inequalities

Consider the following inequalities. (i) 2x $$-$$ 1 > 7 (ii) 2x $$-$$ 9 Which one of the following expressions below satisfies the above two inequalities?

A superadditive function $f(\cdot)$ satisfies the following property $$ f\left(x_1+x_2\right) \geq f\left(x_1\right)+f\left(x_2\right) $$ Which of the following functions is a supe...

Consider a differentiable function f (x) on the set of real numbers such that f(-1) = 0 and |f'(x)| ≤ 2. Given these conditions, which one of the following inequalities is necessar...

Michael lives 10 km away from where I live. Ahmed lives 5 km away and Susan lives 7 km away from where I live. Arun is farther away than Ahmed but closer than Susan from where I li...

If x>y>1, which of the following must be true? $$$\begin{array}{l}\mathrm i.\;\ln\left(\mathrm x\right)>\ln\left(\mathrm y\right)\;\;\;\;\;\;\;\;\;\;\mathrm{ii}.\;\;\mathrm e^\math...

The set of values of p for which the roots of the equation 3x 2 + 2x + p(p - 1) = 0 are of opposite sign is

Consider two identically distributed zero - mean random variables $$U$$ and $$V.$$ Let the cumulative distribution functions of $$U$$ and $$2V$$ be $$F(x)$$ and $$G(x)$$ respective...

Hari (H), Gita (G), Irfan (I) and Saira (S) are siblings (i.e. brothers and sisters). All were born on 1 st January. The age difference between any two successive siblings (that is...