CBSE Class 10 Maths (Basic) 2026 — Paper 430/4/1

If $\text{HCF}(850,325)$ is $25$, then $\text{LCM}(850,325)$ is:

The value of $k$ for which the equation $2k{x}^2-6x+3=0$ has real and equal roots, is :

Two wooden solid hemispheres of same radii $r$, are joined at a point, as shown in the figure. The total surface area of the object is:

$PT$ is tangent to the circle with centre $O$ and radius $5$ cm. $OP$ intersects the circle at $Q$. If $PQ=x$, then $P{T}^2$ equals:

Probability of getting an irrational number at random from the numbers $\sqrt{3},\sqrt{4},3\sqrt{9},3\sqrt{8},\sqrt{5},0,4^{\frac{3}{2}}$ is :

The graph of polynomial $p(x)=k$ is shown here. Number of zeroes of polynomial $p(x)$ is :

The sum of first $n$ terms of an A.P. is $50\sqrt{2}$. If the first and the last terms are $\sqrt{2}$ and $19\sqrt{2}$ respectively, then the value of $n$ is:

While calculating mean of a grouped frequency distribution using step deviation method $\left(u=\frac{x-a}{h}\right)$ it was found that $\bar{x}=62$, $a=47.5$, $h=5$. The value of $\bar{u}$ is:

A card is drawn from a well shuffled deck of $52$ cards. The probability of getting an ace or a ten is:

The distance between the points $(-4,2)$ and $(1,0)$ is :

A cone with slant height $10$ cm and radius $6$ cm is surmounted on a hemisphere of the same radius. The height of the toy is:

In the given figure, $PQ$ and $PR$ are two tangents drawn to a circle with centre $O$. If $\angle ORQ=25^{\circ }$, then the measure of $\angle PQR$ is:

The value of $\sin 90^{\circ }\cos 90^{\circ }-{\sin }^{2}60^{\circ }$ is:

$n^{\text{th}}$ term of the A.P. $-\frac{3}{2},\frac{3}{2},\frac{9}{2},\dots$ is :

In the given figure, $PQ\parallel BC$. If $AP:AB=3:7$, then $AQ:QC$ equals:

If $\sin \theta =\frac{1}{7}$, then $\tan \theta$ is :

$7\times 29\times 23+1$ is :

Chord $AB$ subtends an angle of $40^{\circ }$ at the centre of the circle of radius $9$ cm. The length of arc $AB$ is:

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

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

If $\sin (A-B)=\frac{1}{2}$ and $\tan (A+B)=\sqrt{3}$, where $0^{\circ }\le A+B<90^{\circ }$ and $A>B$, then find the values of $A$ and $B$.

If $\alpha ,\beta$ are the zeroes of the polynomial $p(x)=6x^2-5x-3$, then find the value of $\frac{1}{\alpha }+\frac{1}{\beta }$.

One zero of the polynomial $4x^2-12x+(2k+1)$ is five times the other. Find the value of $k$.

A $(-2,3)$ and B $(4,1)$ are end points of the diameter of a semi-circle. The semi-circle intersects the $y$-axis at point P. Find the co-ordinates of the point P.

In the given figure, $AP$, $AQ$ and $BC$ are tangents to the circle with centre $O$. If $AB=6$ cm, $AC=7$ cm and $BC=5$ cm, then what is the length of $AP$?

In the given figure, $TP$ is tangent to a circle with centre $O$. Diameter $BA$ when produced meets the tangent at $T$. If $\angle ABP=35^{\circ }$, then find the measure of $\angle PTA$.

In the given figure, $QR\parallel CB$ and $RP\parallel AC$. If $BR=10$ cm, $QA=12$ cm, $BP=12$ cm and $PC=18$ cm, then find the lengths of $AR$ and $QC$.

Prove that a parallelogram circumscribing a circle, is a rhombus.

Prove that $\frac{\cot A-\cos A}{\cot A+\cos A}=\frac{\sec A-\tan A}{\sec A+\tan A}$.

Prove that $(\mathrm{cosec}A-\sin A)(\sec A-\cos A)=\frac{1}{\tan A+\cot A}$.

The vertices of a rhombus $ABCD$ are $A(-3,-4)$, $B(5,-3)$, $C(1,4)$ and $D(-7,3)$. Find the length of both the diagonals. Hence, find area of the rhombus $ABCD$.

The line segment joining the points $A(-5,1)$ and $B(7,6)$ is trisected at the points $P$ and $Q$ such that $P$ is nearer to $A$. If $P$ lies on the line $x+y=k$, then find the value of $k$.

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 $\sqrt{3}=1.73$)

Solve the following equations graphically : $x+y=7$ and $2x-5y=7$.

Observe the figure given above. It shows six identical rectangular enclosures made by using fencing wire mesh. These enclosures are used to protect baby animals in a zoo. Dimensions of each enclosure is $x$ feet $\times$ $y$ feet. The total length of fencing required is $152$ feet and area of each enclosure is $80$ square feet. Based on the above, answer the following questions :

The Air Quality Index (AQI) is a scale from $0$ to $500$ that indicates air quality, with higher numbers signifying more pollution and greater health concerns. The Central Pollution Control Board's air quality standards map AQI ranges to categories (Good, Satisfactory, Moderate, Poor, Very Poor, Severe), as shown in the figure. Mansi collected the daily data of AQI of her city for a month and presented it as given below.

'Gilli Danda' is a very popular traditional game of India which is played with two wooden sticks — the larger one is called 'Danda' and the smaller one 'Gilli'. 'Danda' — It is cylindrical in shape with diameter $4$ cm and length $42$ cm. Gilli — It is cylindrical in the middle with identical conical ends of the same radius $1.5$ cm and length $2.8$ cm. The length of the cylindrical part is $7$ cm. Based on the above, answer the following questions: