Mathematics Tes...

Find the minimum value of sin x + cos 2x

The differential equation of the family of curves y = c₁e^x + c₂e^-x is:

The equation of a normal to the parabola \(y^{2}=4 x\) which passes through the point \((6,0)\) is:

If \(y=e^{x+e^{x+e^{x+\cdots \infty}}}\), then \(\frac{d y}{d x}\) is:

\(\lim _{x \rightarrow 0} \frac{\sin \left(\pi \cos ^{2} x\right)}{x^{2}}\) equals:

The solution of the differential equation \(x \frac{d y}{d x}+2 y=x^{2}(x \neq 0)\) with \(y(1)=1\), is:

Find the root of equation x² + kx + 2 = 0 where, k is the arithmetic mean of root of equation x² + 6x + 8 = 0. 

Two letters were randomly chosen from the word \(G U I T A R I S T\). Find the probability that the letters are \(R\) and \(T\).

If \(y=\tan ^{-1}\left[\frac{3 a^{2} x-x^{3}}{a\left(a^{2}-3 x^{2}\right)}\right],\) then find out \(\frac{d y}{d x}\)

For the following LPP:

\(\text { Max. } Z=-0.1 x_{1}+0.5 x_{2} \)

\(2 x_{1}+5 x_{2} \leq 80 \)

\(x_{1}+x_{2} \leq 20 \)

\(x_{1}, x_{2} \geq 0\)

to get the optimum solution, the values of \(x_{1}, x_{2}\) are: