Mathematics Mock Test - 11

If the coordinates of $A$ and $B$ are $(1,2,3)$ and $(7,8,7)$, then the projections of the line segment $AB$ on the coordinate axes are:

A coin is tossed $3$ times. If $X$ is a random variable representing the number of tails, then the mathematical expectation of $X$ is:

Nisha needs $\text{₹}2,00,000$ (after 50% subsidy) in 4 years for her daughter's education. If the interest rate is 8% p.a., how much does she need to save annually? (Assume $\frac{1.08^4-1}{0.08}=4.5$)

An objective function $Z=ax+by$ is maximum at points $(9,3)$ and $(5,7)$. If $a,b\ge 0$ and $ab=16$, then the maximum value of the function is:

A company has a variable cost $V(x)=3x^2+3500$ and a fixed cost of $\text{₹}2000$. The marginal cost of producing $50$ units is: