A manufacturer sells $x$ items at a price of rupees $\left(6-\frac{x}{40}\right)$ each. The cost price of $x$ items is ₹ $\left(\frac{x}{5}+193\right)$. The maximum profit in ₹ __________ is

The following is p.d.f. of continuous random variable X

$$ \mathrm{f}(x)= \begin{cases}\frac{x}{8} & , \text { if } 0 < x < 4 \\ 0 & , \text { otherwise }\end{cases} $$

Then $F(0.5), F(1.7)$ and $F(5)$ is respectively

The equation of the tangent to the curve $\left(1+x^2\right) y=2-x$, where it crosses the X -axis, is

If $y=\alpha \log x+\beta x^3-x$ has extreme values at $x=-1$ and $x=1$, then $\alpha$ and $\beta$ are respectively