CBSE Class 10 Maths (Standard) 2026 — Paper 30/3/1

The roots of the quadratic equation $(x-1{)}^2=16$ are :

In the given figure, $PQ$ and $PR$ are tangents to a circle with centre $O$ and radius $3$ cm. If $\angle QPR=60^{\circ }$, then the length of each tangent is :

In $△DEF$, $AB\parallel EF$. The value of $x$ is :

$(3\times 11\times 13+3)$ is :

Two dice are rolled together. The probability that the sum of the numbers obtained is divisible by $6$, is :

The number of multiples of $4$ lying between $12$ and $250$ is :

A cone of maximum size is carved out from a solid cube of edge length $l$. The volume of the cone is :

Equation of another line parallel to the line represented by $2x-6y=7$ is :

If the length of the shadow of a tower is $\sqrt{3}$ times that of its height, then altitude of the Sun is :

If the roots of the quadratic equation $\sqrt{3}{x}^2-kx+2\sqrt{3}=0$ are real and equal, then the value(s) of $k$ is/are :

The $n^{\text{th}}$ term of the A.P. $\frac{-1}{3},\frac{2}{3},\frac{5}{3},\frac{8}{3},\dots$ is :

In the given figure, $PT$ is a tangent to the circle with centre $O$ and radius $r$. If $\angle POT=45^{\circ }$, then the length of $OP$ is :

It is given that $△ABC\sim △QRP$ such that $AB=9$ cm, $BC=5$ cm and $PR=2$ cm. Length of side $QR$ is :

The sum and product of zeroes of a quadratic polynomial $p(x)$ are $-\frac{1}{3}$ and $2$ respectively. The polynomial $p(x)$ is :

Given that $\sin 2\alpha =\frac{\sqrt{3}}{2}$, the value of $\sin 3\alpha$ is :

The median and mode of a distribution are $25.2$ and $26.1$ respectively. The mean of the distribution is :

In the given figure, $△ABC$ is an equilateral triangle. $AD$ is a median of the triangle joining the points $A\left(0,\frac{5\sqrt{3}}{2}\right)$, $D(0,0)$. Points $B$ and $C$ are (in same order) :

The value of $\left(\frac{1}{2}{\tan }^{2}45^{\circ }-{\cos }^{2}60^{\circ }\right)$ is :

In the question, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option.

Find the length of the plank that can be used to measure the lengths $4$ m $20$ cm and $5$ m $4$ cm exactly, in the least time.

In an A.P., the first term is $32$ and the last term is $-10$. If the common difference is $-2$, then find the number of terms and their sum.

Find the sum of the first $28$ terms of an A.P. whose $n^{\text{th}}$ term is given by $a_n=3n-2$.

Find the coordinates of a point on the line $x+y=5$ which is equidistant from $(6,4)$ and $(5,2)$.

The diagonals of a quadrilateral $ABCD$ intersect each other at the point $O$ such that $\frac{AO}{OC}=\frac{BO}{OD}$. Show that quadrilateral $ABCD$ is a trapezium.

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.

Prove that : $(\sin A+\sec A{)}^2+(\cos A+\csc A{)}^2=(1+\sec A\csc A{)}^2$

Prove that $\sqrt{5}$ is an irrational number.

Find two consecutive negative integers, sum of whose squares is $481$.

A point $P(x,7)$ divides a line segment joining the points $A(-5,4)$ and $B(7,9)$ in a certain ratio. Find the ratio and hence find the value of $x$.

In the given figure, $PA$ is the tangent to the circle with centre $O$ such that $OA=10$ cm, $AB=8$ cm and $AB\perp OP$. Find the length of $PB$.

The median of the following data is $137$. Find the values of $x$ and $y$, given that total of frequencies is $68$.

Find mean and mode of the following distribution :

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 $BX=4XY$.

Solve the following system of equations graphically : $x-2y=3$, $3x-8y=7$

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 $\sqrt{3}=1.73$)

During a theatre drama, a backdrop of building arches was used. The shape of the curve shown below can be represented by the polynomial $p(x)=-x^2+2x+8$, where $x$ is the length (in feet) on stage level. Based on the figure given above, answer the following questions:

A group of friends wanted to play cards with two identical packs together. While shuffling the cards, three cards are dropped. Rest of the cards are shuffled and one card is drawn at random. Assuming that the dropped cards were a queen of hearts, a ten of spades and an ace of clubs, answer the following questions :

A model of Leafy Ball Fountain is made to be kept on the tabletop. Water gently cascades down the ball into a decorative cylindrical pool where it is recycled. The diameter of the spherical ball is $21$ cm. For the cylindrical pool, the outer diameter is $50$ cm and the inner diameter is $40$ cm. The height of the solid base is $14$ cm and the height of the water filled is $7$ cm. Observe the figure and answer the following questions: