Class 10 Mathematics (Standard) 2026 Board Exam

Assertion (A) : $\text{H.C.F. }(36{\text{ m}}^2,18\text{ m})=18\text{ m}$, where m is a prime number.
Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.

Prove that $4-2\sqrt{5}$ is an irrational number given that $\sqrt{5}$ is irrational.

The dimensions of a window are $156\text{cm}\times 216\text{cm}$. 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.

If sum and product of zeroes of a polynomial are $(-3)$ and $(-2)$ respectively, then a polynomial is

An arch of a railway bridge, built on Chenab riverbed, is shown in the above diagram. It is a parabolic arch connecting two hills at P and Q. If the parabolic curve is represented by the polynomial $p(x)=-0.0025x^2-0.025x+136$.
Observe the diagram and based on above information, answer the following questions :
(i) Write the co-ordinates of point A.
(ii) Find the span of the arch.
(iii) (a) Write the zeroes of the polynomial using diagram and verify the relationship between sum of zeroes and polynomials.
OR
(iii) (b) Find the values of $p(x)$ at $x = 100$ and $x = -100$. Are they same ?

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

Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

Use graphical method to solve the system of linear equations : $y = -3$ and $x + 2y = 4$.

Use graphical method to solve the system of linear equations : $x = -3$ and $5x - 2y = -5$.

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