Class 11th

$\frac{x}{4}=cost-sint...\left(1\right)$

$\frac{y}{5}=cost+sint$ . . . . (2)

(1)² + (2)² gives

${\left(\frac{x}{4}\right)}^2+{\left(\frac{y}{5}\right)}^2=2$

InA-O-H, if EN of ' A' is 2.1 then it will be neutral, as X_A-X₀=X₀-X_H. (where X is EN)

Bond order in N $N_2$ and O $O_2^{2+}$ is 3 (calculated by energy level diagram)

The order of stability of resonating structures: carrying no charge $>$  carrying minimum charge and each atom having octet complete.

Variance of 2001, 2003, 2006, 2007, 2009, 2010 is same as variance of 1, 3, 6, 7, 9, 10

mean =  $\frac{1+3+6+7+9+10}{6}=6$

var (x) =  $\frac{1^2+3^2+6^2+7^2+9^2+10^2}{6}?36$

var (x) = 10

  $\sim \left(p\to q\right)=p\wedge \sim q$

A quadrilateral is a square and it is not a rhombus

area of quad PACB = LR = 8

$P=1+\frac{2}{3}+\frac{6}{3^2}+\frac{10}{3^3}+\frac{14}{3^4}+...+\infty$

$\frac{P}{3}=\frac{1}{3}=\frac{2}{3^2}+\frac{6}{3^3}+\frac{10}{3^4}+...+\infty$

$\frac{2P}{3}=1+\frac{1}{3}+\left[\frac{4}{3^2}+\frac{4}{3^3}+\frac{4}{3^4}+...+\infty \right]$

$\frac{2P}{3}=\frac{\frac{4}{3}}{1-\frac{1}{3}}\Rightarrow P=3$

$f\left(x\right)=x^2+x+\left(\frac{\lambda +1}{\lambda }\right)$

$f\left(1\right)<0\Rightarrow 2+\left(\frac{\lambda +1}{\lambda }\right)<0$

$\frac{3\lambda +1}{\lambda }<0\Rightarrow \lambda \in \left(-\frac{1}{3},0\right)$