Mathematics Mock Test - 7

In what ratio must tea at $\text{₹}50$ per kg be mixed with tea at $\text{₹}75$ per kg so the mixture is worth $\text{₹}60$ per kg?

Let $X$ and $Y$ be two independent Binomial random variables such that $X\sim B(2,p)$ and $Y\sim B(4,p)$. If $P(X\ge 1)=5/9$, find (i) $P(Y=4)$ and (ii) $V(2X-Y)$.

A bond has $\text{₹}3,500$ as its par value, redeemable at $7\%$ at the end of 8 years. What will be the present value of the bond if the annual yield rate is $8\%$? Take $(1.08{)}^{-8}=0.54$ and $\frac{1-(1.08{)}^{-8}}{0.08}=5.75$.

If $y=1+\frac{1}{x}+\frac{1}{x^2}+\frac{1}{x^3}+\dots \infty$ with $|x|>1$, then $\frac{dy}{dx}$ is:

Shyam needs a minimum of 150 units of carbohydrates and 120 units of proteins. Product A provides 16 units of carbohydrates and 11 units of proteins, while product B provides 10 units of carbohydrates and 20 units of proteins. The cost of product A is $\text{₹}50$ and product B is $\text{₹}60$. Formulate this situation as a Linear Programming Problem where $x$ and $y$ are units of products A and B respectively.