Maths

A feasible region of a system of linear inequalities is said to be __________ if it can be enclosed within a circle.

In a LPP, if the objective function $Z=ax+by$ has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points gives the same __________ value.

If the feasible region for a LPP is __________, then the optimal value of the objective function $Z=ax+by$ may or may not exist.

In a LPP, the objective function is always __________.

In a LPP, the linear inequalities or restrictions on the variables are called __________.

The probability of a man hitting a target is $\frac{1}{10}$ . The least number of shots required, so that the probability of his hitting the target at least once is greater than $\frac{1}{4}$ , is(Probability)

Suppose a differentiable function $f\left(x\right)$ satisfies the(Functions)

identity $f(x+y)=f\left(x\right)+f\left(y\right)+x{y}^2+x^{2}y$ , for all real $x$ and $y$ . If ${\mathrm{l}\mathrm{i}\mathrm{m}}_{x\to 0} \frac{f\left(x\right)}{x}=1$ then $f^{\mathrm{\text{'}}}\left(3\right)$ is equal to

If the system of equations

$x-2y+3z=9$

$2x+y+z=b$

$x-7y+az=24$

has infinitely many solutions, then $a-b$ is equal to

If the system of equations

If the equation of a plane $P$ , passing through the intersection of the planes, $x+4y-z+7$ $=0$ and $3x+y+5z=8$ is $ax+by+6z=15$ for some $a,b\in R$ , then the distance of the point $(\mathrm{3,2},-1)$ from the plane $P$ is(