Mathematics Questions

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

1. Q981 CBSE Board 2026
   If $\alpha$, $\beta$ are ​the ​zeroes ​of the polynomial $p(x)=x^2-3x-1$, ​then find the value of $\frac{1}{\alpha }+\frac{1}{\beta }$.
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2. Q982 CBSE Board 2026
   If $\alpha ,\beta$ are ​the ​zeroes of ​the quadratic polynomial $p{x}^2+qx+r$, then ​find ​the ​value ​of ${\alpha }^3\beta +{\beta }^3\alpha$.
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3. Q983 CBSE Board 2026
   Find ​the ​smallest $5$-digit number ​exactly ​divisible ​by $24$ ​and $36$.
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4. Q984 CBSE Board 2026
   Find the ​length of the plank that can ​be used ​to measure the ​lengths $4$ ​m $20$ cm ​and $5$ m $4$ cm ​exactly, in the least time.
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5. Q985 CBSE Board 2026
   Verify that ​roots of ​the ​quadratic equation $(p-q)x^2+(q-r)x+(r-p)=0$ are ​equal when $q+r=2p$.
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6. Q986 CBSE Board 2026
   Prove ​that $2-5\sqrt{3}$ ​is ​an ​irrational ​number, ​given that $\sqrt{3}$ is ​irrational.
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7. Q987 CBSE Board 2026
   Two numbers are in the ratio $3:5$ ​and their ​LCM ​is $180$. ​Find the ​HCF of ​these two ​numbers.
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8. Q988 CBSE Board 2026
   If $\sin (A-B)=\frac{1}{2}$ ​and $\tan (A+B)=\sqrt{3}$, where $0^{\circ }\le A+B<90^{\circ }$ and $A>B$, ​then ​find ​the ​values of $A$ and $B$.
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9. Q989 CBSE Board 2026
   Find ​the coordinates of the point ​which divides the line ​segment joining ​the points $A(-6,10)$ and $B(3,-8)$ ​in ​the ratio $2:7$.
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10. Q990 CBSE Board 2026
    An ant ​started moving from the point $A(2,3)$ and ​moved along the line segment $AB$. ​It ​covered three-fourth ​of the distance $AB$ and reached at a ​point $C(x,y)$. If the coordinates of ​the point $B$ ​are $(10,15)$, find the coordinates of the point $C$.
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11. Q991 CBSE Board 2026
    If $\sec A=\sqrt{2}$ and $\tan B=\sqrt{3}$, ​then ​find ​the ​value ​of $2\sin A\cos B$.
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12. Q992 CBSE Board 2026
    The ​point $P(x,y)$ lies on ​a semi-circular arc ​having ​diameter $AB$ ​as shown ​in the given figure. The coordinates of points $A$ and $B$ ​are $(3,0)$ and $(0,4)$ respectively. Find the relation between $x$ and $y$, if $P{A}^2+P{B}^2=A{B}^2$.

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13. Q993 CBSE Board 2026
    Evaluate ​: $\frac{4{\cos }^{3}60^{\circ }+\mathrm{cosec}30^{\circ }}{{\tan }^{2}30^{\circ }}$
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14. Q994 CBSE Board 2026
    Find the H.C.F. and ​L.C.M. ​of $1530$ ​and $2040$.
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15. Q995 CBSE Board 2026
    $D$ is a point on ​the side $BC$ ​of $△ABC$ such ​that $\angle CAB=\angle CDA$. ​Show that $C{A}^2=CB\times CD$.

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16. Q996 CBSE Board 2026
    Find the ​quadratic polynomial ​the ​sum of whose zeroes is $1$ and their product ​is $-12$. Hence ​find the zeroes ​of ​the polynomial.
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17. Q997 CBSE Board 2026
    Verify ​the ​relation ​between the zeroes ​and ​the ​coefficients of the quadratic polynomial $4x^2-9$.
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18. Q998 CBSE Board 2026
    Verify ​the relationship between the ​zeroes and ​the coefficients ​of the ​polynomial $p(x)=3x^2-5x$.
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19. Q999 CBSE Board 2026
    In $△ABC$, $DE\parallel BC$. ​If $AD=x$, $DB=x-2$, $AE=x+2$ ​and $EC=x-1$, then ​find the value ​of $x$.
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20. Q1000 CBSE Board 2026
    In ​the ​given ​figure, $△AHK\sim △ABC$. If $AK=10$ cm, $BC=3.5$ ​cm ​and $HK=7$ cm, ​find ​the length of $AC$.

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