Olympiad (Class 10) Number Theory — practice questions
18 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice Olympiad (Class 10) Number Theory in the app →For any integer $n$, the expression $n^2 - 1$ is always divisible by 8 when $n$ isThe product of any three consecutive positive integers is always divisible byThe number of trailing zeros at the end of $50!$ isIf $\text{HCF}(a, b) = 12$ and $\text{LCM}(a, b) = 180$, then the number of possible ordered pairs $(a, b)$ isThe largest number that divides 245 and 1029, leaving remainders 5 and 5 respectively, isFor some integer $m$, every odd integer can be written in the formThe square of any odd integer, when divided by 8, leaves remainderThe decimal expansion of $\dfrac{257}{2^3 \cdot 5^4}$ terminates after how many decimal places?How many positive integers less than 1000 are divisible by neither 2 nor 5?If $p$ is a prime and $p \mid a^2$, then which must be true?The unit digit of $7^{2026}$ isThe smallest positive integer that is divisible by every integer from 1 to 10 isIf $a = 2^3 \cdot 3^4 \cdot 5^2$ and $b = 2^4 \cdot 3^2 \cdot 7$, then $\dfrac{\text{LCM}(a,b)}{\text{HCF}(a,bWhich of the following is an irrational number?The remainder when $2^{100}$ is divided by 7 isTwo positive integers have HCF 9 and LCM 90. If one number is 18, the other isThe HCF of two consecutive positive integers isIf $3^x = 4^y = 12^z$ with $x,y,z$ nonzero, then $\dfrac{1}{z}$ equals