The number of real roots of the equation ${e^{\sin x}} - {e^{-\sin x}} - 4 = 0$ is:

The roots of $\frac{x+4}{x-4}+\frac{x-4}{x+4}=\frac{10}{3}$ are:

If $\alpha$ and $\beta$ are the roots of $ax^2 + bx + c = 0$,then the equation whose roots are $2 + \alpha$ and $2 + \beta$ is:

$Quantity \, 1:$ Profit percent for a shopkeeper. The shopkeeper uses a faulty scale while buying cloth from a wholesaler. His scale measures $10 \%$ extra than the actual measurement. While selling,the shopkeeper gives $10 \%$ less and offers a discount of $10 \%$ to the customer.
$Quantity \, 2:$ Profit percent for a man who calculates his profit on the selling price. He marks up the cost of his item by $25 \%$ and then sells the item at a discount of $10 \%$.

If the roots of the equation $x^2 + px + q = 0$ differ by $1$,then:

If $x = 2 + 2^{2/3} + 2^{1/3}$,then $x^3 - 6x^2 + 6x = $