Mathematics Questions

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

1. Q1081 CBSE Board 2026
   Prove that ​the ​system ​of equations given as $2x-3y=7$ and $4x+ky=9$, is inconsistent for $k=-6$. Also, ​obtain ​the solution ​of the system of equations, if $k=-1$.
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2. Q1082 CBSE Board 2026
   When $1$ is subtracted from the numerator and $2$ ​is added to ​the denominator of ​a ​fraction, it becomes $\frac{1}{2}$. When $7$ is ​subtracted from the ​numerator and $2$ is subtracted from the denominator, ​the fraction ​becomes $\frac{1}{3}$. Find the fraction.
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3. Q1083 CBSE Board 2026
   The sum of ​first $n$ ​terms of ​an A.P. is $2n^2+13n$. Find ​its $n^{\text{th}}$ ​term ​and hence $10^{\text{th}}$ term.
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4. Q1084 CBSE Board 2026
   Find ​the ratio ​in which the point P $(6,k)$ divides the line ​segment joining the ​points ​M $(4,2)$ and N $(8,-4)$. Hence ​find ​the value of $k$.
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5. Q1085 CBSE Board 2026
   One ​of the supplementary angles exceeds the other by $120^{\circ }$. Express the given ​information ​as a ​system of ​linear equations in ​two variables. Hence, find ​the measure of ​both the angles.
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6. Q1086 CBSE Board 2026
   $S$ ​is any ​point on the side $QR$ ​of ​a $△PQR$ ​such ​that $\angle PSR=\angle QPR$. ​Prove that $\frac{QR}{RP}=\frac{RP}{RS}$.
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7. Q1087 CBSE Board 2026
   Prove ​that : $\frac{\sin \theta -\cos \theta +1}{\sin \theta +\cos \theta -1}=\frac{1}{\sec \theta -\tan \theta }$
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8. Q1088 CBSE Board 2026
   Find a ​relation between $x$ and $y$ ​such that ​the ​point $P(x,y)$ is ​equidistant ​from the points $A(5,3)$ and $B(1,7)$.
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9. Q1089 CBSE Board 2026
   If the ​point $P(x,y)$ is equidistant from the ​points $(3,6)$ ​and $(-3,4)$, ​obtain the ​relation ​between $x$ and $y$. Hence, find ​the coordinates of point $P$ if it lies on $x$-axis.
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10. Q1090 CBSE Board 2026
    Show that ​the quadrilateral $ABCD$ ​with vertices $A(0,3)$, $B(-2,0)$, $C(0,-5)$ and $D(2,0)$ ​is a kite. Also, find ​the ​length of ​each ​diagonal of the kite $ABCD$.
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11. Q1091 CBSE Board 2026
    If $x=h+a\cos \theta$, $y=k+b\sin \theta$, ​then ​prove ​that : ${\left(\frac{x-h}{a}\right)}^2+{\left(\frac{y-k}{b}\right)}^2=1$
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12. Q1092 CBSE Board 2026
    Prove ​that : $\frac{{\sec }^3\theta }{{\sec }^2\theta -1}+\frac{{\mathrm{cosec}}^3\theta }{{\mathrm{cosec}}^2\theta -1}=\sec \theta \cdot \mathrm{cosec}\theta (\sec \theta +\mathrm{cosec}\theta )$
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13. Q1093 CBSE Board 2026
    In ​an ​A.P., it is given ​that $a=2$, $d=8$ ​and $S_n=90$. ​Find ​the ​value of $n$.
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14. Q1094 CBSE Board 2026
    Prove ​that $\frac{\cot A-\cos A}{\cot A+\cos A}=\frac{\sec A-\tan A}{\sec A+\tan A}$.
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15. Q1095 CBSE Board 2026
    Show ​that the quadrilateral $ABCD$ ​formed by ​joining the points $A(-2,-1)$, $B(1,-1)$, $C(1,2)$ and $D(-2,2)$ in ​order ​is ​a ​square.
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16. Q1096 CBSE Board 2026
    Prove ​that : $\frac{\tan A}{1+\sec A}-\frac{\tan A}{1-\sec A}=2\mathrm{cosec}A$
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17. Q1097 CBSE Board 2026
    If $\frac{\sec \alpha }{\mathrm{cosec}\beta }=p$ ​and $\frac{\tan \alpha }{\mathrm{cosec}\beta }=q$, ​then ​prove ​that $(p^2-q^2){\sec }^2\alpha =p^2$.
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18. Q1098 CBSE Board 2026
    How ​many $4$-digit ​numbers are ​divisible by $7$?
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19. Q1099 CBSE Board 2026
    Prove ​that $(\mathrm{cosec}A-\sin A)(\sec A-\cos A)=\frac{1}{\tan A+\cot A}$.
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20. Q1100 CBSE Board 2026
    Prove ​that $\sqrt{\frac{1-\sin A}{1+\sin A}}=\frac{1}{\sec A+\tan A}$.
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