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Displacement in 4? second
= S? - S?
= (1/2)g [2n - 1]
= (1/2)g [2×4 - 1]
= (1/2) × 9.8 × 7
= 34.3m
As this distance matches with data given in question for position of next drop. So drops are falling at the rate of 1 drop/second.

Hostel fees for BSc students at Vidyasagar University is currently unknown. The hostel fees at Vidyasagar University may differ depending on the facilities availed by the students as well as their gender. Hostel fees may be a part of the admission fees payable by the students at the time of admissions. Candidates looking to get enrolled in the BSc courses at Vidyasagar University are advised to contact the university officials regarding hostel fees at Vidyasagar University.

Body is dropped from height 75m with initial velocity (upward) 10m/s
So, s = ut + ½ at²
-75 = 10t - ½ gt²
5t² - 10t - 75 = 0
By solving t = 5 sec.
In 5sec. balloon covered
h = 10 × 5 = 50m
Now height of balloon = 75 + 50 = 125m

Tuition fees for BSc courses at Vidyasagar University is charged on a per semester basis. The data regarding tuition fee for BSc courses at Vidyasagar University is currently unknown. The unofficial sources claim that the Vidyasagar University BSc course fee in the year 2025 is between INR 1,900 - INR 62,100. Candidates who wish to learn more regarding Vidyasagar University BSc fees can visit the official website for official sources.

ε? = 250 × Potential Gradient
ε? + ε? = 400 × Potential Gradient
(ε? )/ (ε? + ε? ) = 250/400 = 5/8
By solving above
ε? /ε? = 5/3

By shell's law
(sin θ)/ (sin θ') = 4/3 . (i)
For TIR on second surface
sin θ' > sin θc
(θ' + θ' = 90)
sin (90 - θ') > sin θc
cos θ' > sin θc
1 - sin²θ' > sin²θc (By equation (i) )
1 - (3/4 sin θ)² > sin²θc
[sin θc = 3/4]
1 - (9/16)sin²θ > (9/16)
1 - 9/16 > (9/16)sin²θ
7/16 > (9/16)sin²θ
sinθ < √7/3

Columbia University does not ask for work experience for most of the programs, particularly in

Engineering,

Computer Science,

Applied Science, where they prioritize academic excellence. 

But, there are programs such as Business Analytics, Financial Engineering, or Management Science that mandate submission of relevant experience, internships, or research exposures. In addition, Columbia prefers students who have leadership potential, problem-solving ability, and real-world experiences.

Columbia University does not set any minimum eligible scores for international students who want to join the MS programs. But, it is needed for the students to make sure to score above 320 on the GRE and over 700 on GMAT for successful admission.

Also, students who scored nicely and performed well academically and were involved in relevant internships may get some sort of relief in standardized test scores. 

The University of Manchester is one of the top ranked universities in the world. According to Shiksha Popularity Rankings, the Manchester University has an overall ranking of #29 in world and #11 in UK. According to the Times Higher Education effect Rankings and the QS World University Sustainability Rankings, Manchester University is the only institution in the world to rank in the top ten for its social and environmental effect.

Indian students can choose Harvard if they want to pursue courses in STEM related fields, Business, Medicine, Public Policy. Students can also choose Harvard if they want a large Indian student community and exposure to thriving ecosystem of Boston. On the other hand, students can choose Yale if they want pursue courses in Humanities, Arts, Global Affairs or Social Sciences and if they prefer a collaborative, community-driving learning style.

Yes, studying at KTH Royal Institute of Technology is usually considered expensive for Indian students. Undergraduate courses, except for architecture, cost SEK 423,000 (INR 38.6 L), whereas graduate courses cost SEK 360,000 (INR 32.8 L). Apart from this, the monthly cost of living ranges between SEK 9,450 - 12,350 (INR 86.2K - 1.2L). This includes housing, food, public transportation and personal expenses.

Candidates can definitely consider pursuing BSc from Soundarya Institute of Management and Science. The institute offer courses in affiliation with Bangalore University. It is accredited by NAAC ranked B+. SIMS Bangalore is also recognised by the University Grants Commission (UGC). The institute has created a good reputation of its own with education being offered for more than a decade.

University of Manchester is one of most prominent universities in UK. Manchester University provides around 412 UG and 587 PG courses for international students. 3 faculties that make up University of Manchester each include several schools with strong reputations for successful teaching and research. The university offers a large variety of scholarships for its international and Indian students. The University of Manchester placement rate stands at 96%, and the graduates are employed within 6 months of graduation.

There are a total of 90 seats for the BSc in Psychology course of SIMS Bangalore. The seat allotment for this programme is done based on sanctioned seat intake and the applicants' performance in the selection rounds. Students must note that the seat intake mentioned here is taken from the official website/ sanctioning body. It is still subject to revision and hence, is indicative.

The fee range for the MSc programme at DY Patil University, Navi Mumbai, is INR 2 Lacs to INR 5 lakh. This information is sourced from official website/ sanctioning body and is subject to change. The fee covers various academic expenses like tuition fees, laboratory charges, examination fees, library fees, and other relevant charges. It is important to note that the fee structure is subject to change, and candidates are advised to refer to the official website of the university for the latest and most accurate fee structure. 

Shiksha Popularity Ranking ranks University of Manchester at #31 in world and #10 in UK. The University of Manchester is ranked by top ranking authorities all over the world that are listed below:

Soundarya Institute of Management and Science has a total of 60 seats for BSc in Forensic Sciences. Candidates are admitted to the UG programme as per sanctioned intake and performance in the last qualifying examination. The institute may follow the reservation rules of the state or central government. It must be noted that the mentioned seat intake is as per the official website/ sanctioning body. It is still subject to revision and hence, is indicative.