Mathematics Questions

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

1. Q1141 CBSE Board 2026
   Determine graphically, the ​coordinates of vertices ​of a ​triangle ​whose ​equations are $2x-3y+6=0$; $2x+3y-18=0$ ​and $x=0$. Also, find the area ​of this triangle.
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2. Q1142 CBSE Board 2026
   Aarush bought $2$ pencils and $3$ chocolates for ₹ $11$ ​and Tanish bought $1$ pencil and $2$ chocolates for ​₹ $7$ from the same shop. Represent this situation in the form of a pair ​of linear ​equations. Find ​the ​price of $1$ ​pencil and $1$ chocolate, graphically.
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3. Q1143 CBSE Board 2026
   Venkat can ​row ​a boat in still water at the ​speed ​of $12$ km/h. He ferries tourists $15$ km upstream and $18$ ​km ​downstream in $3$ ​hours. Find the speed ​of the stream.
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4. Q1144 CBSE Board 2026
   The third and ninth term of an ​A.P. ​are $4$ and $-8$ respectively. ​

   1. (i)​Which term of the ​A.P. ​is zero?
   2. (ii)​Find the value of $n$ if $S_n=-36$.
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5. Q1145 CBSE Board 2026
   A ​fraction becomes $\frac{5}{6}$ ​when $3$ is added to both the ​numerator and the denominator. If $2$ is added to both the ​numerator and the denominator, the fraction ​becomes $\frac{9}{11}$. Express the ​given information algebraically as a system of linear equations in two variables. Hence, ​find the original ​fraction.
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6. Q1146 CBSE Board 2026
   In ​the given figure, $△ABC$ ​is ​a ​right angled triangle ​with $\angle A=90^{\circ }$. $AD$ is ​perpendicular to $BC$. Prove that:

   1. (i)$△DBA\sim △DAC$
   2. (ii)$D{A}^2=DB\times DC$ ​
   3. (iii)Find the area of $△ABC$ when $DB=9$ cm ​and $DC=16$ cm.

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7. Q1147 CBSE Board 2026
   Solve ​for $x$: $\frac{x-2}{x-3}+\frac{x-4}{x-5}=\frac{10}{3}$; $x\ne 3,5$.
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8. Q1148 CBSE Board 2026
   The ​median ​of the following data is $137$. ​Find the ​values ​of $x$ and $y$, given that ​total of frequencies is $68$.
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9. Q1149 CBSE Board 2026
   A person ​on tour has $\text{₹}5400$ for his expenses. If ​he extends his tour by $5$ days, he has to cut down his daily ​expenses ​by $\text{₹}180$. ​Find the ​original duration of the tour and ​daily ​expense.
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10. Q1150 CBSE Board 2026
    Express $\frac{24}{18-x}-\frac{24}{18+x}=1$ as ​a quadratic equation in ​standard form and ​find the discriminant ​of the ​quadratic equation, ​so obtained. Also, find the ​roots ​of the equation.
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11. Q1151 CBSE Board 2026
    Express $x-\frac{1}{x}=3$ as a quadratic ​equation ​in standard form and ​hence ​find its roots. Also, find the value of $a$ for which the equation $x+\frac{1}{x}=a$, when expressed ​as a ​quadratic equation, has real and equal roots.
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12. Q1152 CBSE Board 2026
    A motor boat, whose speed in still ​water is $20$ km/h, takes $1$ hour more ​to go $48$ km upstream than to return downstream to the ​same point. Find ​the ​speed ​of ​the ​stream.
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13. Q1153 CBSE Board 2026
    Find mean ​and ​mode of ​the ​following distribution ​:
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14. Q1154 CBSE Board 2026
    The total cost of ​a certain piece of cloth ​was ​₹$2100$. During special ​sale time, the shopkeeper offered $2$ m extra cloth ​for free, thus reducing the price ​of cloth per ​metre by ₹$120$. What was the original per metre ​price of the cloth and its length?
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15. Q1155 CBSE Board 2026
    $CD$ and $GH$ are respectively the ​bisectors ​of $\angle ACB$ ​and $\angle EGF$ ​such that $D$ and $H$ ​lie on sides $AB$ and $FE$ of $△ABC$ ​and $△EFG$ respectively. ​If $△ABC\sim △FEG$, then show ​that

    1. (i)$\frac{CD}{GH}=\frac{AC}{FG}$ and
    2. (ii)$△DCB\sim △HGE$.
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16. Q1156 CBSE Board 2026
    The sum of squares of ​two ​positive numbers ​is $100$. If ​one ​number exceeds ​the other by $2$, find the numbers.
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17. Q1157 CBSE Board 2026
    Two poles of equal ​heights are standing opposite each other on either side of the road, which is $80$ m ​wide. From a point between them on the ​road, the angles of elevation ​of the ​top of the poles are $60^{\circ }$ and $30^{\circ }$ respectively. ​Find the height of the poles and the ​distance of the point from the poles.
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18. Q1158 CBSE Board 2026
    Prove ​that, if a line is ​drawn parallel to one ​side of a triangle ​to intersect ​the other two sides in ​distinct ​points, the other two ​sides are divided in the same ratio.
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19. Q1159 CBSE Board 2026
    In $△ABC$, $AD$ is a median. $X$ is ​a point on $AD$ such ​that $AX:XD=2:3$. $BX$ is extended so ​that ​it intersects $AC$ ​at $Y$. ​Prove ​that $BX=4XY$.

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20. Q1160 CBSE Board 2026
    In ​the given ​figure, $TP$ ​and $TQ$ are tangents to a ​circle with ​centre $M$, touching another circle with centre $N$ ​at $A$ and $B$ respectively. It is given that $MQ=13$ ​cm, $NB=8$ cm, $BQ=35$ cm ​and $TP=80$ cm.

    1. (i)Name the quadrilateral $MQBN$.
    2. (ii)Is $MN$ parallel to $PA$ ? Justify your answer.
    3. (iii)Find length $TB$.
    4. (iv)Find length $MN$.

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