Mathematics Questions

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

1. Q101
   Find ​the coordinates ​of ​the ​point which divides the join of $(-1,7)$ ​and $(4,-3)$ in ​the ​ratio $2:3$.
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2. Q102
   Find the coordinates of ​the points ​of ​trisection ​of the line ​segment joining (4, -1) and (-2, -3).
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3. Q103
   To conduct Sports ​Day activities, in your rectangular ​shaped school ground ABCD, lines have ​been drawn with chalk powder ​at a ​distance of 1 ​m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as ​shown in Fig. 7.12. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5 th the distance AD on the eighth line and posts a red flag. What is the distance between both ​the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?
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4. Q104
   Find the ​ratio ​in which the ​line ​segment joining ​the points $(-3,10)$ and $(6,-8)$ is divided ​by $(-1,6)$.
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5. Q105
   Find the ratio in which the line ​segment ​joining $A(1,-5)$ and $B(-4,5)$ is ​divided by the $x$-axis. Also ​find the coordinates ​of the point ​of ​division.
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6. Q106
   If $(1,2),(4,y),(x,6)$ ​and $(3,5)$ are the ​vertices of a parallelogram ​taken in ​order, find $x$ ​and $y$.
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7. Q107
   Find ​the coordinates ​of a point $A$, where $AB$ is the ​diameter of ​a circle ​whose centre is $(2,-3)$ and $B$ ​is $(1,4)$.
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8. Q108
   If $A$ and $B$ are $(-2,-2)$ ​and $(2,-4)$ respectively, find ​the coordinates of $P$ such ​that $AP=\frac{3}{7}AB$ and $P$ ​lies on ​the ​line ​segment $AB$.
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9. Q109
   Find the coordinates of ​the ​points which divide ​the line segment ​joining ​A(-2, ​2) and B(2, ​8) into four equal parts.
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10. Q110
    Find the area of a rhombus if its vertices are ​(3, ​0), (4, 5), (-1, ​4) and (-2, ​-1) taken ​in order. [Hint: ​Area of a rhombus ​= $\frac{1}{2}$ (product of its diagonals)]
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11. Q111
    In $△ABC$, ​right-angled ​at ​B, ​AB ​= ​24 cm, ​BC = 7 cm. Determine:

    1. (i)$\sin A,\cos A$
    2. (ii)$\sin C,\cos C$
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12. Q112
    In ​Fig. 8.13, ​find $\tan P-\cot R$.
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13. Q113
    If $\sin A=\frac{3}{4}$, ​calculate $\cos A$ ​and $\tan A$.
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14. Q114
    Given ​15 ​cot ​A = 8, ​find sin A and ​sec ​A.
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15. Q115
    Given $\sec \theta =\frac{13}{12}$, ​calculate ​all other ​trigonometric ​ratios.
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16. Q116
    If angle A and ​angle ​B ​are ​acute angles ​such ​that cos A = cos B, ​then show that ​angle A = angle B.
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17. Q117
    If $\cot \theta =\frac{7}{8}$, ​evaluate: ​

    1. (i)$\frac{(1+\sin \theta )(1-\sin \theta )}{(1+\cos \theta )(1-\cos \theta )}$,
    2. (ii)${\cot }^2\theta$.
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18. Q118
    If $3\cot A=4$, check ​whether $\frac{1-{\tan }^{2}A}{1+{\tan }^{2}A}={\cos }^{2}A-{\sin }^{2}A$ ​or ​not.
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19. Q119
    In ​triangle ​ABC, right-angled ​at B, ​if $\tan A=\frac{1}{\sqrt{3}}$, ​find ​the ​value of:

    1. (i)$\sin A\cos C+\cos A\sin C$
    2. (ii)$\cos A\cos C-\sin A\sin C$
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20. Q120
    In $\Delta PQR$, ​right-angled ​at $Q$, $PR+QR=25$ ​cm and $PQ=5$ cm. ​Determine ​the ​values ​of $\sin P,\cos P$ and $\tan P$.
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