Mathematics Questions

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

1. Q1161 CBSE Board 2026
   In ​the adjoining ​figure, $△ABE\cong △ACD$. Prove ​that ​:

   1. (i)$△ADE\sim △ABC$
   2. (ii)$△BOD\sim △COE$

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2. Q1162 CBSE Board 2026
   In the given figure, quadrilateral PQRS ​circumscribes the ​circle with centre O. ​Prove that the ​opposite sides ​of the quadrilateral PQRS subtend supplementary angles at the ​centre O.

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3. Q1163 CBSE Board 2026
   A faster train takes one ​hour less than a ​slower train for a journey of $200$ ​km. If the speed of the ​slower train is $10$ km/hr ​less ​than that of the faster train, find the speeds of ​the two ​trains.
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4. Q1164 CBSE Board 2026
   A person on ​a tour has ​₹ $4,200$ for expenses. If ​he extends his ​tour for $3$ days, he has ​to cut down his daily expenses by ​₹ $70$. ​Find the original duration ​of the tour.
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5. Q1165 CBSE Board 2026
   $D$ ​is the mid-point of ​side $BC$ of $△ABC$. $CE$ and $BF$ intersect ​at $O$, ​a point on $AD$. $AD$ ​is ​produced to $G$ such that $OD=DG$. Prove that : ​

   1. (i)$OBGC$ is a parallelogram.
   2. (ii)$EF\parallel BC$.
   3. (iii)$△AEF\sim △ABC$.

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6. Q1166 CBSE Board 2026
   The sum of ​numerator and denominator of a ​fraction is $4$ less than twice the ​denominator. ​If each ​of the numerator and denominator is decreased by $1$, the ​fraction ​becomes $\frac{1}{3}$. Find the fraction.
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7. Q1167 CBSE Board 2026
   Sides $AB$, $AC$ and ​altitude $AD$ ​of $△ABC$ ​are ​proportional to sides $PQ$, $PR$ ​and ​altitude $PS$ of ​another triangle $PQR$. Prove that $△ABC\sim △PQR$.
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8. Q1168 CBSE Board 2026
   The ​sum of the areas of two ​squares is $640{\text{m}}^2$. If the ​difference in ​their perimeters is $64$ m, find ​the ​sides of the two ​squares.
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9. Q1169 CBSE Board 2026
   The area of a right-angled triangle ​is $600{\text{cm}}^2$. If the ​base ​of the triangle ​exceeds the altitude ​by $10$ cm, find all ​the three dimensions of the ​triangle.
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10. Q1170 CBSE Board 2026
    Through ​the ​mid-point $Q$ of side $CD$ of a ​parallelogram $ABCD$, ​the line $AR$ is ​drawn which intersects $BD$ ​at $P$ ​and meets $BC$ produced at $R$. ​Prove that:

    1. (i)$AQ=QR$
    2. (ii)$AP=2PQ$
    3. (iii)$PR=2AP$

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11. Q1171 CBSE Board 2026
    Three consecutive positive ​integers are ​such that sum of ​square of the first and the ​product of the ​other ​two is $67$, find the integers.
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12. Q1172 CBSE Board 2026
    $AD$ and $PS$ ​are respectively ​the ​medians ​of $△ABC$ ​and $△PQR$. If $△ABC\sim △PQR$, ​then ​prove that

    1. (i)$△ADC\sim △PSR$
    2. (ii)$\frac{AD}{PS}=\frac{BC}{QR}$.

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13. Q1173 CBSE Board 2026
    A kite is ​flying at a height of $60$ m above the ​ground level. Ravi, ​standing at the roof of the house ​is holding the string straight and observes ​the angle of ​elevation of kite as $30^{\circ }$. From the bottom of the same building, the angle of elevation of kite is $45^{\circ }$. Find the length of the string and height of roof from the ​ground. (Use $\sqrt{3}=1.73$)
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14. Q1174 CBSE Board 2026
    Two poles of equal heights are standing opposite ​to ​each other on either side of the road which is $90$ m wide. From a point between them on the road, the angles ​of ​elevation of the top ​of the poles ​are $30^{\circ }$ and $60^{\circ }$ respectively. Find the height of the poles ​and the distances ​of the point from the poles. [Use $\sqrt{3}=1.732$]
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15. Q1175 CBSE Board 2026
    The angle of elevation ​of the top of a building from the ​foot of the tower is $30^{\circ }$ ​and ​the angle of elevation of the top of ​the tower from the foot of the ​building is $60^{\circ }$. If the tower is $60$ m high, find the height of the building and the ​distance between the building and the tower. ​(Use $\sqrt{3}=1.73$)
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16. Q1176 CBSE Board 2026
    State and ​prove ​Basic Proportionality ​Theorem.
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17. Q1177 CBSE Board 2026
    $ABCD$ is a rectangle of dimensions $80\text{ cm}\times 60\text{ cm}$. ​Another rectangle $PQRS$ ​is drawn inside $ABCD$ ​leaving space of equal ​width $x$ cm along ​the edges of $ABCD$. If area $PQRS$ is half of the area $ABCD$, then ​find the ​value of $x$.
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18. Q1178 CBSE Board 2026
    The angle of elevation of the top of a tower ​as observed from a ​point ​in a horizontal plane through the foot of the ​tower is $30^{\circ }$. ​When the observer moves towards the tower a distance of $100$ m, he finds the angle of elevation of ​the top to be $60^{\circ }$. ​Find ​the height of the tower and the distance of first position from the tower.
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19. Q1179 CBSE Board 2026
    Solve ​the following ​system ​of ​equations graphically ​: $x-2y=3$, $3x-8y=7$
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20. Q1180 CBSE Board 2026
    The mean ​of the following ​frequency ​distribution is $28$. If ​sum of all frequencies ​is $100$, then ​find the ​values of $p$ and $q$ :
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