MCQ
The interval in which the function ${x^3} $ increases less rapidly than $6{x^2} + 15x + 5$, is
- A$( - \infty ,\, - 1)$
- B$(-5 , 1)$
- ✓$(-1 ,5)$
- D$(5 , \infty )$
$\Rightarrow 12x + 15 > 0 \Rightarrow x > - \frac{5}{4}$.
Thus $f(x)$ and $g(x)$ both increases for $x > - \frac{5}{4}$.
It is given that $ f(x)$ increases less rapidly than $g(x)$,
Therefore the function $\phi (x) = f(x) - g(x)$ is decreasing function , which implies that $\phi '(x) < 0$
==> $3{x^2} - 12x - 15 < 0 \Rightarrow - 1 < x < 5$.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$I$. If its digits in units place and tens place are interchanged, the number increases by $36$ ;
$II.$ If its digits in units place and hundreds place are interchanged, the number decreases by $198 .$
Now, suppose that the digits in tens place and hundreds place are interchanged. Then, the number