Mathematics Tes...

Let \(y=y(x)\) be the solution of the differential equation \(\frac{d y}{d x}=2(y+2 \sin x-5) x-2 \cos x\) such that, \(y(0)=7\).

Then \(\mathrm{y}(\pi)\) is equal to:

If \({ }^{{n}} {P}_{{r}}=2760,{ }^{{n}} {C}_{{r}}=23\), then the value of \({r}\) is:

If the mean of 10 observations \(x_{1}, x_{2}, x_{3} \ldots x_{10}\) is 20 , then mean of \(x_{1}+2, x_{2}+4, x_{3}+\) \(6, \ldots x_{10}+20\) is:

Find the rate of change of area of the square at the edge length of 12 cm, if the rate of change of edge length of the square is 2 cm/s.

Let \(x(t)=2 \sqrt{2} \cos t \sqrt{\sin 2 t}\) and

\(y(t)=2 \sqrt{2} \sin t \sqrt{\sin 2 t}, t \in\left(0, \frac{\pi}{2}\right)\)

Then \(\frac{1+\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^2}{\frac{\mathrm{d}^2 \mathrm{y}}{\mathrm{dx}^2}}\) at \(\mathrm{t}=\frac{\pi}{4}\) is equal to:

A continuous random variable \(X\) has the distribution function \(F(x)=0\) if \(x<1\) \(=k(x-1)^{4}\) if \(13\) The value of \(k\) is:

The objective function of a linear programming problem is _______________.

If \(A=\{2,4,6\}, B=\{4,6,7\}\) and \(C=\{2,7\}\), then \((A-B) \times(B-C)\) is:

If \(\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}\) and \(\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}\) are vectors of magnitude \(\alpha\) then the magnitude of the vector \(|\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}|\) is?

A bag contains \(4\) black, \(5\) yellow and \(6\) green balls. Three balls are drawn at random from the bag. What is the probability that all of them are yellow?