MCQ
The absolute minimum value, of the function $f(x)=\left|x^2-x+1\right|+\left[x^2-x+1\right], \quad$ where $[t]$ denotes the greatest integer function, in the interval $[-1,2]$, is :
- ✓$\frac{3}{4}$
- B$\frac{3}{2}$
- C$\frac{1}{4}$
- D$\frac{5}{4}$
Let $g(x)=x^2-x+1$
$=\left(x-\frac{1}{2}\right)^2+\frac{3}{4}$
$\because\left| x ^2- x +1\right| \text { and }\left[ x ^2- x +2\right]$
Both have minimum value at $x =1 / 2$
$\Rightarrow \text { Minimum } f ( x )=\frac{3}{4}+0$
$=\frac{3}{4}$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$x^5 - 40x^4 + px^3 + qx^2 + rx + s = 0$ are in $G.P.$ The sum of their reciprocals is $10$. Then the value of $\left| s \right|$ is