Mathematics Questions

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

1. Q1041 CBSE Board 2026
   If $\sin (A+2B)=\frac{\sqrt{3}}{2}$ and $\cos (A+4B)=0$, $A>B$, ​find $A$ ​and $B$.
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2. Q1042 CBSE Board 2026
   If the HCF of $210$ ​and $55$ ​is expressed ​as $210\times 5+55m$, then ​find ​the ​value of $m$.
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3. Q1043 CBSE Board 2026
   For ​acute angles $A$ and $B$, and $A+2B$ ​and $2A+B$ ​are acute, ​if $\tan (A+2B)=\sqrt{3}$ and $\sin (2A+B)=\frac{1}{\sqrt{2}}$, then find ​the ​measures of ​angles $A$ ​and $B$.
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4. Q1044 CBSE Board 2026
   If $4\tan A=3$, ​then ​find ​the value of $\frac{{\mathrm{cosec}}^{2}A+1}{{\mathrm{cosec}}^{2}A-1}$.
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5. Q1045 CBSE Board 2026
   In ​the given figure, $TP$ is tangent to a ​circle with centre $O$. Diameter $BA$ ​when produced meets ​the tangent ​at $T$. If $\angle ABP=35^{\circ }$, then find the ​measure of $\angle PTA$.

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6. Q1046 CBSE Board 2026
   If $\sin (A+2B)=2\cos 60^{\circ }$ and $A=3B$, find ​the ​measures ​of $A$ and $B$.
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7. Q1047 CBSE Board 2026
   Two ​concentric circles are ​of ​radii $5$ cm and $4$ cm. ​Find ​the length of ​the ​chord of the larger circle which touches the smaller circle.
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8. Q1048 CBSE Board 2026
   In ​the ​given ​figure, $O$ is the centre of ​the ​circle. $PQ$ and $PR$ are tangents. Show that the ​quadrilateral $PQOR$ is ​cyclic.

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9. Q1049 CBSE Board 2026
   In the given ​figure, $AB\parallel DC$. ​If $OB=3OD$ and $CD=1.8$ cm, ​then ​find ​the length $AB$.

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10. Q1050 CBSE Board 2026
    All the red face cards are removed from ​a ​pack of $52$ playing cards. The ​remaining cards are well shuffled and then a card is drawn ​at random. ​Find ​the probability of ​getting a:

    1. (i)red ​card
    2. (ii)a king or queen
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11. Q1051 CBSE Board 2026
    A toy is in the form of a ​cone mounted on ​a hemisphere ​of radius $7$ cm. ​The total height ​of the ​toy is $31$ cm. ​Find the ​total surface area of the toy.

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12. Q1052 CBSE Board 2026
    $\alpha$ ​and $\beta$ ​are ​the zeroes of ​the polynomial $5x^2-16x-10$. Find ​the value of $\frac{\alpha }{\beta }+\frac{\beta }{\alpha }$.
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13. Q1053 CBSE Board 2026
    A ​bag contains $25$ ​balls. Some of them ​are yellow and others are green. One ball ​is drawn at ​random. If probability ​of getting a green ball is $\frac{3}{5}$, ​then find the number of yellow balls.
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14. Q1054 CBSE Board 2026
    In ​the ​given ​figure, $QR\parallel CB$ ​and $RP\parallel AC$. If $BR=10$ cm, $QA=12$ cm, $BP=12$ ​cm and $PC=18$ ​cm, then find ​the ​lengths of $AR$ and $QC$.

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15. Q1055 CBSE Board 2026
    A box consists of $60$ wall ​clocks, out of which $40$ are good, $15$ have minor defects and the remaining ​are broken. A ​trader will reject ​the box, if the clock taken out from the box is ​broken. The trader randomly takes out one clock from the box. What is the probability that :

    1. (i)the box will be rejected ​?
    2. (ii)the clock taken ​out of the ​box has minor defect ?
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16. Q1056 CBSE Board 2026
    A ​square dart board is divided into four equal squares ​as shown in the ​figure ​given below. If a dart hits ​square $APOS$, a player wins ₹ $100$. If a dart hits square $BPOQ$, a player loses ₹ $50$. If a dart hits square $OQCR$, a player loses ₹ $100$ and if it hits square $ORDS$, the player will ​win ₹ $25$. A player takes a ​turn and hits the dart board. What is the probability that

    1. (i)the player loses money ?
    2. (ii)the ​player wins ₹ $100$ ?

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17. Q1057 CBSE Board 2026
    A game of chance consists of spinning an arrow which comes to rest in one ​of the six equal sectors as ​shown in the ​given figure. A person spins an ​arrow ​once. What is the probability ​that the person

    1. (i)wins a laptop ?
    2. (ii)does not get a chance to spin again ?

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18. Q1058 CBSE Board 2026
    A chord $AB$ of ​a circle of radius $14$ cm makes ​a right angle at the ​centre ​of ​the ​circle. ​Find the area of the minor segment.
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19. Q1059 CBSE Board 2026
    An arc of ​length $22$ ​cm subtends ​an angle of $60^{\circ }$ ​at the centre of the circle. Find the area ​of the ​sector of the ​circle made by the arc.
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20. Q1060 CBSE Board 2026
    Prove ​that $\sqrt{5}$ ​is ​an ​irrational number.
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