Mathematics Tes...

If \(f(x)=\frac{x^{2}-9}{x^{2}-2 x-3}, x \neq 3\) is continuous at \(x=3,\) then which one of the following is correct?

The indefinite integral of \(\sin (x)\) w.r.t \(\cos (x)\) is:

The equation of the lines through \((1,1)\) and making angles of \(45^{\circ}\) with the line \(x+y=0\) are:

If the standard deviation of n elements of the series \({x}_{1}, {x}_{2}, {x}_{3} \ldots \ldots .,{x}_{{n}}\) is \(\sigma\), then find the variance of the series \({ax}_{1}, {ax}_{2}, {ax}_{3} \ldots \ldots ., {ax}_{{n}}\) is:

What is \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}|\sin x| d x\) equal to?

If$\alpha$ and$\beta$ are the roots of the equation$a{x}^2+2bx+c=0$ then find the value of$\frac{\alpha }{\beta }+\frac{\beta }{\alpha }$

The \(n^{t h}\) derivative of \(x e^{x}\) vanishes when:

If \(\mathrm{f}(\mathrm{x}), \mathrm{g}(\mathrm{x})\) be twice differential functions on \([0,~2]\) satisfying \(\mathrm{f}^{\prime \prime}(\mathrm{x})=\mathrm{g}^{\prime \prime}(\mathrm{x}), \mathrm{f}^{\prime}(1)\) \(=2 g^{\prime}(1)=4\) and \(f(2)=3 g(2)=9,\) then: