A bakerman sells 5 types of cakes. Profit due to sale of each type of cake is respectively ₹ 2.5, ₹ 3 , ₹ 1.5 and ₹ 1. The demands for these cakes are $$20 \%, 5 \%, 10 \%, 50 \%$$ and respectively, then the expected profit per cake is

If $$m$$ is order and $$n$$ is degree of the differential equation $$\left(\frac{d^2 y}{d x^2}\right)^5+4 \frac{\left(\frac{d^2 y}{d x^2}\right)}{\left(\frac{d^3 y}{d x^3}\right)}+\left(\frac{d^3 y}{d x^3}\right)=x^2$$ then

If $$\theta+\phi=\alpha$$ and $$\tan \theta=k \tan \phi($$ where $$K>1)$$, then the value of $$\sin (\theta-\phi)$$ is

With usual notations, perimeter of a triangle $$A B C$$ is 6 times the arithmetic mean of sine of its angles. If $$\mathrm{a}=1$$, then measure of angle $$\mathrm{A}=$$