Mathematics Questions

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

1. Q661
   A ​shuttle cock ​used for ​playing badminton ​has the shape of ​the ​combination ​of

   1. (a)a cylinder and a sphere
   2. (b)a cylinder and a hemisphere
   3. (c)a sphere and a cone
   4. (d)frustum of a cone and a hemisphere
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2. Q662
   A cone is cut through ​a ​plane ​parallel to ​its base and then the ​cone that is formed on one side of that plane is ​removed. The new part that is ​left over on the other side of ​the plane is called

   1. (a)a frustum of a cone
   2. (b)cone
   3. (c)cylinder
   4. (d)sphere
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3. Q663
   A hollow cube of internal edge ​22 cm is filled with spherical marbles ​of diameter 0.5 cm and it ​is assumed that $\frac{1}{8}$ space of the ​cube remains ​unfilled. Then ​the number of ​marbles that the cube can ​accommodate is

   1. (a)142296
   2. (b)142396
   3. (c)142496
   4. (d)142596
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4. Q664
   A metallic spherical ​shell ​of internal ​and external ​diameters $4\text{cm}$ ​and $8\text{cm}$, respectively is melted ​and recast into the form ​a cone ​of base diameter $8\text{cm}$. The height of the cone is

   1. (a)12 cm
   2. (b)14 cm
   3. (c)15 cm
   4. (d)18 cm
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5. Q665
   A metallic spherical shell of internal and ​external diameters $4$ cm and $8$ cm, ​respectively is melted and recast into the ​form a cone of base ​diameter $8$ cm. The ​height ​of the cone is

   1. (a)$12$ cm
   2. (b)$14$ cm
   3. (c)$15$ cm
   4. (d)$18$ cm
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6. Q666
   A solid ​piece of iron in ​the form ​of a cuboid ​of dimensions $49\text{cm}\times 33\text{cm}\times 24\text{cm}$ ​is ​moulded to form a solid sphere. The ​radius of the sphere is

   1. (a)21 cm
   2. (b)23 cm
   3. (c)25 cm
   4. (d)19 cm
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7. Q667
   A mason constructs a wall of dimensions $270\text{cm}\times 300\text{cm}\times 350\text{cm}$ with ​the bricks ​each of size $22.5\text{cm}\times 11.25\text{cm}\times 8.75\text{cm}$ and it is ​assumed ​that $\frac{1}{8}$ space ​is ​covered by ​the mortar. Then the number of bricks used to construct the wall is

   1. (a)11100
   2. (b)11200
   3. (c)11000
   4. (d)11300
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8. Q668
   Twelve solid ​spheres ​of the ​same ​size are made by melting a solid metallic cylinder of ​base ​diameter $2\text{cm}$ ​and height $16\text{cm}$. The diameter of each sphere is

   1. (a)4 cm
   2. (b)3 cm
   3. (c)2 cm
   4. (d)6 cm
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9. Q669
   Twelve solid ​spheres ​of the same ​size ​are ​made by ​melting a solid metallic cylinder of base diameter $2$ ​cm ​and height $16$ cm. The diameter of each sphere is

   1. (a)$4$ cm
   2. (b)$3$ cm
   3. (c)$2$ cm
   4. (d)$6$ cm
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10. Q670
    The radii of the top and bottom ​of ​a bucket of slant ​height 45 cm are 28 ​cm and ​7 ​cm, respectively. The ​curved surface area of the bucket is

    1. (a)$4950$ cm${}^2$
    2. (b)$4951$ cm${}^2$
    3. (c)$4952$ cm${}^2$
    4. (d)$4953$ cm${}^2$
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11. Q671
    A medicine-capsule is ​in the ​shape of a cylinder of diameter 0.5 cm with two ​hemispheres stuck ​to each of its ends. ​The length of entire ​capsule is 2 cm. ​The capacity of the ​capsule is

    1. (a)$0.36{\text{cm}}^3$
    2. (b)$0.35{\text{cm}}^3$
    3. (c)$0.34{\text{cm}}^3$
    4. (d)$0.33{\text{cm}}^3$
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12. Q672
    If two solid hemispheres of same base radius $r$ ​are ​joined together ​along their bases, then curved surface area of ​this ​new ​solid is

    1. (a)$4\pi r^2$
    2. (b)$6\pi r^2$
    3. (c)$3\pi r^2$
    4. (d)$8\pi r^2$
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13. Q673
    A right circular cylinder ​of ​radius $r$ cm ​and height $h$ ​cm ($h>2r$) just ​encloses ​a sphere ​of diameter

    1. (a)$r$ cm
    2. (b)$2r$ cm
    3. (c)$h$ cm
    4. (d)$2h$ cm
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14. Q674
    During conversion ​of ​a solid from ​one ​shape to another, the volume of the ​new shape will

    1. (a)increase
    2. (b)decrease
    3. (c)remain unaltered
    4. (d)be doubled
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15. Q675
    The diameters of the two circular ends of ​the ​bucket are ​44 cm and ​24 cm. ​The height of the bucket is 35 cm. ​The capacity of the bucket ​is

    1. (a)$32.7$ litres
    2. (b)$33.7$ litres
    3. (c)$34.7$ litres
    4. (d)$31.7$ litres
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16. Q676
    In a right ​circular cone, the ​cross-section made by a ​plane parallel to ​the ​base ​is ​a

    1. (a)circle
    2. (b)frustum of a cone
    3. (c)sphere
    4. (d)hemisphere
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17. Q677
    Volumes of two ​spheres ​are in the ​ratio 64:27. The ​ratio ​of ​their surface areas is

    1. (a)3 : 4
    2. (b)4 : 3
    3. (c)9 : 16
    4. (d)16 : 9
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18. Q678
    Two identical ​solid hemispheres ​of ​equal ​base radius $r$ ​cm ​are stuck together along their bases. ​The total surface area of the combination is $6\pi r^2$.
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19. Q679
    Write 'True' ​or 'False' and justify your answer: A solid cylinder of ​radius $r$ and height $h$ is placed over another cylinder of ​same height and radius. ​The total surface area ​of ​the shape ​so formed ​is $4\pi rh+4\pi r^2$.
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20. Q680
    A solid cone of radius $r$ and height $h$ is ​placed over a solid ​cylinder having same base ​radius ​and ​height as ​that of a cone. The total ​surface area of the combined ​solid is $\pi r\left[\sqrt{r^2+h^2}+3r+2h\right]$.
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