Mathematics Tes...

If \(x+\frac{1}{x}=4\), then find the value of \(x^{4}+\frac{1}{x^{4}}\).

If f(x) = x^a + a^x and g(x) = x^a – a^x, find the value of f(x) + g(x).

The order of a differential equation whose solution is y = a cos x + b sin x, where a and b are arbitrary constants, is

\(a=\frac{\sqrt{7}+\sqrt{11}}{\sqrt{11}-\sqrt{7}} ;\) and \(b=\frac{1}{a}\);then the value of\(\left(6 a^{2}-35 a b+6 b^{2}\right)\) is:

\(\int \cos \sqrt{x} d x=?\)

The diagonals of a parallelogram PQRS are along the lines x + 3y = 4 and 6x - 2y = 7. Then PQRS must be a

\(\int e 3 \log x\left(x^{4}+1\right)^{-1} d x\) is equal to

If the sets A and B are defined as

A = {(x, y) : y =1/x, 0 ≠ x ∈ R}

B = {(x, y) : y = -x, x ∈ R}, then