay as penalty, if he ​has delayed the work ​by ​30 days?
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13. Q73
    A sum of $\text{Rs }700$ is to be used to give seven cash prizes ​to students of ​a school for their overall academic performance. If each ​prize ​is $\text{Rs }20$ less than its preceding prize, ​find the value ​of each of ​the prizes.
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14. Q74
    In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each ​class will plant, will be the same as the class, in which they are studying, e.g., ​a section of Class I will plant 1 tree, a section of Class II will plant 2 ​trees and so on till Class XII. There are ​three sections ​of each class. How ​many trees will be ​planted ​by the students?
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15. Q75
    A spiral is made up of successive semicircles, with centres alternately ​at $A$ and $B$, starting with centre at $A$, of radii $0.5$ cm, $1.0$ ​cm, $1.5$ cm, $2.0$ cm, $\dots$ as shown ​in Fig. $5.4$. ​What is the total length ​of such ​a spiral made ​up ​of thirteen consecutive semicircles? (Take $\pi =\frac{22}{7}$.)
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16. Q76
    200 logs are stacked in the ​following manner: ​20 logs in the bottom row, 19 in the next row, 18 in ​the row next to ​it and so ​on (see ​Fig. 5.5). ​In how many rows are the 200 logs placed and how many logs are in the ​top row?
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17. Q77
    In a potato race, ​a bucket is placed at the ​starting ​point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a ​straight line. There are ten ​potatoes in the line (see Fig. 5.6). A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it ​in the bucket, runs back to pick up the ​next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run? [Hint: To pick up the first potato and the second ​potato, the total distance (in metres) run by a competitor is $2\times 5+2\times (5+3)$.]
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18. Q78
    Fill in the blanks ​using the correct word given in brackets: ​

    1. (i)All circles are ​____. (congruent, similar)
    2. (ii)All squares are ____. (similar, congruent)
    3. (iii)All ​____ triangles are ​similar. (isosceles, equilateral)
    4. (iv)Two polygons of the same number of ​sides are similar, if (a) their ​corresponding angles are ​____ and (b) their corresponding sides are ____. (equal, proportional)
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19. Q79
    Give ​two different ​examples of pair ​of:

    1. (i)​similar ​figures
    2. (ii)non-similar ​figures
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20. Q80
    State ​whether the following quadrilaterals ​are similar ​or ​not:

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