Mathematics Questions

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

1. Q461
   In ​Fig. 6.5, ​if $\angle D=\angle C$, ​then is ​it ​true that $△ADE\sim △ACB$? Why?
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2. Q462
   Is it true to say that if ​in two triangles, an angle of one triangle is equal to ​an angle ​of another triangle and ​two sides of one ​triangle are proportional to the ​two sides of ​the other triangle, ​then the triangles are similar? Give reasons for your answer.
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3. Q463
   In a triangle PQR, PR^2 ​- PQ^2 = ​QR^2 ​and M ​is a point on side ​PR such that QM ​is perpendicular to PR. Prove that QM^2 ​= PM x MR.
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4. Q464
   Find ​the value ​of $x$ ​for which $DE\parallel AB$ ​in ​Fig. ​6.8.

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5. Q465
   In ​Fig. 6.9, ​if $\angle 1=\angle 2$ ​and $△NSQ\cong △MTR$, then prove ​that $△PTS\sim △PRQ$.

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6. Q466
   Diagonals of a trapezium ​PQRS intersect each ​other at ​the point ​O, PQ $\parallel$ ​RS and PQ = 3 RS. ​Find ​the ratio of the areas of triangles POQ and ROS.
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7. Q467
   In Fig. ​6.10, if $AB\parallel DC$ ​and AC ​and PQ intersect each other at the ​point O, ​prove ​that $OA\cdot CQ=OC\cdot AP$.

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8. Q468
   Find ​the ​altitude of an equilateral ​triangle ​of ​side 8 ​cm.
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9. Q469
   If $△ABC\sim △DEF$, $AB=4$ ​cm, $DE=6$ ​cm, $EF=9$ ​cm and $FD=12$ cm, find ​the perimeter ​of $△ABC$.
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10. Q470
    In ​Fig. ​6.11, ​if ​DE $\parallel$ BC, find the ratio ​of ar (ADE) and ​ar ​(DECB).

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11. Q471
    ABCD ​is a ​trapezium in which $AB\parallel DC$ and P and Q ​are points ​on AD ​and BC, respectively such that $PQ\parallel DC$. ​If $PD=18$ cm, $BQ=35$ cm and $QC=15$ cm, find ​AD.
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12. Q472
    Corresponding sides ​of two ​similar ​triangles ​are in the ratio of $2:3$. If the area ​of the smaller triangle ​is $48$ cm${}^2$, find the area of the ​larger triangle.
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13. Q473
    In a ​triangle ​PQR, N is a point on ​PR ​such that ​QN is ​perpendicular to PR. If PN.NR ​= QN^2, prove that angle PQR = 90 degrees.
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14. Q474
    Areas ​of ​two similar triangles are 36 cm${}^2$ and 100 cm${}^2$. If the ​length of a side of the ​larger ​triangle is 20 cm, find the length of the ​corresponding side ​of the smaller ​triangle.
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15. Q475
    In ​Fig. ​6.12, ​if $\angle ACB=\angle CDA$, $AC=8$ cm and $AD=3$ ​cm, ​find BD.

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16. Q476
    A 15 metres ​high ​tower casts a shadow 24 metres long at a ​certain ​time and at ​the same ​time, ​a telephone pole casts a shadow 16 metres long. Find the height of the telephone ​pole.
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17. Q477
    Foot of a 10 m long ladder ​leaning against a vertical wall is 6 ​m away from the base of the ​wall. Find ​the height ​of the point on the wall where ​the ​top of the ladder reaches.
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18. Q478
    The distance ​of the ​point $P(2,3)$ from ​the $x$-axis ​is

    1. (a)$2$
    2. (b)$3$
    3. (c)$1$
    4. (d)$5$
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19. Q479
    The ​distance ​between the ​points $A(0,6)$ ​and $B(0,-2)$ is

    1. (a)6
    2. (b)8
    3. (c)4
    4. (d)2
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20. Q480
    The ​distance ​of ​the ​point $P(-6,8)$ from the ​origin ​is

    1. (a)8
    2. (b)$2\sqrt{7}$
    3. (c)10
    4. (d)6
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