Mathematics Questions

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

1. Q1001 CBSE Board 2026
   Find ​the zeroes of ​the ​polynomial $p(x)=15x^2-19x+6$.
   Open question → 🔒 Log in to view the solution
2. Q1002 CBSE Board 2026
   In an A.P., the first ​term is $32$ and the ​last term ​is $-10$. If the common ​difference is $-2$, ​then find the number ​of terms and ​their sum.
   Open question → 🔒 Log in to view the solution
3. Q1003 CBSE Board 2026
   Vertices of ​a ​right triangle $ABC$ with $\angle B=90^{\circ }$ ​are $A(3,4)$, $B(1,1)$ ​and $C(-8,7)$. ​Find ​the ​value of $\tan A$.
   Open question → 🔒 Log in to view the solution
4. Q1004 CBSE Board 2026
   If $\alpha ,\beta$ are ​the ​zeroes ​of ​the polynomial $p(x)=6x^2-5x-3$, then ​find the ​value ​of $\frac{1}{\alpha }+\frac{1}{\beta }$.
   Open question → 🔒 Log in to view the solution
5. Q1005 CBSE Board 2026
   One zero of ​a ​quadratic polynomial is ​twice the ​other. If the ​sum of ​zeroes is $(-6)$, find the ​polynomial.
   Open question → 🔒 Log in to view the solution
6. Q1006 CBSE Board 2026
   In ​the ​figure given ​above, $△ABC\sim △XYZ$, ​then ​find ​the values of $x$ ​and $y$.

   Open question → 🔒 Log in to view the solution
7. Q1007 CBSE Board 2026
   If ​one zero of the ​polynomial $p(x)=(k-1)x^2-(4k+1)x+10$ is $5$, ​find ​the ​value ​of $k$.
   Open question → 🔒 Log in to view the solution
8. Q1008 CBSE Board 2026
   Find the sum ​of ​the first $28$ ​terms ​of an A.P. ​whose $n^{\text{th}}$ term ​is given ​by $a_n=3n-2$.
   Open question → 🔒 Log in to view the solution
9. Q1009 CBSE Board 2026
   Using ​distance formula, ​prove that the ​points $A(2,3)$, $B(-7,0)$ and $C(-1,2)$ are ​collinear.
   Open question → 🔒 Log in to view the solution
10. Q1010 CBSE Board 2026
    One ​zero of the polynomial $4x^2-12x+(2k+1)$ ​is ​five ​times ​the ​other. Find the value ​of $k$.
    Open question → 🔒 Log in to view the solution
11. Q1011 CBSE Board 2026
    In the ​given ​figure, $XY\parallel QR$, $\frac{PQ}{XQ}=\frac{7}{3}$ ​and $PR=6.3$ cm. ​Find ​the length ​of $YR$.

    Open question → 🔒 Log in to view the solution
12. Q1012 CBSE Board 2026
    The coordinates ​of the ​centre ​of a circle ​are $(x-7,2x)$. Find the value(s) of '$x$', ​if the circle passes through the ​point $(-9,11)$ and ​has radius $5\sqrt{2}$ units.
    Open question → 🔒 Log in to view the solution
13. Q1013 CBSE Board 2026
    If ​the points $A(4,5)$, $B(m,6)$, $C(4,3)$ and $D(1,n)$ taken ​in this ​order are the vertices of ​a parallelogram $ABCD$, then find ​the ​values of $m$ and $n$.
    Open question → 🔒 Log in to view the solution
14. Q1014 CBSE Board 2026
    If $A(a,0)$, $B(1,1)$ ​and $C(0,b)$ form ​a triangle, right ​angled at $B$ ​when ​joined, then establish a relation between $a$ ​and $b$.
    Open question → 🔒 Log in to view the solution
15. Q1015 CBSE Board 2026
    The sum of ​first $n$ ​terms of an A.P. ​is given by $S_n=4n^2-n$. Find ​the $25^{\text{th}}$ ​term ​of this A.P.
    Open question → 🔒 Log in to view the solution
16. Q1016 CBSE Board 2026
    In the given ​figure, $AB\parallel DE$ ​and $AC\parallel DF$. Show that $△ABC\sim △DEF$. If $BC=10$ ​cm, $EB=CF=5$ cm ​and $AB=7$ cm, then find the ​length $DE$.

    Open question → 🔒 Log in to view the solution
17. Q1017 CBSE Board 2026
    A ​circle is inscribed in a right ​triangle $ABC$, right ​angled at $B$. If ​the lengths of the two ​sides containing the right angle are $8$ cm and $15$ ​cm, ​find the radius of the incircle.
    Open question → 🔒 Log in to view the solution
18. Q1018 CBSE Board 2026
    A $(-2,3)$ ​and B $(4,1)$ are end points ​of the diameter ​of ​a ​semi-circle. The semi-circle ​intersects the $y$-axis at point P. ​Find the ​co-ordinates of the point P.
    Open question → 🔒 Log in to view the solution
19. Q1019 CBSE Board 2026
    In ​the ​adjoining figure, $AP=\frac{1}{2}AB$ ​and $PQ\parallel BC$. If $CQ=3$ cm, then find the ​length ​of $AC$.

    Open question → 🔒 Log in to view the solution
20. Q1020 CBSE Board 2026
    In the ​figure ​given ​below, $\angle 1=\angle 2$ ​and $\frac{BE}{BC}=\frac{CD}{AB}$. ​Prove that $△BDE\sim △BAC$.

    Open question → 🔒 Log in to view the solution