Mathematics Questions

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

1. Q1061 CBSE Board 2026
   Prove that $\sqrt{2}$ ​is ​an ​irrational ​number.
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2. Q1062 CBSE Board 2026
   A circle ​of diameter $20$ ​cm is equally ​divided ​into five sectors. Find the area and ​perimeter ​of one of the sectors.
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3. Q1063 CBSE Board 2026
   Prove ​that $\frac{2+3\sqrt{5}}{7}$ is ​an irrational number, given that $\sqrt{5}$ is ​an ​irrational number.
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4. Q1064 CBSE Board 2026
   Prove ​that a parallelogram ​circumscribing ​a ​circle, is a rhombus.
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5. Q1065 CBSE Board 2026
   Given ​that $\sqrt{5}$ is ​an ​irrational number, prove that $3+2\sqrt{5}$ ​is also ​an ​irrational ​number.
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6. Q1066 CBSE Board 2026
   Neha claimed that there does not ​exist ​any irrational number ​between $1$ and $2$. Raunak claimed ​that $\sqrt{2}$ lies ​between $1$ and $2$ and $\sqrt{2}$ is an irrational number. Who do you think is correct ? ​Justify by proving either $\sqrt{2}$ as ​an irrational number or otherwise.
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7. Q1067 CBSE Board 2026
   In a ​class test, ​Veer scored $6$ more than ​twice as ​many marks as Kevin scored. If ​one of them had scored $4$ more ​marks, their total score would have been $40$. Find ​the marks obtained by Veer and Kevin.
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8. Q1068 CBSE Board 2026
   Prove that ​: $(\sin A+\sec A{)}^2+(\cos A+\csc A{)}^2=(1+\sec A\csc A{)}^2$
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9. Q1069 CBSE Board 2026
   Solve the ​linear ​equations $3x+y=14$ and $y=2$ ​graphically.
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10. Q1070 CBSE Board 2026
    Find the ratio in which the $x$-axis ​divides the line segment joining the ​points $(-6,5)$ ​and $(-4,-1)$. Also, ​find the ​point ​of ​intersection.
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11. Q1071 CBSE Board 2026
    Find the coordinates ​of ​the ​points of ​trisection of ​the line ​segment joining the points $A(-1,4)$ and $B(-3,-2)$.
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12. Q1072 CBSE Board 2026
    Points $P(6,0)$, $Q(2,8)$ and $R(-2,4)$ ​are vertices of $△PQR$. It is given ​that $MN\parallel QR$ such that $\frac{PM}{MQ}=\frac{1}{3}$. ​Using ​distance ​formula and ratio formula, show ​that $\frac{MN}{QR}=\frac{1}{4}$.

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13. Q1073 CBSE Board 2026
    In the ​given figure, chord $AB$ subtends ​an angle ​of $120^{\circ }$ at the ​centre of the circle with radius $7$ cm. ​Find

    1. (i)​perimeter of major sector $OACB$, and
    2. (ii)area of ​the shaded segment, if area of $△OAB=21.2{\text{cm}}^2$.

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14. Q1074 CBSE Board 2026
    Chord $AB$ ​of a ​circle ​with centre $O$ and radius $21$ mm subtends an angle of $120^{\circ }$ at ​the centre. Find the perimeter ​of the shaded ​region. (Use $\sqrt{3}=1.73$)

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15. Q1075 CBSE Board 2026
    A chord ​of a circle of ​radius $14$ ​cm subtends ​a ​right angle at the centre. Find the ​area of ​the corresponding ​

    1. (i)minor segment
    2. (ii)major segment.
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16. Q1076 CBSE Board 2026
    Each root of a ​quadratic equation $a{x}^2+bx+c=0$ ​is $2$ ​more than ​each ​of the ​roots of the equation $3x^2-2x=1$. Find the roots ​of the quadratic equation $a{x}^2+bx+c=0$.
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17. Q1077 CBSE Board 2026
    Solve ​the following pair ​of ​linear ​equations: $31x+43y-117=0$; $43x+31y=105$.
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18. Q1078 CBSE Board 2026
    In ​an A.P., ​the $15^{\text{th}}$ term exceeds the $8^{\text{th}}$ ​term ​by $21$. ​If the ​sum of the first $10$ terms is $55$, then form the ​A.P.
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19. Q1079 CBSE Board 2026
    Find the ​coordinates of ​the ​points ​of trisection of ​the ​line segment ​joining the points $P(5,-4)$ ​and $Q(-4,2)$.
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20. Q1080 CBSE Board 2026
    Solve the following ​system ​of equations ​graphically ​: $x+3y=6$ and $2x-3y=12$ Also, ​find the area of the triangle ​formed by the ​lines $x+3y=6$, $x=0$ and $y=0$.
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