CBSE Class 10 Maths (Basic) 2026 — Paper 430/5/1

$7\times 11\times 13+5$ is

The roots of the quadratic equation $x^2+9=0$ are

The distance between the points $(-2,5)$ and $(5,-2)$ is

A cylinder of radius $r$ is surmounted on a hemisphere of same radius. If total height of the object is $13$ cm, then its inner surface area is

Which of the following statements is not always true?

If value of $\cot \theta$ is $\sqrt{5}$, then $\sin \theta$ equals

A chord $QR$ subtends an angle of $105^{\circ }$ at the centre $O$ of the circle. The measure of $\angle RQP$ is

The probability of getting sum greater than $10$, when two dice are rolled together, is

The graph of a polynomial $p(x)$ is shown here. The number of zeroes of the polynomial $p(x)$ is

$n^{\text{th}}$ term of the A.P. : $\frac{-1}{3},\frac{4}{3},3,\dots$ is

In the given figure, $DE\parallel BC$. If $AD:AB=1:3$ and $AE=2.5$ cm, then $AC$ equals

The value of $k$ for which sum of the zeroes of the polynomial $p(x)=3x^2-kx+6$ is $2$, is

A bag contains some red and some white balls. A ball is drawn at random from the bag. If the probability of getting a red ball is $\frac{2}{7}$, then the probability of getting a white ball is

If $-26,x,2$ are in A.P., then the value of $x$ is

$PQ$ is tangent to a circle at a point $P$ on the circle. The number of tangents which can be drawn to the circle parallel to $PQ$, is

A card is drawn from a well-shuffled deck of $52$ playing cards. The probability of getting a queen of spade is

The length of a pendulum is $70$ cm and it describes an arc of length $88$ cm when it swings. The angle subtended by the arc at the centre is

The total surface area of a solid cone of radius $7$ cm and slant height $25$ cm, is

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 $\sec A=\sqrt{2}$ and $\tan B=\sqrt{3}$, then find the value of $2\sin A\cos B$.

Evaluate : $\frac{4{\cos }^{3}60^{\circ }+\mathrm{cosec}30^{\circ }}{{\tan }^{2}30^{\circ }}$

Find the H.C.F. and L.C.M. of $1530$ and $2040$.

If $A(a,0)$, $B(1,1)$ and $C(0,b)$ form a triangle, right angled at $B$ when joined, then establish a relation between $a$ and $b$.

In the given figure, $AB\parallel DC$. If $OB=3OD$ and $CD=1.8$ cm, then find the length $AB$.

Prove that $\sqrt{2}$ is an irrational number.

Points $P(6,0)$, $Q(2,8)$ and $R(-2,4)$ are vertices of $△PQR$. It is given that $MN\parallel QR$ such that $\frac{PM}{MQ}=\frac{1}{3}$. Using distance formula and ratio formula, show that $\frac{MN}{QR}=\frac{1}{4}$.

In an A.P., it is given that $a=2$, $d=8$ and $S_n=90$. Find the value of $n$.

How many $4$-digit numbers are divisible by $7$?

Prove that $\sqrt{\frac{1-\sin A}{1+\sin A}}=\frac{1}{\sec A+\tan A}$.

If $\alpha ,\beta$ are zeroes of the polynomial $p(x)=5x^2-7x-3$, then form a quadratic polynomial whose zeroes are $\frac{2}{\alpha }$ and $\frac{2}{\beta }$.

Find the zeroes of the polynomial $p(x)=3x^2+7x-20$ and verify the relationship between its zeroes and the coefficients.

Chord $AB$ of a circle subtends an angle of $120^{\circ }$ at the centre $O$ of the circle. Find the length of arc $AB$, if radius of the circle is $21$ cm.

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.

$ABCD$ 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 $x$.

A train covers a distance of $90$ km at a uniform speed. Had the speed been $15$ km/h more, it would have taken $30$ minutes less for the same journey. Find the original speed of the train.

Find mean and mode of the following data:

Seema daily goes to a park to exercise on machines available there. When Seema spent $15$ minutes on exercise bicycle and $30$ minutes on double cross walker, she received a message of burning $435$ calories on her fitness watch. When she spent $30$ minutes on exercise bicycle and $40$ minutes on double cross walker, she received a message of burning $690$ calories. To find the number of calories burned per minute on each machine, answer the following:

There are many varieties of mushrooms available in the world. One such mushroom 'Amanita muscaria' has an upper part which is like a red cap (hemispherical) and a lower part which is like a white stem (cylindrical). The hemispherical cap's radius $=3$ cm and the cylindrical stem is $2$ cm high with diameter $1.4$ cm. Considering the mushroom a solid object, answer the following questions:

In a circular museum hall of radius $14$ m, some statues are displayed. Statues are kept inside the inner concentric circle of radius $7$ m. One such statue lying in sector $OAB$ is fenced along line segments $OA$, $AP$, $PB$ and $BO$, where $P$ is a point on the outer circle. Based on the above information, answer the following questions: