Mathematics Questions

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

1. Q881 CBSE Board 2026
   In the given figure, $PQ$ and $PR$ are two tangents ​drawn ​to a ​circle with ​centre $O$. ​If $\angle ORQ=25^{\circ }$, then the ​measure of $\angle PQR$ ​is:

   1. (a)$65^{\circ }$
   2. (b)$25^{\circ }$
   3. (c)$50^{\circ }$
   4. (d)$75^{\circ }$
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2. Q882 CBSE Board 2026
   The numbers $x,x+4$ ​and $x+8$ are ​in ​A.P. with common difference :

   1. (a)$x$
   2. (b)$4+x$
   3. (c)$4$
   4. (d)$0$
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3. Q883 CBSE Board 2026
   The ​value ​of $(\cos 90^{\circ }-\sin 90^{\circ })$ is ​:

   1. (a)$-1$
   2. (b)greater than $0$
   3. (c)equal to the value of $\tan 45^{\circ }$
   4. (d)$0$
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4. Q884 CBSE Board 2026
   The value of $\frac{{\tan }^{2}60^{\circ }-1}{{\tan }^{2}60^{\circ }+1}$ ​is equal to ​the ​value of ​which ​of the following ​?

   1. (a)$\tan 60^{\circ }$
   2. (b)$\cos 60^{\circ }$
   3. (c)$\sec 60^{\circ }$
   4. (d)$\sin 60^{\circ }$
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5. Q885 CBSE Board 2026
   In the given figure, $PA$ ​is a tangent ​from an external ​point $P$ ​to ​a circle with ​centre $O$. ​If $\angle POB=125^{\circ }$, then $\angle APO$ is ​equal to :

   1. (a)$25^{\circ }$
   2. (b)$65^{\circ }$
   3. (c)$90^{\circ }$
   4. (d)$35^{\circ }$
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6. Q886 CBSE Board 2026
   In the given figure, $PA$ and $PB$ ​are tangents ​to a circle ​centred ​at $O$. ​If $\angle OAB=15^{\circ }$, then $\angle APB$ equals ​:

   1. (a)$30^{\circ }$
   2. (b)$15^{\circ }$
   3. (c)$45^{\circ }$
   4. (d)$10^{\circ }$
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7. Q887 CBSE Board 2026
   A bag ​contains some red and some white ​balls. A ball is drawn ​at random from the bag. If the probability of ​getting a red ​ball is $\frac{2}{7}$, then the probability of getting a white ball ​is

   1. (a)$\frac{1}{14}$
   2. (b)$\frac{5}{7}$
   3. (c)$\frac{1}{7}$
   4. (d)$\frac{2}{7}$
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8. Q888 CBSE Board 2026
   If $\sin \theta =\frac{\sqrt{3}}{2}$, ​then the value ​of $2\sqrt{3}\cdot \cos \frac{\theta }{2}$ ​is:

   1. (a)$3$
   2. (b)$2\sqrt{3}$
   3. (c)$\frac{3}{2}$
   4. (d)$\sqrt{3}$
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9. Q889 CBSE Board 2026
   It ​is ​given ​that $△ABC\sim △QRP$ ​such ​that $AB=9$ ​cm, $BC=5$ cm and $PR=2$ ​cm. Length of side $QR$ ​is :

   1. (a)$0.9$ cm
   2. (b)$\frac{5}{18}$ cm
   3. (c)$\frac{10}{9}$ cm
   4. (d)$3.6$ cm
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10. Q890 CBSE Board 2026
    Three tennis balls are just ​packed ​in a ​cylindrical jar. ​If radius of ​each ball is $r$, ​volume of air inside the jar is

    1. (a)$2\pi r^3$
    2. (b)$3\pi r^3$
    3. (c)$5\pi r^3$
    4. (d)$4\pi r^3$
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11. Q891 CBSE Board 2026
    An arc of ​length $2.2$ ​cm subtends an angle $\theta$ ​at ​the centre of the circle ​with ​radius $2.8$ ​cm. ​The value of $\theta$ is :

    1. (a)$50^{\circ }$
    2. (b)$60^{\circ }$
    3. (c)$45^{\circ }$
    4. (d)$30^{\circ }$
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12. Q892 CBSE Board 2026
    The perimeter ​of ​sector ​of ​a circle of radius $21$ ​cm ​and ​central angle $60^{\circ }$, is

    1. (a)$22$ cm
    2. (b)$44$ cm
    3. (c)$64$ cm
    4. (d)$273$ cm
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13. Q893 CBSE Board 2026
    The ​value of $\sin 90^{\circ }\cos 90^{\circ }-{\sin }^{2}60^{\circ }$ is:

    1. (a)$\frac{1}{4}$
    2. (b)$\frac{3}{4}$
    3. (c)$-\frac{3}{4}$
    4. (d)$\frac{5}{4}$
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14. Q894 CBSE Board 2026
    Which ​of the following ​statements is ​not ​true ​?

    1. (a)$\sin 0^{\circ }=\cos 0^{\circ }$
    2. (b)$\tan 30^{\circ }=\cot 60^{\circ }$
    3. (c)$\sin 30^{\circ }=\cos 60^{\circ }$
    4. (d)$\sin 45^{\circ }=\frac{1}{\sec 45^{\circ }}$
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15. Q895 CBSE Board 2026
    One ​of ​the possible values ​of $A$, for ​which $\cos 2A=\cos A$, is :

    1. (a)$0^{\circ }$
    2. (b)$30^{\circ }$
    3. (c)$45^{\circ }$
    4. (d)$90^{\circ }$
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16. Q896 CBSE Board 2026
    Which ​of the ​following ​is ​not ​defined for $x=90^{\circ }$ ​?

    1. (a)$\cot x$
    2. (b)$\text{cosec}x$
    3. (c)$\tan \left(\frac{x}{2}\right)$
    4. (d)$\sec x$
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17. Q897 CBSE Board 2026
    The length ​of ​the ​arc of the sector of a circle ​with ​radius $21$ cm and of central ​angle $60^{\circ }$, ​is :

    1. (a)$22$ cm
    2. (b)$44$ cm
    3. (c)$88$ cm
    4. (d)$11$ cm
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18. Q898 CBSE Board 2026
    In the ​given ​figure, PA and ​PB ​are tangents ​to a ​circle centred at O. ​If $\angle AOB=130^{\circ }$, then $\angle APB$ is equal to :

    1. (a)$130^{\circ }$
    2. (b)$50^{\circ }$
    3. (c)$120^{\circ }$
    4. (d)$90^{\circ }$
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19. Q899 CBSE Board 2026
    If $-26,x,2$ ​are ​in ​A.P., ​then ​the value ​of $x$ is

    1. (a)$14$
    2. (b)$-13$
    3. (c)$-12$
    4. (d)$-14$
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20. Q900 CBSE Board 2026
    The ​area (in ${\text{cm}}^2$) ​of a sector ​of ​a ​circle of radius $14$ cm cut off by an ​arc of length $22$ ​cm is:

    1. (a)$77$
    2. (b)$308$
    3. (c)$154$
    4. (d)$462$
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