Maths

Let f(x) = ax² + bx + c be such that f(1) = 3, f(-2) = $\lambda$  and f(3) = 4. If f(0) + f(1) + f(-2) + f(3) = 14, then $\lambda$  is equal to:

Let A and B be any two 3 * 3 symmetric and skew symmetric matrices respectively. Then which of the following is NOT true?

Let A and B be any two 3 × 3 symmetric and skew symmetric matrices respectively. Then which of the following is NOT true?

Let , be the roots of the equation $x^2-\sqrt[]{2}x+\sqrt[]{6}=0$ and $\frac{1}{{\alpha }^2}+1,\frac{1}{{\beta }^2}+1$ be the roots of the equation x2 + ax + b = 0. Then the roots of the equation

$x^2-\left(a+b-2\right)x+\left(a+b+2\right)=0$ are:

Let S = $\left\{x\in \left[-6,3\right]-\left\{-2,2\right\}:\frac{\left|x+3\right|-1}{\left|x\right|-2}\ge 0\right\}$ and T = $\left\{x\in Z:x^2-7\left|x\right|+9\le 0\right\}.$ Then the number of element is $S\cap T$ is :

In a LPP, the maximum value of the objective function $Z=ax+by$ is always finite.

In a LPP, the minimum value of the objective function $Z=ax+by$ is always 0 if the origin is one of the corner points of the feasible region.

The maximum value of the objective function $Z=ax+by$ in a LPP always occurs at only one corner point of the feasible region.

If the feasible region for a LPP is unbounded, maximum or minimum of the objective function $Z=ax+by$  may or may not exist.

The feasible region for an LPP is always a __________ polygon.