Mathematics Tes...

Let \(f(x)\) and \(g(x)\) be twice differentiable functions on [0,2] satisfying \(f^{\prime \prime}(x)=g^{\prime \prime}(x), f^{\prime}(1)=4, g^{\prime}(1)=\) \(6, f(2)=3\) and \(\mathrm{g}(2)=9 .\) Then what is \(\mathrm{f}(\mathrm{x})-\mathrm{g}(\mathrm{x})\) at \(\mathrm{x}=4\) equal to?

The range of the function \(f(x)=\frac{1}{(2-\sin 3 x)}\) is

If \(\mathrm{A} \& \mathrm{B}\) are two symmetric matrices of same order, then \((A B A)^{r}\) is

If sum of the squares of zeros of the quadratic polynomial \(f(x)=x^{2}-8 x+k\) is \(40,\) find the value of \(k\)

If \(\frac{1}{\log _{a} x}+\frac{1}{\log _{c} x}=\frac{2}{\log _{b} x}\), then \(a, b\) and \(c\) are in

If \(A=\left[\begin{array}{ll}2 & 7 \\ 1 & 5\end{array}\right],\) then what is \(A+3 A^{-1}\) equal to?

If \(\tan ^{-1} 2 x+\tan ^{-1} 3 x=\frac{\pi}{4},\) then \(x\) is equal to