Mathematics Questions

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

1. Q901 CBSE Board 2026
   The sum and product of zeroes ​of a ​quadratic ​polynomial $p(x)$ are $-\frac{1}{3}$ ​and $2$ respectively. ​The polynomial $p(x)$ ​is ​:

   1. (a)$3x^2-x+6$
   2. (b)$x^2+\frac{1}{3}x-2$
   3. (c)$3x^2-x+2$
   4. (d)$-3x^2-x-6$
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2. Q902 CBSE Board 2026
   $PQ$ ​is tangent to a ​circle ​with ​centre $O$. ​If $\angle POR=65^{\circ }$, ​then $m\angle PTR$ is

   1. (a)$65^{\circ }$
   2. (b)$58.5^{\circ }$
   3. (c)$57.5^{\circ }$
   4. (d)$45^{\circ }$
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3. Q903 CBSE Board 2026
   For ​an ​acute angle $\theta$, ​if $\sin \theta =\frac{1}{9}$, ​then value of $\frac{9\mathrm{cosec}\theta +1}{9\mathrm{cosec}\theta -1}$ is

   1. (a)$0$
   2. (b)$\frac{80}{81}$
   3. (c)$1$
   4. (d)$\frac{82}{80}$
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4. Q904 CBSE Board 2026
   The ​number of conical bottles of radius $2$ cm and height $1.2$ ​cm that can be filled from a ​cylindrical bottle ​of radius $6$ cm and height $8$ cm, full of ​liquid, ​is

   1. (a)$60$
   2. (b)$130$
   3. (c)$180$
   4. (d)$18$
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5. Q905 CBSE Board 2026
   $n^{\text{th}}$ term ​of the A.P. $-\frac{3}{2},\frac{3}{2},\frac{9}{2},\dots$ is ​:

   1. (a)$\frac{3n}{2}-3$
   2. (b)$3n-\frac{9}{2}$
   3. (c)$\frac{3n-9}{2}$
   4. (d)$3n+\frac{3}{2}$
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6. Q906 CBSE Board 2026
   If $\sqrt{3}\sin A=\cos A$, ​then the measure ​of $A$ ​is ​:

   1. (a)$90^{\circ }$
   2. (b)$60^{\circ }$
   3. (c)$45^{\circ }$
   4. (d)$30^{\circ }$
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7. Q907 CBSE Board 2026
   At an instant, the length ​of shadow of a stick is found to ​be $\sqrt{3}$ ​times the ​length of the stick ​as shown in the figure below. ​The Sun's altitude at that ​instant is ​:

   1. (a)$30^{\circ }$
   2. (b)$45^{\circ }$
   3. (c)$60^{\circ }$
   4. (d)$90^{\circ }$
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8. Q908 CBSE Board 2026
   In the given ​figure, the angle ​of depression of ​the ​foot ​of ​building $CD$ from ​the top of tower $AB$ is :

   1. (a)$60^{\circ }$
   2. (b)$30^{\circ }$
   3. (c)$45^{\circ }$
   4. (d)$90^{\circ }$
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9. Q909 CBSE Board 2026
   The ​hour hand of a clock is $7$ cm long. The ​angle swept by ​it between $7:00$ a.m. and $8:10$ ​a.m. ​is ​:

   1. (a)${\left(\frac{35}{4}\right)}^{\circ }$
   2. (b)${\left(\frac{35}{2}\right)}^{\circ }$
   3. (c)$35^{\circ }$
   4. (d)$70^{\circ }$
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10. Q910 CBSE Board 2026
    Area of a ​segment ​of ​a circle of radius $r$ ​and ​central angle $60^{\circ }$ ​is :

    1. (a)$\frac{\pi r^2}{2}-\frac{1}{2}{r}^2$
    2. (b)$\frac{2\pi r}{4}-\frac{\sqrt{3}}{4}{r}^2$
    3. (c)$\frac{\pi r^2}{6}-\frac{\sqrt{3}}{4}{r}^2$
    4. (d)$\frac{2\pi r}{4}-r^2\sin 60^{\circ }$
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11. Q911 CBSE Board 2026
    $PQ$ ​is tangent ​to ​a circle at a point $P$ on the circle. The number ​of tangents which can be drawn ​to ​the circle parallel ​to $PQ$, is

    1. (a)$2$
    2. (b)$1$
    3. (c)many
    4. (d)zero
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12. Q912 CBSE Board 2026
    The minute hand of ​a clock is $21$ ​cm long. The distance ​covered by the ​tip of the ​minute hand ​from $2:10$ ​pm to $2:25$ pm ​is:

    1. (a)$346.5$ cm
    2. (b)$33$ cm
    3. (c)$66$ cm
    4. (d)$16.5$ cm
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13. Q913 CBSE Board 2026
    Given that $\sin 2\alpha =\frac{\sqrt{3}}{2}$, the ​value ​of $\sin 3\alpha$ is :

    1. (a)$\frac{3\sqrt{3}}{4}$
    2. (b)$\frac{1}{2}$
    3. (c)$1$
    4. (d)$\frac{\sqrt{3}}{4}$
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14. Q914 CBSE Board 2026
    The ​distance ​between ​the points $(a\cos \theta +b\sin \theta ,0)$ ​and $(0,a\sin \theta -b\cos \theta )$ is

    1. (a)$\sqrt{a^2+b^2}$
    2. (b)$a^2-b^2$
    3. (c)$\sqrt{a^2-b^2}$
    4. (d)$a^2+b^2$
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15. Q915 CBSE Board 2026
    In the ​given ​figure, $PQ\parallel YZ$ ​such ​that $XP:PY=2:3$. ​If $PQ=5$ cm, ​then $YZ$ equals

    1. (a)$12.5$ cm
    2. (b)$10$ cm
    3. (c)$15$ cm
    4. (d)$7.5$ cm
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16. Q916 CBSE Board 2026
    One ​ticket is ​drawn at random from ​a ​bag containing $50$ tickets numbered $1$ to $50$. The probability that the drawn ​ticket has a number which is a multiple of $7$ ​is :

    1. (a)$\frac{1}{5}$
    2. (b)$\frac{7}{50}$
    3. (c)$\frac{3}{25}$
    4. (d)$\frac{4}{25}$
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17. Q917 CBSE Board 2026
    In ​the ​given ​figure, $PQ\parallel BC$. If $AP:AB=3:7$, ​then $AQ:QC$ equals:

    1. (a)$3:7$
    2. (b)$3:10$
    3. (c)$7:3$
    4. (d)$3:4$
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18. Q918 CBSE Board 2026
    In the ​adjoining ​figure, the angle ​of elevation of ​the ​point $C$ from ​the point $B$, is ​:

    1. (a)$30^{\circ }$
    2. (b)$45^{\circ }$
    3. (c)$22.5^{\circ }$
    4. (d)$67.5^{\circ }$
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19. Q919 CBSE Board 2026
    The largest possible right circular cone is carved out of a solid ​hemisphere of ​radius ​'$r$' as shown in the ​figure ​below. The ​slant height of ​the cone is ​:

    1. (a)$r$
    2. (b)$2r$
    3. (c)$\sqrt{2}r$
    4. (d)$\sqrt{3}r$
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20. Q920 CBSE Board 2026
    The radius ​of the largest ​sphere ​that ​can be carved ​out ​from a solid ​cube of side $14$ cm is :

    1. (a)$7$ cm
    2. (b)$14$ cm
    3. (c)$14\sqrt{2}$ cm
    4. (d)$7\sqrt{2}$ cm
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