Mathematics Tes...

\(y=\left|\begin{array}{cc}3 x & 4 x^2 \\ -1 & x^2\end{array}\right|\), find \(\frac{d y}{d x}\)

Corner points of the feasible region for an LPP are \((0,2),(3,0),(6,0)\) and \((0,5)\). Let \(F=4 x\) \(+6 y\) be the objective function. Find the value of the maximum value of \(\mathrm{F}\) - minimum value of \(\mathrm{F}\).

If \(y+b=m_{1}(x+a)\) and \(y+b=m_{2}(x+a)\) are the equations of the two tangents to the parabola \(y^{2}=4 a x\), then:

A company produces two types of goods, \(A\) and \(B\), that require gold and silver. Each unit of type \(A\) requires \(3 \mathrm{gm}\) of silver and \(1 \mathrm{gm}\) of gold while that of type \(B\) requires \(1 \mathrm{gm}\) of silver and \(2 \mathrm{gm}\) of gold. The company can produce \(9 \mathrm{gm}\) of silver and \(8 \mathrm{gm}\) of gold. If each unit of type \(A\) brings a profit of Rs 40 and that of type \(B\) Rs 50. What is the maximum profit?

In any group, the number of improper subgroups is:

The plane x - 3y + 5z - 8 = 0 makes an angle sin^-1 (∝) with Z -axis. The value of ∝ is equal to

A box contains 3 white and 2 black balls. Two balls are drawn at random one after the other. If the balls are not replaced, what is the probability that both the balls are black?

What is the number of outcomes when a coin is tossed and then a die is rolled only in case a head is shown on the coin?

If \(y=(\tan x)^{\tan x^{\tan x} }\) then the value of \(\frac{d y}{d x}\) at \(x=\frac{\pi}{4}\):