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

The HCF of $2^2\times 3^3$ and $3^2\times 2^3$ is :

A letter is selected from the letters of the word FEBRUARY. The probability that it is a vowel is :

Which of the following numbers will not end with $0$ for any natural number $n$ ?

The system of linear equations $px+qy=r$ and $p_{1}x+q_{1}y=r_1$ has a unique solution, if :

Which of the equations among the following is/are quadratic equation(s) ? $q_1:x^2+x=(x+1{)}^2$, $q_2:x-1=x^2-1$, $q_3:x^4=x^2$, $q_4:\sqrt{x}=x^2\sqrt{x}+1$

The discriminant of the quadratic equation $a{x}^2+x+a=0$ is :

The distance between points $(3,0)$ and $(0,-3)$ is :

If $△ABC\sim △ADE$ in the adjoining figure, then which of the following is true ?

In the adjoining figure, if $EA\parallel SR$ and $PE=x$ cm, then the value of $5x$ is :

Which of the following graphs represents a polynomial with both zeroes being positive ?

The system of equations $x=2$ and $x=3$ has :

The numbers $x,x+4$ and $x+8$ are in A.P. with common difference :

Which of the following statements is not true ?

If $\sqrt{3}\sin A=\cos A$, then the measure of $A$ is :

In the adjoining figure, the angle of elevation of the point $C$ from the point $B$, is :

In the adjoining figure, the slant height of the conical part is :

The upper limit of the median class of the above data is :

If for a data, median is $5$ and mode is $4$, then mean is equal to :

Find the coordinates of the point which divides the line segment joining the points $A(-6,10)$ and $B(3,-8)$ in the ratio $2:7$.

One zero of a quadratic polynomial is twice the other. If the sum of zeroes is $(-6)$, find the polynomial.

In the adjoining figure, $AP=\frac{1}{2}AB$ and $PQ\parallel BC$. If $CQ=3$ cm, then find the length of $AC$.

Evaluate : ${\sin }^{2}30^{\circ }-{\cos }^{2}45^{\circ }+{\cot }^{2}60^{\circ }$

If $\sin (A+2B)=2\cos 60^{\circ }$ and $A=3B$, find the measures of $A$ and $B$.

Given that $\sqrt{5}$ is an irrational number, prove that $3+2\sqrt{5}$ is also an irrational number.

Solve the following system of equations graphically : $x+3y=6$ and $2x-3y=12$ Also, find the area of the triangle formed by the lines $x+3y=6$, $x=0$ and $y=0$.

One of the supplementary angles exceeds the other by $120^{\circ }$. Express the given information as a system of linear equations in two variables. Hence, find the measure of both the angles.

If the point $P(x,y)$ is equidistant from the points $(3,6)$ and $(-3,4)$, obtain the relation between $x$ and $y$. Hence, find the coordinates of point $P$ if it lies on $x$-axis.

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

Prove that the lengths of tangents drawn from an external point to a circle are equal.

In the adjoining figure, $AB$ is the diameter of the circle with centre $O$. Two tangents $p$ and $q$ are drawn to the circle at points $A$ and $B$ respectively. Prove that $p\parallel q$. Further, a line $CD$ touches the circle at $E$ and $\angle BCD=110^{\circ }$. Find the measure of $\angle ADC$.

Express $\frac{24}{18-x}-\frac{24}{18+x}=1$ as a quadratic equation in standard form and find the discriminant of the quadratic equation, so obtained. Also, find the roots of the equation.

The sum of squares of two positive numbers is $100$. If one number exceeds the other by $2$, find the numbers.

In the adjoining figure, $△OAB$ is an equilateral triangle and the area of the shaded region is $750\pi {\text{ cm}}^2$. Find the perimeter of the shaded region.

The mode of the following data is $3.286$ : Find the mean and median of the above data.

A watermelon vendor arranged the watermelons similar to shown in the adjoining picture : The number of watermelons in subsequent rows differ by '$d$'. The bottommost row has $101$ watermelons and the topmost row has $1$ watermelon. There are $21$ rows from bottom to top. Based on the above information, answer the following questions :

As a part of school project, Mishika and Sahaj created a bird-bath from the cylindrical log of wood by scooping out the hemispherical depression from one end of the cylinder as shown in the figure given below. Cylinder has a length $2$ m out of which $0.6$ m is in earth and the diameter is $1.4$ m. On the basis of the above information, answer the following questions :

A flagstaff, $7.32$ m long is fitted at the top of $10$ m tall building. The flagstaff is supported by the ropes which are tied to the point $P$ on the ground which is $x$ m away from the base of the building. It is given that $l_1$ is the length of rope from point $P$ to the base of the flagstaff and $l_2$ is the length of rope from point $P$ to the top of flagstaff. Rope $l_1$ makes an angle of $30^{\circ }$ with the horizontal and $\theta$ be the angle which rope $l_2$ makes with the horizontal as shown in the figure. Based on the above information, answer the following questions : (Use $\sqrt{2}=1.4$ and $\sqrt{3}=1.732$)