Class 12th

Area of ?

$=\frac{1}{2}\left|\begin{array}{ccc}\hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill \\ \hfill x\hfill & \hfill y\hfill & \hfill 1\hfill \\ \hfill -x\hfill & \hfill y\hfill & \hfill 1\hfill \end{array}\right|$

-> $\left|\frac{1}{2}\left(xy+xy\right)\right|=\left|xy\right|$

->Area (D) = |xy| = |x (– 2x² + 54x)|

$\frac{d\left(\Delta \right)}{dx}=\left|\left(-6x^2+108x\right)\right|\Rightarrow \frac{d\Delta }{dx}=0$  at x = 0 and 18

->at x = 0, minima

and at x = 18 maxima

Area (D) = |18 (– 2 (18)² + 54 * 18)| = 5832

(a – 1) * 2 + (b – 2) * 5 + (g – 3) * 1 = 0

2a + 5b + g – 15 = 0

Also, P lie on line

a + 1 = 2λ

b – 2 = 5λ

g – 4 = λ

2 (2λ – 1) + 5 (5λ + 2) + λ + 4 – 15 = 0

4λ + 25λ + λ – 2 + 10 + 4 – 15 = 0

30λ – 3 = 0

$\lambda =\frac{1}{10}$  

a + b + g = (2λ – 1) + (5λ + 2) + (λ + 4)

$=8\lambda +5=\frac{8}{10}+5=5.8$

Group number = 11 (Atomic number = 111)

Coca alkaloid or cocaine is obtained from Erythroxylum coca.

Functional group should get the lowest possible number.

Please find the solution below:

The boiling point of alcohol increases with increase in the number of carbon atoms. So, hexanol has maximum boiling point.

 

Complete reaction is as follows:

The given reaction is called hydroboration oxidation.

Adenine forms hydrogen bonds with thymine whereas cytosine forms hydrogen bonds with guanine.

The 'X' in reaction is 3-hydroxybutanal. It is an aldol reaction. Complete reaction is an follows: