Maths NCERT Exemplar Solutions Class 12th Chapter Twelve: Overview, Questions, Preparation

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, 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 unbounded, maximum or minimum of the objective function $Z=ax+by$  may or may not exist.

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 $a$ and $b$ are real numbers such that $(2+\alpha {)}^4=a+b\alpha$ , where $\alpha =\frac{-1+i\sqrt[]{3}}{2}$ , then $a+b$ is equal to:

Contrapositive of the statement:

If a function $f$ is differentiable at $a$ , then it is also continuous at $a$ ', is:

If for some positive integer $n$ , the coefficients of three consecutive terms in the binomial expansion of $(1+x{)}^{\mathrm{N}+5}$ are in the ratio $5:10:14$ , then the largest coefficient in the expansion is:

Let $\alpha$ and $\beta$ be roots of $x^2-3x+p=0$ and $\gamma$ and $\delta$ be the roots of $x^2-6x+q=0$ . If $\alpha ,\beta$ , $\gamma ,\delta$ , form a geometric progression. Then ratio $(2q+p):(2q-p)$ is:

Let $f$ be a twice differentiable function on $\left(\mathrm{1,6}\right)$ . If $f\left(2\right)=8,f^{\mathrm{\text{'}}}\left(2\right)=5,f^{\mathrm{\text{'}}}\left(x\right)\ge 1$ and $f$ " $\left(x\right)\ge 4$ , for all $x\in \left(\mathrm{1,6}\right)$ , then: