CBSE Class 10 Maths (Standard) 2026 — Paper 30/5/1

The value of $k$ for which the equation $k{x}^2-6x-4=0$ has real and equal roots, is

The line segment joining the points $P(-4,-2)$ and $Q(10,4)$ is divided by the y-axis in the ratio :

If the zeroes of a polynomial $p(x)$ are $-3$ and $8$, then $p(x)$ equals

In the given figure, $PQ$ is tangent to the circle with centre $O$. $S$ is a point on the circle such that $\angle SQT=55^{\circ }$. The $m\angle QPS$ is

Devansh proved that $△ABC\sim △PQR$ using SAS similarity criteria. If he found $\angle C=\angle R$, then which of the following was proved true?

While calculating mean of a grouped frequency distribution, step deviation method was used $\left(\frac{x-a}{h}=u\right)$. It was found that $\bar{x}=64$, $h=5$ and $a=62.5$. The value of $\bar{u}$ is

A conical cavity of maximum volume is carved out from a wooden solid hemisphere of radius $10$ cm. Curved surface area of the cavity carved out is (use $\pi =3.14$)

If $a_n$ represents the $n^{\text{th}}$ term of the A.P. $-\frac{15}{4},-\frac{10}{4},-\frac{5}{4},\dots$ then the value of $a_{16}-a_{12}$ is :

The value of $p$ for which roots of the quadratic equation $x^2-px+6=0$ are rational, is

Which of the following can not be the probability of an event?

A card is drawn at random from a well shuffled deck of $52$ playing cards. The probability that it is either a ten or a king is :

A camping tent in hemispherical shape of radius $1.4$ m, has a door opening of area $0.50$ m${}^2$. Outer surface area of the tent is :

An arc of length $2.2$ cm subtends an angle $\theta$ at the centre of the circle with radius $2.8$ cm. The value of $\theta$ is :

For an acute angle $\theta$, if $\sin \theta =\frac{1}{9}$, then value of $\frac{9\mathrm{cosec}\theta +1}{9\mathrm{cosec}\theta -1}$ is

In the given figure, $PQ\parallel YZ$ such that $XP:PY=2:3$. If $PQ=5$ cm, then $YZ$ equals

Meena calculates that the probability of her winning the first prize in a lottery is $0.08$. If total $800$ tickets were sold, the number of tickets bought by her, is

A wire is attached from a point $A$ on the ground to the top of a pole $BC$, making an angle of elevation as $60^{\circ }$. If $AB=5\sqrt{3}$ m, then length of the wire is

Simplest form of $\frac{\sec A}{\sqrt{{\sec }^{2}A-1}}$ is

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

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

Prove that $2-5\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

Vertices of a right triangle $ABC$ with $\angle B=90^{\circ }$ are $A(3,4)$, $B(1,1)$ and $C(-8,7)$. Find the value of $\tan A$.

Using distance formula, prove that the points $A(2,3)$, $B(-7,0)$ and $C(-1,2)$ are collinear.

In the given figure, $AB\parallel DE$ and $AC\parallel DF$. Show that $△ABC\sim △DEF$. If $BC=10$ cm, $EB=CF=5$ cm and $AB=7$ cm, then find the length $DE$.

Evaluate : $\frac{{\sin }^{3}60^{\circ }-\tan 30^{\circ }}{{\cos }^{2}45^{\circ }}$

For acute angles $A$ and $B$, and $A+2B$ and $2A+B$ are acute, if $\tan (A+2B)=\sqrt{3}$ and $\sin (2A+B)=\frac{1}{\sqrt{2}}$, then find the measures of angles $A$ and $B$.

A bag contains $25$ balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $\frac{3}{5}$, then find the number of yellow balls.

A circle of diameter $20$ cm is equally divided into five sectors. Find the area and perimeter of one of the sectors.

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.

The sum of first $n$ terms of an A.P. is $2n^2+13n$. Find its $n^{\text{th}}$ term and hence $10^{\text{th}}$ term.

A circle centered at $(2,1)$ passes through the points $A(5,6)$ and $B(-3,K)$. Find the value(s) of $K$. Hence find length of chord $AB$.

Prove that the point $P$ dividing the line segment joining the points $A(-1,7)$ and $B(4,-3)$ in the ratio $3:2$ lies on the line $x-3y=-1$. Also find the length of $PA$ and $PB$.

Solve the system of linear equations $x=4$ and $3x-2y=6$ graphically.

The dimensions of a window are $156$ cm $\times$ $216$ cm. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

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.

The mean of the following frequency distribution is $28$. If sum of all frequencies is $100$, then find the values of $p$ and $q$ :

Find median and mode of the following distribution :

$PQ$ 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 $PA$.

An arch of a railway bridge, built on the Chenab riverbed, is shown in the diagram. It is a parabolic arch connecting two hills at $P$ and $Q$. The parabolic curve is represented by the polynomial $p(x)=-0.0025x^2-0.025x+136$. Observe the diagram and, based on the above information, answer the following questions :

A wall mounted lamp, made of fabric, is shown below. Lamp has cuboidal shape, open from top and bottom. A spherical bulb of diameter $7$ cm is latched with a very thin rod. (Ignore the rod while making calculations.) Dimensions of the cuboid are $24$ cm $\times$ $12$ cm $\times$ $17$ cm.

Elevated water storage tanks are built to store and supply water to nearby colonies. In the diagram given above, $AB$ is an elevated water tank and $CD$ is a nearby multistorey building. The building is $54$ metres away from the water tank. From a window ($W$) of the building, the angle of elevation of top of the tank is $45^{\circ }$ and angle of depression of its foot is $30^{\circ }$.