CBSE Class 10 Maths (Basic) 2026 — Paper 430/2/1

The HCF of the smallest prime number and the smallest 3-digit number is $2^m{5}^n$. The respective values of $m$ and $n$ are :

Which of the following system of equations has a unique solution ?

If the equation $q{x}^2+px-r=0$ $(q\ne 0)$ has real and equal roots, then which of the following is true ?

If $x=-1$ is a root of the equation $a{x}^2-bx+3=0$, then :

In the given figure, the length of hypotenuse of the right $△AOB$ is :

In the given figure, if $ME\parallel SU$, then which of the following statements is correct ?

In the given figure, if $△ACP\sim △DCP$, then :

The graph of a quadratic polynomial is shown in the figure. The sum and product of zeroes of the polynomial respectively are :

The sum of the age (in years) of a father and three times the age of his daughter is $59$. If the age of the father is $x$ years and that of his daughter is $y$ years, the equation representing the given information is :

The $10^{\text{th}}$ term of the A.P. $\sqrt{2},\sqrt{8},\sqrt{18},\dots$ is :

The value of $(\cos 90^{\circ }-\sin 90^{\circ })$ is :

One of the possible values of $A$, for which $\cos 2A=\cos A$, is :

At an instant, the length of shadow of a stick is found to be $\sqrt{3}$ times the length of the stick as shown in the figure below. The Sun's altitude at that instant is :

The largest possible right circular cone is carved out of a solid hemisphere of radius '$r$' as shown in the figure below. The slant height of the cone is :

If for a frequency distribution, the mean is $\frac{3}{4}$ times the median, then mode is :

Consider the given data : The difference of lower limit of the median class and upper limit of the modal class is :

An unbiased die is thrown once. The probability of getting an even prime number greater than 2 is :

Select the correct answer from the codes (a), (b), (c) and (d) as given below.

Select the correct answer from the codes (a), (b), (c) and (d) as given below.

The point $P(x,y)$ lies on a semi-circular arc having diameter $AB$ as shown in the given figure. The coordinates of points $A$ and $B$ are $(3,0)$ and $(0,4)$ respectively. Find the relation between $x$ and $y$, if $P{A}^2+P{B}^2=A{B}^2$.

Verify the relation between the zeroes and the coefficients of the quadratic polynomial $4x^2-9$.

In the figure given below, $\angle 1=\angle 2$ and $\frac{BE}{BC}=\frac{CD}{AB}$. Prove that $△BDE\sim △BAC$.

Triangle $ABC$ is an isosceles right triangle, right angled at $B$. Find the value of ${\sin }^{2}A+{\cos }^{2}C$.

Neha claimed that there does not exist any irrational number between $1$ and $2$. Raunak claimed that $\sqrt{2}$ lies between $1$ and $2$ and $\sqrt{2}$ is an irrational number. Who do you think is correct ? Justify by proving either $\sqrt{2}$ as an irrational number or otherwise.

Prove that the system of equations given as $2x-3y=7$ and $4x+ky=9$, is inconsistent for $k=-6$. Also, obtain the solution of the system of equations, if $k=-1$.

Show that the quadrilateral $ABCD$ with vertices $A(0,3)$, $B(-2,0)$, $C(0,-5)$ and $D(2,0)$ is a kite. Also, find the length of each diagonal of the kite $ABCD$.

If $\sin A+{\sin }^{2}A=1$, find the value of ${\cos }^{2}A+{\cos }^{4}A$. Also, using the above, prove that ${\tan }^{2}A\times {\sec }^{2}A=1$.

T is a point on the line PS produced of a parallelogram PQRS and QT intersects RS at V. Prove that $△PQT\sim △RVQ$.

Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

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.

In the given figure, quadrilateral PQRS circumscribes the circle with centre O. Prove that the opposite sides of the quadrilateral PQRS subtend supplementary angles at the centre O.

ABCD is a square. With centres A, B, C and D, four quadrants (each touching two of the remaining three) are drawn inside the square ABCD as shown in the figure. If the area of the shaded region is $42{\text{ cm}}^2$, find the side of the square ABCD. Also, find the perimeter of the shaded region.

The median of the following data is $525$. If the sum of all the frequencies is $100$, find the values of $p$ and $q$.

A multistorey building is constructed with stilt parking. There is a provision of lift, as well as staircase from the ground floor to the top floor. The number of stairs from the ground floor to the first floor is $10$, from the first floor to the second floor is $24$, from the second floor to the third floor is $38$, and so on. Based on the above information, answer the following questions :

Climate change and global warming are influencing storm behaviour, particularly in terms of intensity and rainfall. Strong winds and storms often cause uprooting and/or breaking of trees, which damage the vehicles standing underneath the trees. On a particular day, during a high intensity storm, a tree broke such that its broken part formed an angle of $30^{\circ }$ with the ground. The distance between the base of the tree to the point where the top touches the ground is found to be $10$ m. Based on the above information, answer the following questions :

For a cricket tournament involving $8$ countries, a special trophy, as shown below, is designed. The height and diameter of the cylindrical part are $14$ cm and $6$ cm respectively and the diameter of the spherical ball on the top is $7$ cm. Based on the above information, answer the following questions :