Mathematics Questions

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

1. Q861 CBSE Board 2026
   A car is moving away from the base of ​a $30$ ​m high tower. The ​angle ​of elevation ​of the top of the tower from the car at an instant, when the car is $10\sqrt{3}$ ​m away from the base of the tower, is ​:

   1. (a)$30^{\circ }$
   2. (b)$45^{\circ }$
   3. (c)$90^{\circ }$
   4. (d)$60^{\circ }$
   Open question → 🔒 Log in to view the solution
2. Q862 CBSE Board 2026
   If $2\sin A=1$, ​then the ​value of $\tan A+\cot A$ is :

   1. (a)$\sqrt{3}$
   2. (b)$\frac{4}{\sqrt{3}}$
   3. (c)$\frac{\sqrt{3}}{2}$
   4. (d)$1$
   Open question → 🔒 Log in to view the solution
3. Q863 CBSE Board 2026
   In ​the ​given figure, $DE\parallel BC$. If $AD:AB=1:3$ and $AE=2.5$ cm, ​then $AC$ ​equals

   1. (a)$7.5$ cm
   2. (b)$5$ cm
   3. (c)$10$ cm
   4. (d)$2.5$ cm
   Open question → 🔒 Log in to view the solution
4. Q864 CBSE Board 2026
   In two concentric circles ​with centre $O$, the ​radius ​of the outer circle is $25$ ​cm. Chord $PQ$ of the outer circle is ​tangent to the inner circle ​at $R$. ​If $PQ=14$ cm, then the radius ​of the inner circle is:

   1. (a)$\sqrt{429}$ cm
   2. (b)$24$ cm
   3. (c)$\sqrt{674}$ cm
   4. (d)$20$ cm
   Open question → 🔒 Log in to view the solution
5. Q865 CBSE Board 2026
   The $n^{\text{th}}$ ​term ​of ​the ​A.P. $\frac{-1}{3},\frac{2}{3},\frac{5}{3},\frac{8}{3},\dots$ ​is :

   1. (a)$3n-4$
   2. (b)$n-\frac{4}{3}$
   3. (c)$\frac{n-2}{3}$
   4. (d)$\frac{n-4}{3}$
   Open question → 🔒 Log in to view the solution
6. Q866 CBSE Board 2026
   When $\sin A=\frac{1}{3}$, ​the ​value of $\cot A$ ​is

   1. (a)$\frac{2\sqrt{2}}{3}$
   2. (b)$2\sqrt{2}$
   3. (c)$\frac{1}{2\sqrt{2}}$
   4. (d)$3$
   Open question → 🔒 Log in to view the solution
7. Q867 CBSE Board 2026
   A card is drawn at random from a well ​shuffled ​deck of $52$ playing cards. ​The ​probability that it is either a ten ​or a king ​is :

   1. (a)$\frac{1}{26}$
   2. (b)$\frac{2}{13}$
   3. (c)$\frac{1}{13}$
   4. (d)$\frac{8}{26}$
   Open question → 🔒 Log in to view the solution
8. Q868 CBSE Board 2026
   If ​in a $△ABC$, $AB=6$ ​cm ​and $DE\parallel BC$ ​such ​that $AE=\frac{1}{3}AC$, then ​the length ​of $BD$ ​is

   1. (a)$2$ cm
   2. (b)$3$ cm
   3. (c)$4$ cm
   4. (d)$5$ cm
   Open question → 🔒 Log in to view the solution
9. Q869 CBSE Board 2026
   A cone with slant ​height $10$ cm and radius $6$ cm ​is surmounted on ​a hemisphere of the ​same radius. The ​height ​of the toy ​is:

   1. (a)$12$ cm
   2. (b)$16$ cm
   3. (c)$14$ cm
   4. (d)$10$ cm
   Open question → 🔒 Log in to view the solution
10. Q870 CBSE Board 2026
    The ​system of equations $x=2$ ​and $x=3$ has ​:

    1. (a)unique solution $(2,3)$
    2. (b)two solutions $(2,0)$ and $(3,0)$
    3. (c)no solution
    4. (d)infinitely many solutions
    Open question → 🔒 Log in to view the solution
11. Q871 CBSE Board 2026
    The $10^{\text{th}}$ term of ​the ​A.P. $\sqrt{2},\sqrt{8},\sqrt{18},\dots$ ​is ​:

