Mathematics Tes...

The problem of maximizing \(z=x_1-x_2\) subject to constraints \(x_1+x_2 \leq 10, x_1 \geq 0, x_2 \geq 0\) and \(x_2 \leq 5\) has:

\(\int_{1}^{4} \frac{x^{2}+x}{\sqrt{2 x+1}} d x\) is equal to:

What is the general solution of the differential equation x² dy + y² dx = 0 ?

Where c is the constant of integration.

If \(f(x)=x^{3}+3 x^{2}+3 x-7\), then find the value of \(\frac{d f(x)}{d x}\) at \(x=2\).

The conic \(x^{2}+x y+y^{2}+x+y=1\) is:

Find the conjugate of \(\frac{1+i}{1-i}\).

The quadratic equation \(7 x^{2}-28 x+21\) have roots \(\alpha\) and \(\beta\). And \(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{k}{\alpha \beta}\) then find the value of \(k\).

From a pack of a well-shuffled deck of cards, two cards are drawn together at random. What is the probability of both the cards being Ace?

If the mean of a set of observations \(x_{1}, x_{2}, x_{3}, \ldots, x_{10}\) is 50 , then the mean of \(x_{1}+5, x_{2}+10, x_{3}+15, \ldots\), \(x_{10}+50\) is:

If \(y=\cos ^{2} x^{2}\), find \(\frac{d y}{d x}\)