Class 10 Mathematics (Standard) 2024 Board Exam

If two positive integers $p$ and $q$ can be expressed as $p=18a^2{b}^4$ and $q=20a^3{b}^2$, where $a$ and $b$ are prime numbers, then $\text{LCM}(p,q)$ is :

(A) Prove that $5-2\sqrt{3}$ is an irrational number. It is given that $\sqrt{3}$ is an irrational number.
OR
(B) Show that the number $5\times 11\times 17+3\times 11$ is a composite number.

In a teachers' workshop, the number of teachers teaching French, Hindi and English are $48,80$ and $144$ respectively. Find the minimum number of rooms required if in each room the same number of teachers are seated and all of them are of the same subject.

If $\text{HCF}(2520,6600)=40$ and $\text{LCM}(2520,6600)=252\times k$, then the value of $k$ is

Can the number $(15{)}^n$, $n$ being a natural number, end with the digit $0$ ? Give reasons.

Prove that $\sqrt{5}$ is an irrational number.

Explain why $7\times 11\times 13+13$ and $7\times 6\times 5\times 4\times 3\times 2\times 1+5$ are composite numbers.

Can the number $8^n$, $n$ being a natural number, end with the digit $0$ ? Give reasons.

If the sum of zeroes of the polynomial $p(x)=2x^2-k\sqrt{2}x+1$ is $\sqrt{2}$, then value of $k$ is :

The zeroes of a polynomial $x^2+px+q$ are twice the zeroes of the polynomial $4x^2-5x-6$. The value of $p$ is :