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The differential equation is rearranged to dt/dx - xt = -e? ²/², where t = 1/ (y+1).
This is a linear first-order differential equation. The integrating factor (I.F.) is e^ (∫-x dx) = e? ²/².
The solution is t * (I.F.) = ∫ Q (x) * (I.F.) dx + c.
t * e? ²/² = ∫ -e? ²/² * e? ²/² dx + c = ∫ -1 dx = -x + c.
Substituting t = 1/ (y+1) back: e? ²/² / (y+1) = -x + c.
Using the initial condition y (2) = 0:
e? ²/ (0+1) = -2 + c ⇒ c = e? ² + 2.
The solution is e? ²/² / (y+1) = 2 + e? ² - x.

Given f (x) = ax^2 + bx + c.
f (-1) = a - b + c = 2
f' (x) = 2ax + b, so f' (-1) = -2a + b = 1
f' (x) = 2a, so f' (-1) = 2a = 1/2

From 2a = 1/2, we get a = 1/4.
Substituting a into -2a + b = 1: -2 (1/4) + b = 1 => -1/2 + b = 1 => b = 3/2.
Substituting a and b into a - b + c = 2: 1/4 - 3/2 + c = 2 => -5/4 + c = 2 => c = 13/4.

So, f (x) = (1/4)x^2 + (3/2)x + 13/4 = (1/4) (x^2 + 6x + 13).
We need to find f (1):
f (1) = (1/4) (1^2 + 6 (1) + 13) = (1/4) (1 + 6 + 13) = (1/4) (20) = 5.

The highest package offered during the placement drive 2024 stood at INR 19 LPA. Check out the highest packages offered during the College of Engineering, Bharati Vidyapeeth placements during seasons 2022-2024 from the table below:

The average fees for MCA course can vary largely depending upon the type of college/ institution ie. whether the college is government or private, because generally government colleges offer more affordable MCA programs, with total course fees potentially in the range of Rs. 432 to Rs. 3.34 Lacs for the entire program. On the other hand, in private colleges, MCA fees can vary widely, from around Rs. 50,000 to over Rs. 22 Lacs for the complete program, reflecting higher costs for advanced facilities, industry connections, and specialised courses.

The kind of clinical exposure students get in top Optometry colleges are -

• Hands-on patient examination in eye hospitals

• Training in refraction, vision therapy, and contact lenses

• Exposure to advanced diagnostic tools

• Internships in multi-specialty hospitals and eye institutes

Candidates can see the way given below -

• Check which college has better tie up with hospital  

• Check records of placement

• Look at lab and other facilities

• Look at the quality of faculty

Optometry syllabus includes a balance between classroom learning as well as applied and practical training. In course, there are subjects like ocular physiology, contact lens technology and even optometric instruments that students study and also go through practical sessions.

Also clinical postings and internships in hospitals help them diagnose refractive errors, manage vision therapy and even assist in specialised eye care. 

Both courses include core subjects such as anatomy, optics and even ocular diseases. But there are also some key differences like BSc Optometry is more academically oriented which focuses more on Science and theory behind eye care.

But B.Optom is more about clinical practice and patient care with more structured hospital training. 

Deakin University is highly renowned for offering best academic programs for its international and Indian students. Deakin offers 300+ degree programs at undergraduate, postgraduate, research, and double degree levels for its Indian students. Some popular programme opted by international students at Deakin include Engineering, Business, Education, Nursing, and more. The top programs opted by Deakin University alumni are listed below:

• Business
• Psychology
• Information Technology
• Accounting
• Business Administration and Management

Yes Optometry courses place a strong focus on practical training and hospital exposure. Students go through laboratory work, clinical postings and even hands-on sessions with diagnostic equipment.

Most colleges make it sure that hospital internships are there during final year, where students usually examine patients under some supervision.

This experience not only helps them apply theoretical knowledge in real scenarios but also build confidence in them and even develop essential skills in them that are required for careers as clinical optometrists or specialists.

Admission to South Asian University (SAU) is based on both entrance tests and merit. Candidates can apply through the SAU Entrance Test or by submitting scores from recognised national-level tests, depending on the programme and their country of origin. The university accepts national entrance exams such as JEE Main, GATE, CAT, MAT, and others. 

The admission fee for SIMS Pune MBA course is currently unknown. The total tuition fee for SIMS Pune MBA course is INR 18.73 lakh. Generally, the admission feesfor the MBA course is a portion of the total tuition fee. Candidates will be informed of the admission fee payable by them if they manage to clear the SNAP exam with an appropriate rank.

CuSO? 5H? O is blue vitriol which is represented as [Cu (H? O)? ]. H? O.SO? Here, secondary valencies are 4 H? O and 1H? O molecule outside coordination sphere is involved in hydrogen bonding.

Yes, South Asian University (SAU) is considered a good college, particularly for students from SAARC nations, due to its highly qualified faculty, rigorous and research-oriented curriculum, diverse student body, and a vibrant academic and intellectual environment. The university boasts highly qualified, well-trained, and experienced faculty members with strong research backgrounds and significant expertise. 

The SIMS Pune fees for the MBA course in 2025 is INR 22.1 lakh. This aforementioned fee amount is comprised of several fee components including tuition fee, hostel fee, one-time payments and other fees. The tuition fee is charged on an annual basis at SIMS Pune. Candidates can visit the official website of SIMS Pune to learn more about the MBA course at SIMS Pune. 

PES University conducts PESSAT for admission into BBA programme. The minimum eligibility for the programme is passing Class 12 with atleast 50% of aggregate marks. Scoring 60% in Class 12 makes the candidate eligible for admission into BBA. However, the candidate must qualify PESSAT and the subsequent personal interview round to get a confirmed seat in the course at the university.