Let $${L_1},$$ $${L_2},$$ $${L_3}$$ be the lines of intersection of the planes $${P_2}$$ and $${P_3},$$ $${P_3}$$ and $${P_1},$$ $${P_1}$$ and $${P_2},$$ respectively.
STATEMENT - 1Z: At least two of the lines $${L_1},$$ $${L_2}$$ and $${L_3}$$ are non-parallel and
STATEMENT - 2: The three planes doe not have a common point.
Let a and b be non-zero real numbers. Then, the equation
$$(a{x^2} + b{y^2} + c)({x^2} - 5xy + 6{y^2}) = 0$$ represents :
Let $$g(x) = {{{{(x - 1)}^n}} \over {\log {{\cos }^m}(x - 1)}};0 < x < 2,m$$ and $$n$$ are integers, $$m \ne 0,n > 0$$, and let $$p$$ be the left hand derivative of $$|x - 1|$$ at $$x = 1$$. If $$\mathop {\lim }\limits_{x \to {1^ + }} g(x) = p$$, then
The total number of local maxima and local minima of the function
$$f(x) = \left\{ {\matrix{
{{{(2 + x)}^3},} & { - 3 < x \le - 1} \cr
{{x^{2/3}},} & { - 1 < x < 2} \cr
} } \right.$$ is