Mathematics Questions

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

1. Q501
   Point $P(0,2)$ ​is ​the ​point of ​intersection of the $y$-axis and perpendicular bisector ​of ​the line ​segment joining the points $A(-1,1)$ and $B(3,3)$.
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2. Q502
   State whether the ​following statement ​is true or false and justify: Points ​A $(3,1)$, ​B $(12,-2)$ and ​C $(0,2)$ ​cannot be the vertices of ​a ​triangle.
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3. Q503
   Points A $(4,3)$, B $(6,4)$, ​C $(5,-6)$ and D $(-3,5)$ are the ​vertices of a parallelogram. State whether ​this statement ​is ​true ​or false, and ​justify your ​answer.
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4. Q504
   A circle ​has its centre ​at the origin and a point $P(5,0)$ lies on it. ​The ​point $Q(6,8)$ lies outside ​the circle.
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5. Q505
   The point A $(2,7)$ lies ​on ​the ​perpendicular ​bisector of line segment joining the ​points P $(6,5)$ and ​Q $(0,-4)$.
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6. Q506
   Point $P(5,-3)$ is ​one of the two ​points of trisection ​of ​the ​line segment ​joining the ​points $A(7,-2)$ ​and $B(1,-5)$.
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7. Q507
   Points ​A $(-6,10)$, B $(-4,6)$ ​and ​C $(3,-8)$ are ​collinear such ​that $AB=\frac{2}{9}AC$.
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8. Q508
   The point $P(-2,4)$ lies ​on a ​circle of radius ​6 ​and ​centre $C(3,5)$.
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9. Q509
   State whether the following is true ​or ​false and ​justify: The points $A(-1,-2)$, $B(4,3)$, $C(2,5)$ ​and $D(-3,0)$ in ​that ​order form a rectangle.
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10. Q510
    Name the type ​of ​triangle ​formed by the ​points $A(-5,6)$, $B(-4,-2)$ ​and $C(7,5)$.
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11. Q511
    Find the ​points on ​the $x$-axis which are ​at ​a distance ​of $2\sqrt{5}$ ​from the point $(7,-4)$. How ​many such ​points are there?
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12. Q512
    What type of ​a ​quadrilateral do the points $A(2,-2)$, $B(7,3)$, $C(11,-1)$ ​and $D(6,-6)$ ​taken ​in ​that order, ​form?
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13. Q513
    Find the value ​of $a$, ​if ​the distance ​between the points $A(-3,-14)$ and $B(a,-5)$ ​is $9$ units.
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14. Q514
    Find a point ​which is ​equidistant from ​the points $A(-5,4)$ and $B(-1,6)$. ​How many such points are there?
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15. Q515
    Find ​the coordinates of the point $Q$ on the $x$-axis ​which lies on the perpendicular bisector of ​the line segment joining the points $A(-5,-2)$ ​and $B(4,-2)$. Name the ​type of triangle ​formed by the ​points $Q$, $A$ and $B$.
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16. Q516
    Find the value of $m$ ​if ​the points $(5,1)$, $(-2,-3)$ ​and $(8,2m)$ ​are ​collinear.
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17. Q517
    If ​the point A $(2,-4)$ is equidistant from ​P $(3,8)$ ​and ​Q $(-10,y)$, find ​the values of $y$. Also find distance PQ.
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18. Q518
    Find the area ​of ​the ​triangle whose vertices ​are $(-8,4)$, $(-6,6)$ ​and $(-3,9)$.
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19. Q519
    In what ratio does the ​x-axis divide the ​line segment joining the ​points $(-4,-6)$ and $(-1,7)$? Find the ​coordinates of ​the ​point of division.
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20. Q520
    Find the ​ratio ​in which the ​point $P\left(\frac{3}{4},\frac{5}{12}\right)$ divides the line segment joining the ​points $A\left(\frac{1}{2},\frac{3}{2}\right)$ ​and $B(2,-5)$.
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