    1. (a)$\sqrt{162}$
    2. (b)$\sqrt{200}$
    3. (c)$\sqrt{54}$
    4. (d)$\sqrt{94}$
    Open question → 🔒 Log in to view the solution
12. Q872 CBSE Board 2026
    If $a$, $b$ ​and $c$ are ​in ​A.P., ​then ​:

    1. (a)$2a$, $3b$ and $4c$ are also in A.P.
    2. (b)$a-2$, $b-2$ and $c-2$ are also in A.P.
    3. (c)$\frac{a}{2}$, $\frac{b}{3}$ and $\frac{c}{4}$ are also in A.P.
    4. (d)$a+2$, $b+3$ and $c+4$ are also in A.P.
    Open question → 🔒 Log in to view the solution
13. Q873 CBSE Board 2026
    If $TP$ and $TQ$ ​are two ​tangents to a circle with centre $O$ from an ​external point $T$ ​so that $\angle POQ=120^{\circ }$, ​then $\angle PTQ$ is equal ​to :

    1. (a)$60^{\circ }$
    2. (b)$70^{\circ }$
    3. (c)$80^{\circ }$
    4. (d)$90^{\circ }$
    Open question → 🔒 Log in to view the solution
14. Q874 CBSE Board 2026
    From ​a point ​on the ground, ​which is $60$ m away from the foot of a vertical ​tower, the angle of elevation of the top of the tower is found ​to be $45^{\circ }$. The height (in metres) of the ​tower is ​:

    1. (a)$10\sqrt{3}$
    2. (b)$30\sqrt{3}$
    3. (c)$60$
    4. (d)$30$
    Open question → 🔒 Log in to view the solution
15. Q875 CBSE Board 2026
    The value of $k$ ​for which ​sum of the ​zeroes ​of the ​polynomial $p(x)=3x^2-kx+6$ ​is $2$, is

    1. (a)$2$
    2. (b)$-6$
    3. (c)$-2$
    4. (d)$6$
    Open question → 🔒 Log in to view the solution
16. Q876 CBSE Board 2026
    If $\cos A=\frac{3}{5}$, ​then ​the ​value ​of $\tan A$ is:

    1. (a)$\frac{4}{5}$
    2. (b)$\frac{5}{4}$
    3. (c)$\frac{3}{4}$
    4. (d)$\frac{4}{3}$
    Open question → 🔒 Log in to view the solution
17. Q877 CBSE Board 2026
    In the given figure, $PT$ is a ​tangent ​to the circle with centre $O$ ​and radius $r$. ​If $\angle POT=45^{\circ }$, then the length of $OP$ ​is ​:

    1. (a)$r\sqrt{2}$
    2. (b)$\sqrt{2r}$
    3. (c)$2r$
    4. (d)$r^2$
    Open question → 🔒 Log in to view the solution
18. Q878 CBSE Board 2026
    $\frac{1+{\tan }^{2}A}{1+{\cot }^{2}A}$ ​equals to ​:

    1. (a)${\tan }^{2}A$
    2. (b)$-1$
    3. (c)$-{\tan }^{2}A$
    4. (d)${\cot }^{2}A$
    Open question → 🔒 Log in to view the solution
19. Q879 CBSE Board 2026
    A camping tent in hemispherical ​shape of radius $1.4$ ​m, has a door ​opening of area $0.50$ ​m${}^2$. Outer surface ​area of ​the tent ​is :

    1. (a)$11.78$ m${}^2$
    2. (b)$12.32$ m${}^2$
    3. (c)$11.82$ m${}^2$
    4. (d)$12.86$ m${}^2$
    Open question → 🔒 Log in to view the solution
20. Q880 CBSE Board 2026
    From a point $P$, tangents $PQ$ ​and $PR$ are drawn to ​a circle ​with ​centre $O$ and radius $6$ ​cm. If $OP=10$ cm, then ​area of quadrilateral $PQOR$ ​is :

    1. (a)$48{\text{cm}}^2$
    2. (b)$24{\text{cm}}^2$
    3. (c)$96{\text{cm}}^2$
    4. (d)$72{\text{cm}}^2$
    Open question → 🔒 Log in to view the solution