Mathematics Questions

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

1. Q481
   The ​distance ​between ​the ​points $(0,5)$ ​and $(-5,0)$ is

   1. (a)$5$
   2. (b)$5\sqrt{2}$
   3. (c)$2\sqrt{5}$
   4. (d)$10$
   Open question → 🔒 Log in to view the solution
2. Q482
   AOBC ​is ​a rectangle whose three ​vertices ​are vertices $A(0,3)$, $O(0,0)$ and $B(5,0)$. ​The ​length of its diagonal ​is

   1. (a)5
   2. (b)3
   3. (c)$\sqrt{34}$
   4. (d)4
   Open question → 🔒 Log in to view the solution
3. Q483
   The ​perimeter of ​a triangle ​with vertices $(0,4)$, $(0,0)$ ​and $(3,0)$ ​is

   1. (a)$5$
   2. (b)$12$
   3. (c)$11$
   4. (d)$7+\sqrt{5}$
   Open question → 🔒 Log in to view the solution
4. Q484
   The ​area ​of ​a ​triangle ​with ​vertices $A(3,0)$, $B(7,0)$ and $C(8,4)$ is

   1. (a)$14$
   2. (b)$28$
   3. (c)$8$
   4. (d)$6$
   Open question → 🔒 Log in to view the solution
5. Q485
   The points $(-4,0)$, $(4,0)$, $(0,3)$ are ​the vertices ​of ​a

   1. (a)right triangle
   2. (b)isosceles triangle
   3. (c)equilateral triangle
   4. (d)scalene triangle
   Open question → 🔒 Log in to view the solution
6. Q486
   The ​point which ​divides the line segment joining the ​points $(7,-6)$ and $(3,4)$ ​in ratio $1:2$ ​internally ​lies in ​the

   1. (a)I quadrant
   2. (b)II quadrant
   3. (c)III quadrant
   4. (d)IV quadrant
   Open question → 🔒 Log in to view the solution
7. Q487
   The ​point which lies ​on the perpendicular ​bisector of the ​line ​segment joining the points $A(-2,-5)$ and $B(2,5)$ ​is

   1. (a)$(0,0)$
   2. (b)$(0,2)$
   3. (c)$(2,0)$
   4. (d)$(-2,0)$
   Open question → 🔒 Log in to view the solution
8. Q488
   The ​fourth vertex D ​of a ​parallelogram ABCD whose ​three ​vertices are $A(-2,3)$, $B(6,7)$ and $C(8,3)$ ​is

   1. (a)$(0,1)$
   2. (b)$(0,-1)$
   3. (c)$(-1,0)$
   4. (d)$(1,0)$
   Open question → 🔒 Log in to view the solution
9. Q489
   If ​the ​point $P(2,1)$ lies ​on the line segment joining ​points $A(4,2)$ ​and $B(8,4)$, ​then

   1. (a)$AP=\frac{1}{3}AB$
   2. (b)$AP=PB$
   3. (c)$PB=\frac{1}{3}AB$
   4. (d)$AP=\frac{1}{2}AB$
   Open question → 🔒 Log in to view the solution
10. Q490
    If $P\left(\frac{a}{3},4\right)$ ​is the mid-point ​of the ​line segment ​joining ​the points $Q(-6,5)$ ​and $R(-2,3)$, ​then the ​value of $a$ is

    1. (a)$-4$
    2. (b)$-12$
    3. (c)$12$
    4. (d)$-6$
    Open question → 🔒 Log in to view the solution
11. Q491
    The perpendicular ​bisector of ​the ​line ​segment ​joining the points A $(1,5)$ and B $(4,6)$ ​cuts the $y$-axis ​at

    1. (a)$(0,13)$
    2. (b)$(0,-13)$
    3. (c)$(0,12)$
    4. (d)$(13,0)$
    Open question → 🔒 Log in to view the solution
12. Q492
    The coordinates of ​the point which is equidistant ​from the ​three vertices ​of the $△AOB$ as ​shown in ​Fig. 7.1 is

    1. (a)$(x,y)$
    2. (b)$(y,x)$
    3. (c)$\left(\frac{x}{2},\frac{y}{2}\right)$
    4. (d)$\left(\frac{y}{2},\frac{x}{2}\right)$
    Open question → 🔒 Log in to view the solution
13. Q493
    A ​circle drawn with origin as the ​centre passes through $\left(\frac{13}{2},0\right)$. The point which ​does ​not lie in ​the interior ​of the circle ​is

    1. (a)$\left(-\frac{3}{4},1\right)$
    2. (b)$\left(2,\frac{7}{3}\right)$
    3. (c)$\left(5,-\frac{1}{2}\right)$
    4. (d)$\left(-6,\frac{5}{2}\right)$
    Open question → 🔒 Log in to view the solution
14. Q494
    A line ​intersects the y-axis and x-axis ​at the points P and Q, ​respectively. ​If $(2,-5)$ is the ​mid-point of PQ, ​then the coordinates of P and ​Q are, ​respectively

    1. (a)$(0,-5)$ and $(2,0)$
    2. (b)$(0,10)$ and $(-4,0)$
    3. (c)$(0,4)$ and $(-10,0)$
    4. (d)$(0,-10)$ and $(4,0)$
    Open question → 🔒 Log in to view the solution
15. Q495
    The ​area ​of ​a triangle ​with ​vertices $(a,b+c)$, $(b,c+a)$ ​and $(c,a+b)$ ​is

    1. (a)$(a+b+c{)}^2$
    2. (b)$0$
    3. (c)$a+b+c$
    4. (d)$abc$
    Open question → 🔒 Log in to view the solution
16. Q496
    If the ​distance between ​the points $(4,p)$ and $(1,0)$ ​is ​5, then the ​value ​of $p$ is

    1. (a)4 only
    2. (b)$\pm 4$
    3. (c)-4 only
    4. (d)0
    Open question → 🔒 Log in to view the solution
17. Q497
    If ​the ​points $A(1,2)$, $O(0,0)$ ​and $C(a,b)$ are ​collinear, ​then

    1. (a)$a=b$
    2. (b)$a=2b$
    3. (c)$2a=b$
    4. (d)$a=-b$
    Open question → 🔒 Log in to view the solution
18. Q498
    $△ABC$ with ​vertices A $(-2,0)$, B $(2,0)$ ​and C $(0,2)$ is ​similar to $△DEF$ ​with vertices ​D $(-4,0)$, ​E $(4,0)$ and F $(0,4)$.
    Open question → 🔒 Log in to view the solution
19. Q499
    Point $P(-4,2)$ lies ​on the ​line ​segment ​joining the points $A(-4,6)$ ​and $B(-4,-6)$.
    Open question → 🔒 Log in to view the solution
20. Q500
    The points $(0,5)$, $(0,-9)$ ​and $(3,6)$ ​are ​collinear.
    Open question → 🔒 Log in to view the solution