Mathguru

isi, cmi practice problem: Let $f:\mathbb{N} \to \mathbb{N}$ satisfying the conditions: (i) $x - f(x) = 19 \left[ \frac{x}{19} \right] - 90 \left[ \frac{f(x)}{90} \right]$ (ii) $1900 < f(1900) < 2000$ where $[x]$ denotes the ...

isi, cmi practice problem: Let $f(x) = \left[ \frac{1}{\cos\{x\}} \right]$, where $[\,\cdot\,]$ and $\{\,\cdot\,\}$ denote the greatest integer and fractional part functions respectively. Then find the range of the function $f$...

isi, cmi practice problem: Let $A$ be a non-empty set of real numbers and $f: A \to A$ such that $f(f(x)) = x$ for all $x$ in $A$. Then which of the followings are true. (a) a bijection ...

isi, cmi practice problem: Let $g(x) = x^5 + x^4 + x^3 + x^2 + x + 1$. What is the remainder when $g(x^{12})$ is divided by the polynomial $g(x)$ ? (a) 6 (b) $5 - x$ (c) $4 - x + x^2$ (d) $3 - x + x^2 - x^3$