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Mathematics Questions

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

Chapters

Ch01 Real NumbersCh01 Real NumbersCh02 PolynomialsCh02 PolynomialsCh03 Pair of Linear EquationsCh03 Pair of Linear Equations in Two VariablesCh04 Quadratic EquationsCh04 Quadratic EquationsCh05 Arithmetic ProgressionsCh05 Arithmetic ProgressionsCh06 TrianglesCh06 TrianglesCh07 Coordinate GeometryCh07 Coordinate GeometryCh08 Introduction to Trigonometry and its ApplicationsCh08 TrigonometryCh09 Applications of TrigonometryCh09 CirclesCh10 CirclesCh10 ConstructionsCh11 Areas Related to CirclesCh11 Areas Related to CirclesCh12 Surface Areas and VolumesCh12 Surface Areas and VolumesCh13 StatisticsCh13 Statistics and ProbabilityCh14 ProbabilityA1 Proofs in MathematicsA2 Mathematical Modelling
  1. Q641
    In Fig. ​11.5, ​a square of ​diagonal 8 ​cm is inscribed in a ​circle. ​Find the area ​of ​the shaded region.
    Fig. 11.5
    Fig. 11.5
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  2. Q642
    Find ​the ​area of a sector of a circle ​of radius 28 ​cm and central ​angle .
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  3. Q643
    The wheel ​of ​a motor cycle is of radius 35 cm. How ​many revolutions per ​minute must the wheel make so ​as to ​keep a ​speed of 66 km/h?
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  4. Q644
    A cow is tied with a rope ​of ​length ​14 m ​at the corner of a rectangular field ​of ​dimensions 20 ​m 16 m. Find the area ​of the field in which the cow can graze.
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  5. Q645
    Find the ​area of ​the flower ​bed ​(with semi-circular ends) ​shown in Fig. 11.6.
    38 cm 10 cm Fig. 11.6
    Fig. 11.6
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  6. Q646
    In Fig. ​11.7, ​is a diameter of ​the circle, ​cm ​and ​cm. Find the ​area of ​the shaded region (Use ).
    A B C Fig. 11.7
    Fig. 11.7
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  7. Q647
    Find the area of ​the ​shaded field shown in Fig. 11.8. ​The ​field is a rectangle 8 ​m by 4 m with ​a semicircle of radius ​5 m attached below the left part; the total left ​side is 6 m.
    8 m 4 m 6 m semicircle radius 5 m
    Fig. 11.8
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  8. Q648
    Find ​the area of the shaded region in Fig. ​11.9. The outer rectangle is 26 m by 12 m, and the unshaded inner region is a stadium shape (rectangle with two semicircular ends) leaving ​a 4 ​m ​border at ​top and bottom and ​a 3 m ​border at left and right.
    4 m 4 m 3 m 3 m 12 m 26 m Fig. 11.9
    Fig. 11.9 shaded region
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  9. Q649
    Find the area ​of ​the ​minor segment of a circle of radius ​14 cm, when ​the angle ​of the corresponding ​sector is .
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  10. Q650
    Find the area of the shaded region in Fig. ​11.10, where arcs ​drawn with centres , , and intersect in ​pairs at ​mid-points , , and of the ​sides , , and , respectively of ​a square (Use ).
    A P B S Q D R C 12 cm Fig. 11.10
    Fig. 11.10
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  11. Q651
    In Fig. 11.11, ​arcs are drawn by taking vertices ​A, B and C of an ​equilateral triangle of ​side 10 cm to intersect the sides BC, CA and AB ​at their respective ​mid-points ​D, E and F. Find the area of the shaded region. (Use .)
    A B C F E D Fig. 11.11
    Fig. 11.11 -- equilateral triangle with three arcs of radius 5 cm centred at the vertices.
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  12. Q652
    In Fig. ​11.12, ​arcs have ​been drawn with ​radii 14 cm ​each and with ​centres ​P, Q and ​R. Find the area of the shaded region.
    P Q R Fig. 11.12
    Fig. 11.12
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  13. Q653
    A ​circular park ​is surrounded by a road 21 m wide. ​If ​the radius ​of ​the park is 105 m, find ​the area of the ​road.
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  14. Q654
    In Fig. ​11.13, arcs have been ​drawn of radius 21 cm ​each with ​vertices A, B, C ​and D of quadrilateral ABCD as centres. ​Find the ​area of the shaded region.
    A B C D Fig. 11.13
    Fig. 11.13
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  15. Q655
    A piece of wire 20 cm long is bent into the form ​of an arc of ​a circle subtending an angle ​of ​at ​its ​centre. Find the ​radius of the circle.
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  16. Q656
    A ​cylindrical ​pencil ​sharpened at one ​edge ​is the combination ​of
    1. (a)a cone and a cylinder
    2. (b)frustum of a cone and a cylinder
    3. (c)a hemisphere and a cylinder
    4. (d)two cylinders.
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  17. Q657
    A surahi is the combination of
    1. (a)a sphere and a cylinder
    2. (b)a hemisphere and a cylinder
    3. (c)two hemispheres
    4. (d)a cylinder and a cone
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  18. Q658
    A ​plumbline (sahul) ​is ​the ​combination of ​(see Fig. 12.2)
    Fig. 12.2
    Fig. 12.2
    1. (a)a cone and a cylinder
    2. (b)a hemisphere and a cone
    3. (c)frustum of a cone and a cylinder
    4. (d)sphere and cylinder
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  19. Q659
    The shape ​of a glass (tumbler) ​(see Fig. 12.3) is ​usually in ​the ​form ​of
    Marks (out of 90) Number of candidates More than or equal to 804 More than or equal to 706 More than or equal to 6011 More than or equal to 5017 More than or equal to 4023 More than or equal to 3027 More than or equal to 2030 More than or equal to 1032 More than or equal to 034
    Fig. 12.3
    1. (a)a cone
    2. (b)frustum of a cone
    3. (c)a cylinder
    4. (d)a sphere
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  20. Q660
    The ​shape of ​a , in the game (see ​Fig. ​12.4), is ​a combination of
    Fig. 12.4
    Fig. 12.4
    1. (a)two cylinders
    2. (b)a cone and a cylinder
    3. (c)two cones and a cylinder
    4. (d)two cylinders and a cone
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