Mathematics Questions

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

1. Q1021 CBSE Board 2026
   Diagonals $AC$ and $BD$ ​of ​square $ABCD$ ​intersect at $P$. Coordinates of points $B$ and $D$ are $(9,-2)$ and $(1,6)$ respectively. ​

   1. (i)Find ​the co-ordinates of point $P$.
   2. (ii)Find the ​length of the side of ​the square.

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2. Q1022 CBSE Board 2026
   Prove ​that : $\sqrt{\frac{1+\sin A}{1-\sin A}}=\sec A+\tan A$.
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3. Q1023 CBSE Board 2026
   Two chords $AB$ ​and $CD$ intersect each other ​at the ​point $E$ ​as shown ​in ​the given ​figure. Prove that $△AED\sim △CEB$.

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4. Q1024 CBSE Board 2026
   Find ​the coordinates of ​a point on the line $x+y=5$ ​which ​is ​equidistant from $(6,4)$ ​and $(5,2)$.
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5. Q1025 CBSE Board 2026
   Evaluate ​: $\frac{3{\cos }^{2}30^{\circ }-6{\mathrm{cosec}}^{2}30^{\circ }}{{\tan }^{2}60^{\circ }}$
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6. Q1026 CBSE Board 2026
   The diagonals of ​a ​quadrilateral $ABCD$ ​intersect each other at the ​point $O$ such that $\frac{AO}{OC}=\frac{BO}{OD}$. ​Show that ​quadrilateral $ABCD$ is a ​trapezium.
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7. Q1027 CBSE Board 2026
   If $\tan \theta =\frac{24}{7}$, ​then find ​the ​value of $\sin \theta +\cos \theta$.
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8. Q1028 CBSE Board 2026
   If $\tan \theta +\frac{1}{\tan \theta }=2$, ​find ​the ​value ​of ${\tan }^2\theta +\frac{1}{{\tan }^2\theta }$.
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9. Q1029 CBSE Board 2026
   Find ​the ​probability that ​a number selected at random ​from the ​numbers $30,31,32,33,\dots ,60$ is

   1. (i)a ​prime ​number
   2. (ii)a ​multiple of $6$.
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10. Q1030 CBSE Board 2026
    Prove ​that: $\frac{\sin A}{1+\cos A}+\frac{1+\cos A}{\sin A}=2\text{cosec}A$.
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11. Q1031 CBSE Board 2026
    Prove ​that $2+3\sqrt{5}$ is ​an ​irrational ​number, given ​that $\sqrt{5}$ is an ​irrational ​number.
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12. Q1032 CBSE Board 2026
    Evaluate ​: $\frac{{\sin }^{3}60^{\circ }-\tan 30^{\circ }}{{\cos }^{2}45^{\circ }}$
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13. Q1033 CBSE Board 2026
    If $7{\sin }^{2}A+3{\cos }^{2}A=4$, ​then ​find the ​value of $\tan A$.
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14. Q1034 CBSE Board 2026
    In the given ​figure, $AP$, $AQ$ and $BC$ are tangents ​to ​the circle ​with centre $O$. If $AB=6$ cm, $AC=7$ cm and $BC=5$ cm, then what is ​the length of $AP$?

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15. Q1035 CBSE Board 2026
    Evaluate ​: ${\sin }^{2}30^{\circ }-{\cos }^{2}45^{\circ }+{\cot }^{2}60^{\circ }$
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16. Q1036 CBSE Board 2026
    Triangle $ABC$ is ​an isosceles right ​triangle, ​right ​angled at $B$. Find the ​value ​of ${\sin }^{2}A+{\cos }^{2}C$.
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17. Q1037 CBSE Board 2026
    In the ​given ​figure, $△MEN$ is a right ​triangle, ​right-angled at $E$. If $\angle EMN=60^{\circ }$ and $ME=5$ ​cm, ​find the length of $MN$. ​Also, find the value ​of ${\sin }^{2}N$.

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18. Q1038 CBSE Board 2026
    If $\cot \theta =\frac{7}{8}$, ​then ​find ​the value ​of $\frac{(1+\sin \theta )(1-\sin \theta )}{(1+\cos \theta )(1-\cos \theta )}$.
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19. Q1039 CBSE Board 2026
    Prove that ​: $\sqrt{\frac{1-\sin \theta }{1+\sin \theta }}=\sec \theta -\tan \theta$
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20. Q1040 CBSE Board 2026
    Slips of letters ​of the word 'BACKGROUND' are put in ​a bowl and ​thoroughly ​mixed. One slip ​is picked up at random. Find the probability that picked up slip's letter is

    1. (i)a vowel
    2. (ii)present in the word 'BALL'.
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