Intermediate Level in science stream

Recently I have completed my Intermediate Level in science stream from one of the reputed institution of my own country. I want to proceed my further study in the same stream in foreign institution. I think it will be better to inform you about my previous academic background, which will be helpful to you during the selection procedure. I always get a top position in my class and all the teachers highly appreciated me as a very talent and hard working student. I am very much interested to proceed my further study in physics, Mathematics and in Chemistry. I like Mathematics and Physics very much. In Intermediate level I secured distinction marks in both the subject which also reveals my interest on these subject.
After getting information about your institution from my teacher. I had visited your institution's web page and read all about the Undergraduate Program. I have found your institution as one of the best in the field of pure sciences. Finally I came to conclusion that to join your program.
As I am a citizen of least developing country, my economical status is not so sound to pay the tuition fee. So I expect I will get a scholarship for this four years program.
I assure you that If i will get a chance to study at you institution, I will perform my responsibility without any hesitance and any hurdle. As a competent candidate, I feel i have all qualities and skills which are required for the program.
I am looking forward to hearing some good news very soon from your side.
Harry

What is "Intermediate Level in science stream"? I'm curious! :) Will the reader of this essay know what it is?

...from (name of institution), which is one of the reputed institution of (name of country).

I think it will be better to inform you about my previous academic background, which will be helpful to you during the selection procedure. This whole sentence is... not useful. It is stating the obvious and wasting space. Can you replace it with a sentence that tells something about the interests you have developed and the specific direction of study you would like to pursue? What makes your interests and aspirations unique?

After getting information about your institution from my teacher, I had visited your institution's web page and read all about the Undergraduate Program. I have found [name of institution] to be one of the best in the field of pure sciences. Finally I came to conclusion that to join your program.

Ahh, in the last paragraph you seem very sincere and deserving of acceptance. I like that last paragraph a lot!

...perform fulfill my responsibilities without any hesitation or hurdle.

make sure to catch the little errors such as "you institution"

"I want to proceed further in my studies in the same stream at a foreign institution."

"I have found your institution as one of the best in the field of pure sciences" Perhaps you should delve into the specifics of what exactly you think makes the institution the best. Pile on the praise!

"As I am a citizen of least developing country, my economical status is not so sound to pay the tuition fee. So I expect I will get a scholarship for this four years program." Do you "expect" or "hope"? And if you "expect," rather than "hope," do you have any good reason for this? If not, you might want to go with "hope" anyway, on the grounds it sounds a bit humbler.

Recently I have [recently] completed my Intermediate Level in [the] science stream from one of the reputed institutions of my own[in my] country. I want[wish] to proceed my further stud[ies] in the same stream in [a] foreign institution. I think it will be better [would like to] to inform you about my previous academic background, which will[should] be helpful to you during [in] the selection procedure. I [have] always get a [obtained the] top position in my class[,] and all the [my] teachers [have] highly appreciated me[highly] as a very talent[ed] and hard working student.

I am very much interested to[in] proceed[ing] [with] my further stud[ies] in [P]hysics, Mathematics and in Chemistry. I [specially] like Mathematics and Physics very much. In Intermediate level [and] secured distinction marks in both the subjects which also reveal[ing] my interest in the[m.]se subject

After getting [some] information about your[the] institution from my teacher.[,] I had visited your institution's web page and read all about the Undergraduate Program. I have found your institution as one of the best in the field of pure sciences[,]. Finally I and came to [the]conclusion that to join your program. As I am a citizen of least [a] developing country, [and in] my economical [situation] status is not so sound to [unable to] pay the tuition fee. So I expect I will [I sincerely hope to] get a scholarship for this four years program.

I assure you that If i [if I] will get a chance to study at you[r] institution, I will perform my responsibilit[ies] without any hesita[tion] and [despite] any hurdle. As a competent candidate, I feel I have all qualities and skills which are required for the program.

I am looking forward to hearing some good news very soon from your side[very soon].

[sincerely,]

Harry