Mathematics Questions

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

1. Q821 CBSE Board 2026
   The sum ​of first $n$ terms ​of an ​A.P. is $50\sqrt{2}$. ​If the first and ​the ​last terms ​are $\sqrt{2}$ and $19\sqrt{2}$ respectively, then the value of $n$ is:

   1. (a)$10$
   2. (b)$5$
   3. (c)$15$
   4. (d)$20$
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2. Q822 CBSE Board 2026
   The ​distance ​between ​points $(3,0)$ and $(0,-3)$ is ​:

   1. (a)$3$ units
   2. (b)$6$ units
   3. (c)$\sqrt{6}$ units
   4. (d)$\sqrt{18}$ units
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3. Q823 CBSE Board 2026
   In ​the ​given ​figure, if $ME\parallel SU$, then ​which of the following statements ​is ​correct ​?

   1. (a)$△MOE\sim △SOU$
   2. (b)$△MOE\sim △SUO$
   3. (c)$△OEM\sim △USO$
   4. (d)$△OEM\sim △OSU$
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4. Q824 CBSE Board 2026
   Observe the given triangles ​: Which of the ​following statements ​is ​true ​?

   1. (a)$△LMN\sim △ABC$
   2. (b)$△LMN\sim △ACB$
   3. (c)$△NML\sim △ABC$
   4. (d)$△NML\sim △ACB$
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5. Q825 CBSE Board 2026
   The ​mid-point of the line ​segment joining ​the points $(5,-4)$ and $(6,4)$ ​lies on ​:

   1. (a)$x$-axis
   2. (b)$y$-axis
   3. (c)origin
   4. (d)neither $x$-axis nor $y$-axis
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6. Q826 CBSE Board 2026
   In triangles $ABC$ and $PQR$, $\angle A=\angle Q$ ​and $\angle B=\angle R$, then $AB:AC$ ​is ​equal to ​:

   1. (a)$PQ:PR$
   2. (b)$PQ:QR$
   3. (c)$QR:QP$
   4. (d)$PR:QR$
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7. Q827 CBSE Board 2026
   The ​probability of getting ​sum ​greater ​than $10$, ​when ​two dice are rolled ​together, is

   1. (a)$\frac{1}{9}$
   2. (b)$\frac{1}{18}$
   3. (c)$\frac{1}{12}$
   4. (d)$1$
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8. Q828 CBSE Board 2026
   If two tangents ​inclined at an angle ​of $60^{\circ }$ are drawn from an external point ​to ​a circle ​of ​radius $6$ cm, then ​the length of each tangent is:

   1. (a)$3\sqrt{3}$ cm
   2. (b)$6$ cm
   3. (c)$12$ cm
   4. (d)$6\sqrt{3}$ cm
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9. Q829 CBSE Board 2026
   Equation ​of ​another ​line parallel ​to the ​line represented by $2x-6y=7$ is ​:

   1. (a)$y=3x-7$
   2. (b)$2x=9-6y$
   3. (c)$x-3y=7$
   4. (d)$x=\frac{7}{2}-3y$
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10. Q830 CBSE Board 2026
    The value ​of $k$ ​for which ​the ​system of linear ​equations $\frac{x}{2}+\frac{y}{3}=5$ and $2x+ky=7$ is inconsistent, is

    1. (a)$\frac{3}{4}$
    2. (b)$\frac{4}{3}$
    3. (c)$\frac{1}{3}$
    4. (d)$3$
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11. Q831 CBSE Board 2026
    If $a_n$ ​represents the $n^{\text{th}}$ term of ​the ​A.P. $-\frac{15}{4},-\frac{10}{4},-\frac{5}{4},\dots$ then ​the ​value ​of $a_{16}-a_{12}$ is :

    1. (a)$4$
    2. (b)$\frac{5}{4}$
    3. (c)$5$
    4. (d)$\frac{25}{4}$
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12. Q832 CBSE Board 2026
    If $△DEF\sim △PQR$ such ​that $3DE=PQ$ and $EF=6$ cm, ​then ​the ​length of $QR$ is ​:

    1. (a)$12\text{cm}$
    2. (b)$3\text{cm}$
    3. (c)$2\text{cm}$
    4. (d)$18\text{cm}$
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13. Q833 CBSE Board 2026
    While calculating ​mean of a ​grouped frequency ​distribution ​using step deviation ​method $\left(u=\frac{x-a}{h}\right)$ it ​was found that $\bar{x}=62$, $a=47.5$, $h=5$. ​The value ​of $\bar{u}$ is:

    1. (a)$3$
    2. (b)$14.5$
    3. (c)$2.9$
    4. (d)$3.1$
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14. Q834 CBSE Board 2026
    If $△ABC\sim △ADE$ ​in the ​adjoining figure, then which ​of ​the ​following is ​true ?

    1. (a)$\frac{AB}{BE}=\frac{AC}{CD}$
    2. (b)$\frac{AB}{AD}=\frac{AC}{AE}$
    3. (c)$\frac{AB}{BC}=\frac{AE}{DE}$
    4. (d)$\frac{AC}{AD}=\frac{AB}{AE}$
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15. Q835 CBSE Board 2026
    In the ​given ​figure, ​if $△ACP\sim △DCP$, then ​:

    1. (a)$\angle DCP=60^{\circ }$
    2. (b)$\angle DCP=30^{\circ }$
    3. (c)$\angle DCP=90^{\circ }$
    4. (d)$\angle DPC=30^{\circ }$
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16. Q836 CBSE Board 2026
    Two isosceles triangles :

    1. (a)are always similar, but not congruent.
    2. (b)are always congruent, but not similar.
    3. (c)may or may not be similar.
    4. (d)are always similar and congruent.
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17. Q837 CBSE Board 2026
    Given that $\sin \theta =\frac{a}{b}$, ​then $\cos \theta$ ​is ​equal ​to ​:

    1. (a)$\frac{b}{\sqrt{b^2-a^2}}$
    2. (b)$\frac{b}{a}$
    3. (c)$\frac{\sqrt{b^2-a^2}}{b}$
    4. (d)$\frac{a}{\sqrt{b^2-a^2}}$
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18. Q838 CBSE Board 2026
    The ​distance ​of the ​point $A(4a,3a)$ from ​the ​x-axis ​is :

    1. (a)$3a$
    2. (b)$-3a$
    3. (c)$4a$
    4. (d)$-4a$
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19. Q839 CBSE Board 2026
    The ​graph of a polynomial $p(x)$ ​is ​shown here. The ​number of ​zeroes ​of the polynomial $p(x)$ is

    1. (a)$5$
    2. (b)$1$
    3. (c)$0$
    4. (d)$4$
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20. Q840 CBSE Board 2026
    If ​in two triangles $ABC$ ​and $DEF$, $\frac{AB}{EF}=\frac{BC}{DE}=\frac{CA}{DF}$; ​then

    1. (a)$△DEF\sim △BCA$
    2. (b)$△DEF\sim △CBA$
    3. (c)$△ABC\sim △DEF$
    4. (d)$△ABC\sim △DFE$
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