For the frequency distribution :
Variate (x) :      x₁   x₂   x₃ ....  x₁₅
Frequency (f) : f₁    f₂   f₃ ...... f₁₅
where 0 < x₁ < x₂ < x₃ < ... < x₁₅ = 10 and
$$\sum\limits_{i = 1}^{15} {{f_i}} $$ > 0, the standard deviation cannot be :

2$$\pi $$ - $$\left( {{{\sin }^{ - 1}}{4 \over 5} + {{\sin }^{ - 1}}{5 \over {13}} + {{\sin }^{ - 1}}{{16} \over {65}}} \right)$$ is equal to :

Let [t] denote the greatest integer $$ \le $$ t. If for some
$$\lambda $$ $$ \in $$ R - {1, 0}, $$\mathop {\lim }\limits_{x \to 0} \left| {{{1 - x + \left| x \right|} \over {\lambda - x + \left[ x \right]}}} \right|$$ = L, then L is equal to :

The solution curve of the differential equation,

(1 + e^-x)(1 + y²)$${{dy} \over {dx}}$$ = y²,

which passes through the point (0, 1), is :