How many real numbers satisfy the equation |x - 4| + |x - 7| = 15 ?

A mapping f : A → B defined as $f(x)=\frac{2 x+3}{3 x+5}, x \in A$ If f is to be onto, then what are A and B equal to ?

α and β are distinct real roots of the quadratic equation x² + ax + b = 0. Which of the following statements is/are sufficient to find α ? 

1. α + β = 0, α² + β² = 2

2. αβ² = -1, a = 0

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If the sixth term in the binomial expansion of $\left(x^{-\frac{8}{3}}+x^2 \log _{10} x\right)^8$ is 5600, then what is the value of x ?