Mathematics Questions

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

1. Q1181 CBSE Board 2026
   In ​the ​adjoining figure, $△OAB$ is an ​equilateral triangle and the area of the ​shaded region is $750\pi {\text{ cm}}^2$. ​Find the perimeter ​of the shaded region.

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2. Q1182 CBSE Board 2026
   ABCD ​is a square. With centres ​A, B, ​C and D, four quadrants (each touching two of the ​remaining three) are drawn inside the square ABCD as ​shown in the figure. If the area of the shaded region is $42{\text{ cm}}^2$, ​find the side of the square ABCD. Also, find the perimeter of the shaded region.

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3. Q1183 CBSE Board 2026
   A pen stand is made up of wood and is in the shape of a cuboid with four conical depressions and ​cylindrical extensions to hold pens. The depressions are hollowed out from ​the wooden cuboidal stand and cylindrical extensions are made ​up of metal attached separately as shown in the figure ​given below : The dimensions of the cuboidal block of wood are $15$ cm $\times$ $10$ cm $\times$ $3.5$ cm. The radius of each ​conical depression is $0.5$ cm and depth is $1.4$ cm. The radius and height of each cylindrical metal extension are $0.5$ cm and $4.9$ cm respectively.

   1. (i)Find the volume of ​wood in the entire stand.
   2. (ii)Find ​the inner surface area of a conical depression along with that ​of the cylindrical extension. (Use $\sqrt{221}=14.8$)

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4. Q1184 CBSE Board 2026
   In the ​given figure, $CM$ ​and $RN$ are ​respectively the medians ​of $△ABC$ ​and $△PQR$. ​If $△ABC\sim △PQR$, then prove that :

   1. (i)$△AMC\sim △PNR$
   2. (ii)$△CMB\sim △RNQ$

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5. Q1185 CBSE Board 2026
   As shown in the given figure, ​a girl ​of height $90$ cm is walking away from the base of ​a lamp post at a speed of $1.2$ m/s. If ​the ​lamp is $3.6$ m above ​the ground, find the length of her shadow ​after $4$ seconds.

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6. Q1186 CBSE Board 2026
   A ​train covers a distance of $90$ km ​at a uniform speed. Had ​the ​speed been $15$ km/h more, it ​would have taken $30$ minutes less ​for ​the same journey. Find the original speed of the train.
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7. Q1187 CBSE Board 2026
   Two pillars of equal heights stand on either side of a roadway $150$ m wide. ​From a point on the roadway between the pillars, the angles of ​elevation of ​the ​top of the pillars are $60^{\circ }$ and $30^{\circ }$ respectively. ​Find the ​height of the pillars and the position of the point from the pillars.
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8. Q1188 CBSE Board 2026
   Five years ago, Adil was ​thrice ​as old as Bharat. Ten ​years later Adil shall be twice as old as ​Bharat. To know the present ages of Adil and Bharat :

   1. (i)form the linear ​equations ​representing the above information.
   2. (ii)show that the system of equations is consistent with unique solution.
   3. (iii)find the ​present ​ages of Adil and Bharat.
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9. Q1189 CBSE Board 2026
   Find ​median and ​mode ​of ​the ​following ​distribution :
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10. Q1190 CBSE Board 2026
    $O$ and $O^{\prime }$ are the centres of the circles of radius $r$ as shown in figures ​

    1. (i)and ​
    2. (ii)​respectively. Find the ratio of ​area of ​shaded region in figure (i) to that of area of ​shaded region in ​figure (ii).

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11. Q1191 CBSE Board 2026
    The mean of ​the following ​frequency distribution is $35$. ​Find ​the values of $x$ and $y$, if the ​sum ​of ​frequencies is $25$ :
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12. Q1192 CBSE Board 2026
    An ​SBI health insurance ​agent ​found the following data for distribution of ages ​of $100$ policy holders. The health insurance policies are given to persons of age $15$ ​years ​and onwards, but less than $60$ years. Find the modal age and median ​age of the policy holders.
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13. Q1193 CBSE Board 2026
    Find mean ​and ​mode of ​the ​following ​data:
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14. Q1194 CBSE Board 2026
    Find ​the mean ​and the ​mode for the following ​frequency ​distribution :
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15. Q1195 CBSE Board 2026
    A boy standing on a horizontal plane ​is flying a kite ​with a string of length $60$ m, at an angle of elevation of $30^{\circ }$. ​Another boy ​standing on the roof of a $20$ m high building, finds the angle of elevation of same kite to be $45^{\circ }$. If both the boys are on opposite sides of the kite, find the distance of the first boy from the ​base of the ​building. ​Also, find the height of the kite from the ground. (Use $\sqrt{3}=1.73$)
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16. Q1196 CBSE Board 2026
    $PQ$ and $PR$ are two tangents ​to a ​circle with centre $O$ and ​radius $5$ cm. $AB$ is ​another tangent to the circle at $C$ which lies on $OP$. If $OP=13$ cm, then ​find the length $AB$ and $PA$.

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17. Q1197 CBSE Board 2026
    From ​a solid ​cylinder ​whose height is $2.8$ cm and radius $2.1$ ​cm, a conical cavity of the same height and same radius is hollowed out. Find the volume and the total ​surface ​area of the remaining ​solid.
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18. Q1198 CBSE Board 2026
    The mode of ​the following ​data is $3.286$ ​: Find ​the ​mean and median ​of the ​above data.
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19. Q1199 CBSE Board 2026
    The ​median of the ​following ​data is $525$. If the sum ​of all the ​frequencies ​is $100$, find the ​values of $p$ and $q$.
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20. Q1200 CBSE Board 2026
    The following table ​shows the weight (in kg) of $40$ ​students of ​class ​X : Find the mean ​weight and median weight.
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