Class 10 Mathematics (Standard) 2023 Board Exam

Find the least number which when divided by $12,16$ and $24$ leaves remainder $7$ in each case.

Find the greatest number which divides $85$ and $72$ leaving remainders $1$ and $2$ respectively.

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

If $p$ and $q$ are natural numbers and $p$ is the multiple of $q$, then what is the HCF of $p$ and $q$ ?

Prove that $2+\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is an irrational number.

Prove that $4^n$ can never end with digit $0$, where $n$ is a natural number.

Prove that $6-\sqrt{7}$ is irrational number, given that $\sqrt{7}$ is an irrational number.

(a) Find by prime factorisation the LCM of the numbers $18180$ and $7575$. Also, find the HCF of the two numbers.
OR
(b) Three bells ring at intervals of $6,12$ and $18$ minutes. If all the three bells rang at $6$ a.m., when will they ring together again ?

If $n$ is a natural number, then which of the following numbers end with zero ?

The graph of $y = p(x)$ is given, for a polynomial $p(x)$. The number of zeroes of $p(x)$ from the graph is