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58. Let (0, y) be the point on y-axis which is at a distance 4 unit from the line $\frac{x}{3}+\frac{y}{4}=1$

Then, the line $\frac{x}{3}+\frac{y}{4}=1$

4x + 3y = 12.

4x + 3y - 12 = 0

Applicants need to provide Class 12 mark sheets, a valid government-issued ID, recent passport-size photographs, and, if applicable, entrance exam results. Other documents like domicile or reservation certificates might be requested. It's important to double-check the official checklist before uploading.

To apply for the BA course, go to the official NIPS Bhubaneswar website. Navigate to the 'Admission' section, choose your preferred campus and course, and click on 'Apply Now.' Complete the form, upload the necessary documents, pay the application fee, and submit it to initiate your admission.

57. Let a and b be the x & y intercept. Then,

$\frac{x}{a}+\frac{y}{b}=1.$ _____ (1)

Given, a + b = 1. ______ (2) b = 1 -a _____ (3)

and ab = -6 _____ (4)

Putting eqn (B) in (iii) we get a

a (1- a) = - 6

a - a² = - 6

a² - a - 6 = 0

a² + 2a - 3a - 6 = 0

a (a + 2) - 3 (a + 2) = 0

(a + 2) (a -3) = 0

(a + 2) (a -3) = 0.

a = 3 or a = -2.

When a = 3, b = 1- a = 1 - 3 = - 2

When a = - 2, b = 1 - (-2) = 1 + 2 = 3

So, (a, b) = (3, -2) and (-2, 3)

Hence, eqⁿ (1) becomes,

$\frac{x}{3}+\frac{y}{-2}=1$ and $\frac{x}{-2}+\frac{y}{3}=1.$

2x – 3y = 6 and 2y - 3x = 6

Gives the read eqⁿ of lines

The operation * on the set A = {1, 2, 3, 4, 5} is defined as 

a * b = L.C.M. of a and b.

Then, the operation table for the given operation * can be given as:

It can be observed from the obtained table that:

3 * 2 = 2 * 3 = 6 ∉ A, 5 * 2 = 2 * 5 = 10 ∉ A, 3 * 4 = 4 * 3 = 12 ∉ A

3 * 5 = 5 * 3 = 15 ∉ A, 4 * 5 = 5 * 4 = 20 ∉ A 

Hence, the given operation * is not a binary operation.

22. Give, f (x) = 2x – 5.

(i) f (0)= (2 * 0) –5=0 – 5= –5

(ii) f (7)= (2 * 7) –5=14 – 5=9

(iii) f (–3)=2 * (–3) –5= –6 – 5= –11.

56. The given equation of the line is 3x + y + 2 = 0

Yes, a full-time BCom (Hons) is available at Karnavati University. It is an undergraduate degree programme lasting four years. It is offered through the university's Department of Liberal Arts under the Unitedworld School of Liberal Arts and Mass Communication (USLM). The university offers the course in one specialisation. i.e. Economics & Accounts. Candidates who fulfil the preset eligibility criteria can visit the university's official website to apply for BCom (Hons) admission.

To get a seat in the LLM course at Kirit P. Mehta School of Law, candidates are required  to complete the basic eligibility criteria first. Then candidates must have achieved a valid score in the entrance exam CLAT/NMISM Entrance Test/ PGCETL. Further, candidates are required to fill out the application form and submit important documents.

After the conclusion of the complete application form, the college conducts the PI and releases the merit list of selected candidates. Following this, candidates can confirm their seat after paying the requisite amount of course fee.

The binary operation *′ on the set {1, 2, 3 4, 5} is defined as a *′ b = H.C.F of a and b.

The operation table for the operation *′ can be given as:

We observe that the operation tables for the operations * and *′ are the same.

Thus, the operation *′ is same as the operation*.

Yes, students who have graduated with an MBA degree from AIMS Institutes are eligible for jobs offered by government departments and organisations. In general, pursuing an MBA course helps students develop various essential skills. Some of the skills that come in handy at government jobs are strategic thinking, planning & organising, problem solving,  and more. Check out the table below to get an idea of government jobs generally pursued by MBA graduates:

The set eligibility criteria for students seeking admission in IIIT Kalyani BTech states that they must have passed Class12 with Physics and Mathematics as compulsory subjects along with one of the Chemistry/Biotechnology/Biology/Technical Vocational subject with 75% aggregate. In case of SC/ST students relaxation of 10% is permitted.

(i) (2 * 3) * 4 = 1 * 4 = 1

2 * (3 * 4) = 2 * 1 = 1

(ii) For every a, b ∈ {1, 2, 3, 4, 5}, we have a * b = b * a. Therefore, the operation * is commutative.

(iii) (2 * 3) = 1 and (4 * 5) = 1

∴ (2 * 3) * (4 * 5) = 1 * 1 = 1

Yes, admission is currently open for the BA at NIPS Hotel Management Bhubaneswar. Interested candidates are encouraged to apply at the earliest and regularly check the official website for updates on deadlines, entrance exam details, and other admission-related announcements.