List of top Mathematics Questions on Binary operations asked in KEAM

Let ⊙ be a binary operation on Q - {0} defined by a⊙b=\(\frac{a}{b}\). Then 1⊙(2⊙(3⊙4)) is equal to

For any two positive rational numbers m and n, a binary operation * is defined by \(m*n=\frac{m+n}{3}\), then \(\frac{7}{2}*\frac{5}{2}\) is equal to

If $*$ is a binary operation defined by $a*b=\frac{a}{b}+\frac{b}{a}+\frac{1}{ab}$ for positive integers $a$ and $b$, then $2*5$ is equal to

If $*$ is the operation defined by $a * b = a^b$ for $a, b \in \mathbb{N}$, then $(2 * 3) * 2$ is equal to:

An integrating factor of the differential equation \( \sin x \frac{dy}{dx} + 2y \cos x = 1 \) is:

An integrating factor of the differential equation \( \sin x \frac{dy}{dx} + 2y \cos x = 1 \) is:

An integrating factor of the differential equation \( \sin x \frac{dy}{dx} + 2y \cos x = 1 \) is:

The image of the interval [-1, 3] under the mapping $f : R\rightarrow R$ given by $f \left(x\right)=4x^{3}-12x$ is