Mathematics Questions

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

1. Q621
   It is ​proposed to ​build a single circular park equal in area to the sum of ​areas of two circular parks of diameters 16 m ​and 12 m in a ​locality. The ​radius of the new park would be

   1. (a)10 m
   2. (b)15 m
   3. (c)20 m
   4. (d)24 m
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2. Q622
   The ​area of ​the ​circle that ​can be ​inscribed in ​a square of side 6 cm ​is

   1. (a)$36\pi$ cm${}^2$
   2. (b)$18\pi$ cm${}^2$
   3. (c)$12\pi$ cm${}^2$
   4. (d)$9\pi$ cm${}^2$
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3. Q623
   The ​area of ​the ​square that ​can be inscribed in ​a circle of ​radius $8$ cm is

   1. (a)$256{\text{cm}}^2$
   2. (b)$128{\text{cm}}^2$
   3. (c)$64\sqrt{2}{\text{cm}}^2$
   4. (d)$64{\text{cm}}^2$
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4. Q624
   The radius of ​a circle whose ​circumference is equal to the sum of ​the ​circumferences of the ​two circles ​of ​diameters $36\text{cm}$ and $20\text{cm}$ is

   1. (a)56 cm
   2. (b)42 cm
   3. (c)28 cm
   4. (d)16 cm
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5. Q625
   The ​diameter of a circle whose area ​is equal to ​the sum of ​the areas of the two circles of ​radii ​24 cm ​and 7 cm is

   1. (a)31 cm
   2. (b)25 cm
   3. (c)62 cm
   4. (d)50 cm
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6. Q626
   Is the ​area of ​the circle inscribed in ​a ​square of ​side ​a cm, $\pi a^2$ cm${}^2$? Give reasons for ​your answer.
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7. Q627
   Will it be ​true ​to ​say that the ​perimeter ​of a square circumscribing a circle of ​radius $a$ cm is $8a$ cm? Give reasons for ​your answer.
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8. Q628
   In Fig. 11.3, a square is inscribed in a circle of diameter d and ​another square is circumscribing the circle. Is the ​area of the ​outer square four times the area ​of ​the ​inner ​square? Give reasons for your answer.

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9. Q629
   Is it true to say ​that ​area of ​a segment of ​a circle is less than ​the ​area of its corresponding ​sector? ​Why?
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10. Q630
    Is it ​true that the distance travelled by a circular ​wheel of diameter ​d ​cm in one revolution ​is $2\pi d$ ​cm? ​Why?
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11. Q631
    In covering ​a ​distance $s$ ​metres, ​a circular wheel ​of radius $r$ metres ​makes $\frac{s}{2\pi r}$ revolutions. Is this ​statement true? ​Why?
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12. Q632
    The numerical ​value of ​the area ​of a circle is ​greater than the numerical value of ​its ​circumference. Is this statement true? Why?
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13. Q633
    If the length of an arc of a circle ​of radius r is equal to that of ​an arc of a circle of radius 2r, ​then the angle ​of the ​corresponding sector of ​the first ​circle ​is double the angle of the corresponding sector of the other circle. Is this statement false? Why?
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14. Q634
    The areas ​of two sectors of two ​different ​circles ​with ​equal corresponding arc lengths are equal. Is this statement ​true? ​Why?
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15. Q635
    The ​areas of two sectors of two different circles ​are ​equal. ​Is it necessary that their ​corresponding ​arc lengths are equal? Why?
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16. Q636
    Is the area of the largest circle ​that ​can be drawn inside a ​rectangle of ​length $a$ ​cm and ​breadth $b$ cm $(a>b)$ is $\pi b^2$ ​cm${}^2$? Why?
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17. Q637
    Circumferences ​of two circles are equal. ​Is ​it ​necessary that ​their areas ​be equal? ​Why?
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18. Q638
    Areas ​of two circles are ​equal. Is ​it ​necessary ​that their circumferences are equal? Why?
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19. Q639
    Is ​it ​true ​to say that area of a square ​inscribed in ​a ​circle of diameter $p$ ​cm is $p^2$ cm${}^2$? Why?
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20. Q640
    Find the ​radius of a ​circle whose circumference is ​equal to the sum ​of the ​circumferences of two circles ​of radii 15 cm ​and 18 cm.
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