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Let $z_1=x_1+i{y}_1,z_2=x_2+i{y}_2\&z=x+iythen$  

and $\left(z_1-z_2\right)=\frac{\pi }{4}gives\frac{y_1-y_2}{x_1-x_2}=1or{y}_1-y_2=x_1-x_2............\left(i\right)$  

y² – 6x + 9 = 0 .(ii)

as z₁ & z₂ lies on (ii) so ${y_1}^2-6x_1+9=0$    .(iii)

& $y_{2}2-6x_2+9=0.........\left(iv\right)$  

(iii) & (iv) $\left(y_1+y_2\right)\left(y_1-y_2\right)-6\left(x_1-x_2\right)=0$

$\left(x_1-x_2\right)\left(y_1+y_2-6\right)=0from\left(i\right)$

-> $y_1+y_2-6=0i.e.,y_1+y_2=6$  

Simple distillation can be applied for the separation of two liquids has boiling point difference greater than 20°C.

Boiling point of propanol > boiling point of propane (due to H-bonding effect)

The total course fee for BBA LLB (Hons) at Model Institute of Engineering and Technology is INR 90,200. Aspirants who get a seat in the institute need to confirm their admission by paying the course fee. Candidates can pay fee via any of the online payment modes. 

The terms UG SOP (statement of purpose) and UG LOM (letter of motivation) are often used interchangeably and often mean the same thing. Both of these documents discuss an applicant's background and interests in detail. However, UG LOMs may often come with specific instructions and/or word limits that applicants have to adhere to. LOMs may also require students to answer specific queries about their background or academic interests, or discuss their suitability for the said programme in detail.

A4 is in the middle in terms of height.

Let $t=\frac{3}{2}{x}^2+\frac{5}{3}{x}^3+\frac{7}{4}{x}^4+......$

$=\left(2-\frac{1}{2}\right)x^2+\left(2-\frac{1}{3}\right)x^3+\left(2-\frac{1}{4}\right)x^4+......$   

= $2\left(x^2+x^3+x^4+.....\right)-\left(\frac{x^2}{2}+\frac{x^3}{3}+\frac{x^4}{4}+.....\right)$

$=2\frac{x^2}{1-x}+ln\left(1-x\right)+x=\frac{x^2+x}{1-x}+ln\left(1-x\right)=\frac{x\left(1+x\right)}{1-x}+ln\left(1-x\right)$              

$=2\frac{x^2}{1-x}+ln\left(1-x\right)+x=\frac{x^2+x}{1-x}+ln\left(1-x\right)=\frac{x\left(1+x\right)}{1-x}+ln\left(1-x\right)$

$\sum P\left(x\right)=1\Rightarrow k+2k+2k+3k+k=1sok=\frac{1}{9}$

 Now, $P\left(\frac{1<x<4}{x\angle 3}\right)=P\frac{\left(x=2\right)}{P\left(x\angle 3\right)}=\frac{\frac{2k}{9k}}{\frac{k}{9k}+\frac{2k}{9k}}=\frac{2}{3}$  

$\Rightarrow P=\frac{2}{3}$          

So, $5P=\lambda kgives\frac{10}{3}=\lambda \times \frac{1}{9}\Rightarrow \lambda =30$  

Let $l={\displaystyle \underset{6}{\overset{16}{\int }}\frac{lo{g}_e{x}^2}{lo{g}_e{x}^2+lo{g}_e\left(x^2-44x+484\right)}dx..........\left(i\right)}$

By property ${\displaystyle \underset{a}{\overset{b}{\int }}f\left(x\right)dx={\displaystyle \underset{a}{\overset{b}{\int }}f\left(a+b-x\right)dx}}$

$\left(i\right)\Rightarrow l={\displaystyle \underset{6}{\overset{16}{\int }}\frac{lo{g}_e{\left(22-x\right)}^2}{lo{g}_e{\left(22-x\right)}^2+lo{g}_e{x}^2}dx}..........\left(ii\right)$      

(i) + (ii) 2l = ${\displaystyle \underset{6}{\overset{16}{\int }}1dx=10}$

l = 5

La⁺² (z = 57) = 5d¹

Ce⁺² (z = 58) = 4f²

Nd⁺² (z = 60) = 4f⁴

Yb⁺² (z = 70) = 4f¹⁴

Yb⁺² has no unpaired electrons thus diamagnetic in nature.

To prepare their UG SOP, students should prepare a list of things that are to be discussed in the SOP document. This can include their motivations for wanting to join the program, the goals that they have in mind and their relevant achievements and exposure. Applicants may also discuss their co-scholastic achievements and any other exposure that may be relevant or any significant challenges or instances that have had a major impact on their lives, or affected their academic choices.

There are a total of 190 seats for the MBA course at SOIM Nashik. Candidates are admitted to the programme based on fulfilment of eligibility criteria and performance in the interview round. The seat allotment is done as per the sanctioned seat intake. Moreover, the institute may reserve seats for candidates belonging to SC/ST categories. 

 Normal vector to the given plane be

$2\widehat{i}-\widehat{j}+3\widehat{k}so$                   

Equation of line QS :

$\frac{x-1}{2}=\frac{y-3}{-1}=\frac{z-4}{1}=\lambda$

So let P $\left(2\lambda +1,-\lambda +3,\lambda +4\right)$  

Now P lies on given plane so

$4\lambda +2+\lambda -3+8\lambda +4+3=0$  

So, S (-3, 5, 2)

also given R lies on given plane so

6 – 5 + $\gamma$ + 3 = 0 so   $\gamma$ = -4

So, R (3, 5, -4)

SR² = 72

BA curriculum at Kumaraguru College of Liberal Arts and Science spans over 3 years or 6 semesters. The curriculum is designed to create a strong understanding of the basics first before moving to more advanced concepts of the chosen BA course. Candidates can check the whole syllabus for the Kumaraguru College of Liberal Arts and Science BA courses on the official website.

In most cases, universities specify the maximum and minimum length (in characters or words) of the UG SOP in their guidelines. If there is no length specified, you can write a maximum of 1.5 pages. You must try to write a minimum of 600 words and a maximum of a 1000 words. Though most universities do not mind an addition of 50-100 words, applicants must understand that a good SOP does not have to be a verbose one. Hence, the aim should always be to keep the SOP precise, informative and easy-to-read.

Kindly consider the following figure