Mathematics Questions

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

1. Q921 CBSE Board 2026
   The total ​surface ​area ​of a solid hemisphere of diameter ​'$2d$' ​is ​:

   1. (a)$3\pi d^2$
   2. (b)$2\pi d^2$
   3. (c)$\frac{1}{2}\pi d^2$
   4. (d)$\frac{3}{4}\pi d^2$
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2. Q922 CBSE Board 2026
   A hemispherical bowl is made of steel ​of thickness $1$ cm. The outer radius ​of the bowl is $6$ cm. The ​volume of ​steel used ​(in ${\text{cm}}^3$) is :

   1. (a)$182\pi$
   2. (b)$\frac{182}{3}\pi$
   3. (c)$\frac{682}{3}\pi$
   4. (d)$\frac{364}{3}\pi$
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3. Q923 CBSE Board 2026
   A ​card ​is ​drawn ​from a well-shuffled deck ​of $52$ playing cards. The probability of getting a queen ​of spade is

   1. (a)$\frac{1}{26}$
   2. (b)$\frac{1}{52}$
   3. (c)$0$
   4. (d)$\frac{1}{4}$
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4. Q924 CBSE Board 2026
   Volumes of two ​spheres ​are in the ​ratio $64:27$. ​The ratio ​of their surface areas ​is:

   1. (a)$4:3$
   2. (b)$3:4$
   3. (c)$16:9$
   4. (d)$9:16$
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5. Q925 CBSE Board 2026
   The median and mode of ​a ​distribution ​are $25.2$ ​and $26.1$ ​respectively. The mean ​of the distribution is :

   1. (a)$24.75$
   2. (b)$24.25$
   3. (c)$24.3$
   4. (d)$25.5$
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6. Q926 CBSE Board 2026
   An ice-cream cone of radius $r$ and ​height $h$ is completely filled by two spherical scoops of ​ice-cream. ​If ​the radius ​of each spherical scoop is $\frac{r}{2}$, then $h:2r$ ​equals ​:

   1. (a)$1:8$
   2. (b)$1:2$
   3. (c)$1:1$
   4. (d)$2:1$
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7. Q927 CBSE Board 2026
   Meena calculates ​that ​the ​probability of her ​winning the first prize in a lottery is $0.08$. If ​total $800$ tickets were sold, the number of tickets bought ​by her, ​is

   1. (a)$64$
   2. (b)$640$
   3. (c)$100$
   4. (d)$10$
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8. Q928 CBSE Board 2026
   Two dice are ​thrown ​simultaneously. ​The ​probability of getting ​a ​sum of $7$ is :

   1. (a)$\frac{2}{9}$
   2. (b)$\frac{1}{9}$
   3. (c)$\frac{5}{36}$
   4. (d)$\frac{1}{6}$
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9. Q929 CBSE Board 2026
   If $\sin \theta =\frac{1}{7}$, then $\tan \theta$ ​is ​:

   1. (a)$\frac{1}{4\sqrt{3}}$
   2. (b)$\frac{1}{2\sqrt{3}}$
   3. (c)$\frac{4\sqrt{3}}{7}$
   4. (d)$\frac{6}{7}$
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10. Q930 CBSE Board 2026
    In the adjoining figure, ​the ​slant ​height ​of ​the conical part ​is :

    1. (a)$4$ cm
    2. (b)$7$ cm
    3. (c)$5$ cm
    4. (d)$25$ cm
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11. Q931 CBSE Board 2026
    If for ​a frequency distribution, ​the mean ​is $\frac{3}{4}$ times ​the median, then ​mode ​is :

    1. (a)equal to median
    2. (b)$\frac{3}{2}$ times the median
    3. (c)equal to mean
    4. (d)$3$ times the mean
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12. Q932 CBSE Board 2026
    Let '$a$' ​be the ​assumed mean and '$h$' be the class size for a ​grouped data. Which of the following ​is not the ​correct formula to find ​the mean of ​the grouped ​data ?

    1. (a)$\bar{x}=\frac{\sum f_i{x}_i}{\sum f_i}$
    2. (b)$\bar{x}=a+\frac{\sum f_i{d}_i}{\sum f_i}$, where $d_i=x_i-a$
    3. (c)$\bar{x}=a+\frac{\sum f_i{u}_i}{\sum f_i}$, where $u_i=\frac{x_i-a}{h}$
    4. (d)$\bar{x}=a+\frac{\sum f_i{y}_i}{\sum f_i}\times h$, where $y_i=\frac{x_i-a}{h}$
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13. Q933 CBSE Board 2026
    If ​the mean and ​mode of a data are $12$ and $21$ ​respectively, then ​its ​median ​is :

    1. (a)$6$
    2. (b)$13.5$
    3. (c)$15$
    4. (d)$14$
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14. Q934 CBSE Board 2026
    The ​mean ​and ​median of a frequency distribution are $43$ ​and $43.4$ respectively. ​The mode of the distribution is ​:

    1. (a)$43.4$
    2. (b)$42.4$
    3. (c)$44.2$
    4. (d)$49.3$
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15. Q935 CBSE Board 2026
    The length of a pendulum ​is $70$ ​cm and it describes an arc ​of length $88$ ​cm ​when it swings. The angle subtended by the arc at the ​centre is

    1. (a)$36^{\circ }$
    2. (b)$70^{\circ }$
    3. (c)$72^{\circ }$
    4. (d)$80^{\circ }$
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16. Q936 CBSE Board 2026
    A ​card ​is drawn ​from a packet of $50$ identical cards ​numbered ​from $1$ to $50$. ​The probability ​of drawing a number which is a perfect square, is :

    1. (a)$\frac{7}{50}$
    2. (b)$\frac{8}{50}$
    3. (c)$\frac{6}{50}$
    4. (d)$\frac{10}{50}$
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17. Q937 CBSE Board 2026
    In ​the given ​figure, $△ABC$ ​is an ​equilateral triangle. $AD$ is a ​median ​of the triangle ​joining the points $A\left(0,\frac{5\sqrt{3}}{2}\right)$, $D(0,0)$. ​Points $B$ and $C$ are (in same order) :

    1. (a)$(-5,0),(5,0)$
    2. (b)$\left(-\frac{5}{2},0\right),\left(\frac{5}{2},0\right)$
    3. (c)$(-10,0),(10,0)$
    4. (d)$(-5\sqrt{3},0),(5\sqrt{3},0)$
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18. Q938 CBSE Board 2026
    Arc $PQ$ subtends an angle $\theta$ at the ​centre of the ​circle with radius $6.3$ cm. ​If ​arc $PQ=11$ ​cm, then the ​value of $\theta$ is

    1. (a)$10^{\circ }$
    2. (b)$60^{\circ }$
    3. (c)$45^{\circ }$
    4. (d)$100^{\circ }$
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19. Q939 CBSE Board 2026
    A wire ​is attached from a ​point $A$ ​on the ground to the top ​of a pole $BC$, making ​an angle of elevation as $60^{\circ }$. If $AB=5\sqrt{3}$ ​m, ​then length of the wire is

    1. (a)$10$ m
    2. (b)$10\sqrt{3}$ m
    3. (c)$15$ m
    4. (d)$\frac{5}{2}\sqrt{3}$ m
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20. Q940 CBSE Board 2026
    If HCF of $66$ and $99$ ​is ​expressible in ​the form of $55m-132$, ​then ​the value ​of $m$ is :

    1. (a)$4$
    2. (b)$2$
    3. (c)$1$
    4. (d)$3$
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