Maths NCERT Exemplar Solutions Class 12th Chapter Twelve

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

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

Given the following two statements:

$\left(S_1\right):(q\vee p)\to (p\leftrightarrow \sim q)$ is a tautology.

$\left(S_2\right):\sim q\wedge (\sim p\leftrightarrow q)$ is a fallacy. Then:

Given the following two statements:

$\left(S_1\right):(q\vee p)\to (p\leftrightarrow \sim q)$ is a tautology.

$\left(S_2\right):\sim q\wedge (\sim p\leftrightarrow q)$ is a fallacy. Then:

The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations are $\mathrm{5,7},\mathrm{10,12,14,15}$ , then the absolute difference of the remaining two observations is:

The number of elements in the set $\left\{z=a+ib\in C:a,b\in Zand1<\left|z-3+2i\right|<4\right\}$ is

Let $\left\{x\right\}$ and $\left[x\right]$ denote the fractional part of $x$ and the greatest integer $\le x$ respectively of $a$ real number $x$ . if ${\int }_0^n \left\{x\right\}dx,{\int }_0^n \left[x\right]dx$ and $10\left(n^2-n\right),(n\in N,n>1)$ are three consecutive terms of a G.P. then $\mathrm{n}$ is equal to(Integration)

If the variance of the following frequency distribution :

$\begin{array}{lllll}\text{Class}& :& 10-20& 20-30& 30-40\\ \text{Frequency}& :& 2& x& 2\end{array}$ is 50 , then $x$ is equal to:

Let $PQ$ be a diameter of the circle $x^2+y^2=9$ . If $\alpha$ and $\beta$ are the lengths of the perpendiculars from $P$ and $Q$ on the straight line, $x+y=2$ respectively, then the maximum value of $\alpha \beta$ is.

A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is