Mathematics Questions

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

1. Q1101 CBSE Board 2026
   Find ​two consecutive negative integers, ​sum of ​whose ​squares ​is $481$.
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2. Q1102 CBSE Board 2026
   In the ​given figure, $△ABC$ is a right triangle ​in ​which $\angle B=90^{\circ }$, $AB=4$ ​cm and $BC=3$ cm. Find ​the radius ​of the circle inscribed in ​the triangle $ABC$.
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3. Q1103 CBSE Board 2026
   A ​circle touches the ​side $BC$ of a $△ABC$ at $P$ and also touches the ​sides $AB$ and $AC$ produced ​at $Q$ ​and $R$ respectively. ​Prove ​that $AR=\frac{1}{2}(\text{perimeter of }△ABC)$.
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4. Q1104 CBSE Board 2026
   To protect plants from heat, a shed of iron rods ​covered ​with green cloth is ​made. ​The ​lower part of the shed is a cuboid mounted by ​semi-cylinder as shown in the figure. Find the ​area ​of the cloth required to make this shed, if dimensions of the cuboid are $14\text{ m}\times 25\text{ m}\times 16\text{ m}$.

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5. Q1105 CBSE Board 2026
   A ​circle ​centered ​at $(2,1)$ ​passes ​through the points $A(5,6)$ and $B(-3,K)$. Find the value(s) ​of $K$. Hence find length of chord $AB$.
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6. Q1106 CBSE Board 2026
   Prove that ​: $\frac{\sin A-\tan A}{\sin A+\tan A}=\frac{1-\sec A}{1+\sec A}$
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7. Q1107 CBSE Board 2026
   If $\sin A+{\sin }^{2}A=1$, find ​the ​value ​of ${\cos }^{2}A+{\cos }^{4}A$. ​Also, using ​the above, ​prove that ${\tan }^{2}A\times {\sec }^{2}A=1$.
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8. Q1108 CBSE Board 2026
   Prove ​that ​: $(\sin A-\text{cosec}A{)}^2+(\cos A-\sec A{)}^2={\tan }^{2}A+{\cot }^{2}A-1$
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9. Q1109 CBSE Board 2026
   In the given figure, if ​a ​circle touches the ​side $QR$ ​of $△PQR$ at $S$ ​and extended sides $PQ$ and $PR$ at $M$ and $N$ ​respectively, then prove that : $PM=\frac{1}{2}(PQ+QR+PR)$

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10. Q1110 CBSE Board 2026
    Two tangents ​TP and ​TQ are drawn to a circle with centre ​O ​from an external ​point T. ​Prove ​that $\angle PTQ=2\angle OPQ$.
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11. Q1111 CBSE Board 2026
    The internal and external radii of a hollow hemisphere are $5\sqrt{2}$ cm and $10$ cm respectively. A ​cone of height $5\sqrt{7}$ cm and ​radius $5\sqrt{2}$ cm is surmounted on the ​hemisphere as shown in the figure. Find ​the ​total surface area of the object ​in ​terms of $\pi$. (Use $\sqrt{2}=1.4$)

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12. Q1112 CBSE Board 2026
    Prove that the point $P$ dividing ​the line segment joining ​the points $A(-1,7)$ and $B(4,-3)$ in the ​ratio $3:2$ ​lies ​on the ​line $x-3y=-1$. Also find ​the ​length of $PA$ and $PB$.
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13. Q1113 CBSE Board 2026
    $AB$ is ​a ​chord ​of length $24$ cm of a circle ​of radius $15$ cm. The tangents ​at $A$ ​and $B$ intersect at a point $P$. Find ​the length $PA$.
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14. Q1114 CBSE Board 2026
    If $\sin x=p$, then ​prove ​that ​:

    1. (i)$\cot x=\frac{\sqrt{1-p^2}}{p}$
    2. (ii)$\frac{1+{\tan }^{2}x}{1+{\cot }^{2}x}=\frac{p^2}{1-p^2}$
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15. Q1115 CBSE Board 2026
    Prove ​that the lengths ​of ​tangents ​drawn from ​an external point to a ​circle are equal.
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16. Q1116 CBSE Board 2026
    Prove ​that ​a ​rectangle circumscribing ​a circle is ​a ​square.
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17. Q1117 CBSE Board 2026
    A ​solid is in the ​form of a ​cylinder with hemispherical ends. The total ​height of the solid is $20$ cm ​and the diameter of the cylinder is $7$ cm. Find the ​total volume of the solid. $\left(\text{Use }\pi =\frac{22}{7}\right)$
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18. Q1118 CBSE Board 2026
    Find the area ​of ​the sector of a circle of radius $42$ ​cm and of central ​angle $30^{\circ }$. ​Also, find the area of ​the corresponding ​major sector. $\left[\text{Use }\pi =\frac{22}{7}\right]$
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19. Q1119 CBSE Board 2026
    If $\cos \theta +\sin \theta =\sqrt{2}\cos \theta$, then ​prove ​that $\cos \theta -\sin \theta =\sqrt{2}\sin \theta$.
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20. Q1120 CBSE Board 2026
    A ​point $P(x,7)$ ​divides a ​line segment ​joining the points $A(-5,4)$ ​and $B(7,9)$ in ​a certain ​ratio. Find the ratio and hence find the value of $x$.
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