Mathematics Questions

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

1. Q801 CBSE Board 2026
   The ​common ​difference ​of the ​AP ​: $\sqrt{2},2\sqrt{2},3\sqrt{2},4\sqrt{2},\dots$ is ​:

   1. (a)$\sqrt{2}$
   2. (b)$1$
   3. (c)$2\sqrt{2}$
   4. (d)$-\sqrt{2}$
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2. Q802 CBSE Board 2026
   If the ​pair of linear ​equations ​: $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$ is ​consistent and dependent, ​then

   1. (a)$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$
   2. (b)$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}=\frac{c_1}{c_2}$
   3. (c)$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$
   4. (d)$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
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3. Q803 CBSE Board 2026
   If ​value of $\cot \theta$ ​is $\sqrt{5}$, then $\sin \theta$ ​equals

   1. (a)$\frac{1}{\sqrt{6}}$
   2. (b)$\sqrt{6}$
   3. (c)$\frac{\sqrt{5}}{6}$
   4. (d)$\frac{1}{2}$
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4. Q804 CBSE Board 2026
   The ​fourth ​vertex $D$ ​of a parallelogram $ABCD$ whose three ​vertices ​are $A(-4,1)$, $B(4,5)$ and $C(6,1)$ is:

   1. (a)$(-2,-3)$
   2. (b)$(3,-2)$
   3. (c)$(0,-1)$
   4. (d)$(0,1)$
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5. Q805 CBSE Board 2026
   The ​number ​of ​multiples ​of $4$ ​lying between $12$ and $250$ is ​:

   1. (a)$59$
   2. (b)$59.5$
   3. (c)$60$
   4. (d)$61$
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6. Q806 CBSE Board 2026
   In the ​given figure, $DE\parallel BC$. ​If $\frac{AD}{DB}=\frac{1}{3}$ ​and $AC=6$ ​cm, ​then length $AE$ is

   1. (a)$1.5$ cm
   2. (b)$1$ cm
   3. (c)$2$ cm
   4. (d)$3$ cm
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7. Q807 CBSE Board 2026
   While calculating ​mean ​of a grouped frequency distribution, ​step deviation ​method was used $\left(\frac{x-a}{h}=u\right)$. ​It ​was ​found ​that $\bar{x}=64$, $h=5$ and $a=62.5$. The value of $\bar{u}$ is

   1. (a)$0.5$
   2. (b)$1.5$
   3. (c)$0.3$
   4. (d)$7.5$
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8. Q808 CBSE Board 2026
   $ABCD$ is a trapezium in which $AB\parallel DC$ ​and $E,F$ ​are points on $AD$ ​and $BC$ respectively ​such ​that $EF\parallel DC$. ​If $ED=36$ ​cm, $BF=70$ cm and $FC=30$ cm, then ​the length of $AD$ is :

   1. (a)$124$ cm
   2. (b)$120$ cm
   3. (c)$110$ cm
   4. (d)$114$ cm
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9. Q809 CBSE Board 2026
   The graph of polynomial $p(x)=k$ ​is ​shown ​here. Number ​of ​zeroes of ​polynomial $p(x)$ is :

   1. (a)$0$
   2. (b)$1$
   3. (c)$2$
   4. (d)infinitely many
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10. Q810 CBSE Board 2026
    The ​discriminant ​of the ​quadratic ​equation $a{x}^2+x+a=0$ ​is :

    1. (a)$\sqrt{1-4a^2}$
    2. (b)$1-4a^2$
    3. (c)$4a^2-1$
    4. (d)$\sqrt{4a^2-1}$
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11. Q811 CBSE Board 2026
    In ​the given ​figure, ​the length of hypotenuse of the ​right $△AOB$ ​is ​:

    1. (a)$3$ units
    2. (b)$4$ units
    3. (c)$5$ units
    4. (d)$25$ units
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12. Q812 CBSE Board 2026
    The ​co-ordinates ​of ​the ​mid-point of ​the ​line segment joining points $A(p-1,q+1)$ and $B(p+1,q-1)$ are given by :

    1. (a)$(p,q)$
    2. (b)$(2p,2q)$
    3. (c)$\left(\frac{p+1}{2},\frac{q+1}{2}\right)$
    4. (d)$\left(\frac{p-1}{2},\frac{q-1}{2}\right)$
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13. Q813 CBSE Board 2026
    If $△ABC$ and $△DEF$ are similar ​such that $2AB=DE$ ​and $BC=8$ ​cm, then $EF$ is equal ​to :

    1. (a)$4$ cm
    2. (b)$8$ cm
    3. (c)$12$ cm
    4. (d)$16$ cm
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14. Q814 CBSE Board 2026
    Which ​of ​the following ​sequence ​is not ​an ​A.P. ?

    1. (a)$2,\frac{5}{2},3,\frac{7}{2},\dots$
    2. (b)$-1.2,-3.2,-5.2,-7.2,\dots$
    3. (c)$\sqrt{2},\sqrt{8},\sqrt{18},\dots$
    4. (d)$1^2,3^2,5^2,7^2,\dots$
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15. Q815 CBSE Board 2026
    A chord $QR$ subtends ​an ​angle of $105^{\circ }$ ​at the centre $O$ ​of ​the ​circle. The ​measure ​of $\angle RQP$ is

    1. (a)$\frac{75^{\circ }}{2}$
    2. (b)$\frac{105^{\circ }}{2}$
    3. (c)$75^{\circ }$
    4. (d)$15^{\circ }$
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16. Q816 CBSE Board 2026
    The ​ratio in ​which the $x$-axis divides the ​line ​segment joining ​the points $A(-8,4)$ and $B(-6,-2)$ ​is:

    1. (a)$5:1$
    2. (b)$3:1$
    3. (c)$2:1$
    4. (d)$1:2$
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17. Q817 CBSE Board 2026
    A ​cone ​of maximum size is carved out from a ​solid cube of ​edge ​length $l$. The volume ​of ​the cone is :

    1. (a)$\frac{\pi l^3}{12}$
    2. (b)$\frac{\pi l^3}{3}$
    3. (c)$l^3\left(1-\frac{\pi }{3}\right)$
    4. (d)$\frac{\pi l^3}{8}$
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18. Q818 CBSE Board 2026
    In ​the given ​figure, ​a circle is centred at $(1,2)$. ​The diameter of the circle is

    1. (a)$4$
    2. (b)$2\sqrt{2}$
    3. (c)$\sqrt{5}$
    4. (d)$2\sqrt{5}$
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19. Q819 CBSE Board 2026
    A conical ​cavity ​of maximum volume is carved out from ​a wooden ​solid hemisphere of radius $10$ cm. Curved surface area ​of ​the ​cavity carved out is (use $\pi =3.14$)

    1. (a)$314\sqrt{2}{\text{cm}}^2$
    2. (b)$314{\text{cm}}^2$
    3. (c)$\frac{3140}{3}{\text{cm}}^2$
    4. (d)$3140\sqrt{2}{\text{cm}}^2$
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20. Q820 CBSE Board 2026
    If $x\cdot \tan 45^{\circ }\cdot \sin 30^{\circ }=\cos 30^{\circ }\cdot \cot 60^{\circ }$, ​then $x$ is ​equal to

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