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What are the targeted keywords?

I don't see your "quality high-PR backlinks" in Majestic, but maybe they're just being slow.

Your title tags are actually sort of broken. There's the site name repeated two times for no reason. It would not surprise me if Google decides to overwrite them all for being confusing. Meta description for articles is pretty bad, just the post name repeated. If Google did what you asked, you'd have the same text twice in SERPs.

Have you actually checked the HTML source? This is all blatantly obvious from the first glimpse.

You don't need to bother with meta keywords - they've been useless for years.

However, you've got a way bigger issue than the aforementioned. What's the content that you're supposed to rank with? It seems that you're aggregating articles from other sites, or perhaps adding a few sentences of your own to them. Google is likely to show the primary source because it's likely to be a more authoritative site with a similar post title and content. This is a really bad way to compete with schools, because even the local less well known institutions often have enough backlinks from partners, students and alumni.

Added: Do you actually have the keywords in the content? Or pages that target those exact keywords? Doesn't seem so.

There's also minor issues like multiple exclamation marks, broken layout and stuff like that which make the site look non-trustworthy.

Depends on your keywords, which are you trying to rank for and are they high difficulty or low.

Also a quick look at your site and the front page is ridden with links without any text at all. Add some H1 or welcome text explaining what your site is about, its also a good way to target some of your keywords (don't do it more than once or twice or it can hurt instead).

Not sure which software/CMS you are using for this but i think the site could do with a little more text.

You could install a free seo extension called seoquake and check what you can imporve when it comes to seo optimization for your site.

Cleanup a bit. Too many adsense code and that's against Google Adsense tos

The contents of your web site are not original and it appears they have been copied from other web sites. This is the huge NO NO. Unless you publish original content your web site will not rank. Start posting original content with few images or your web site will never rank.

I can't see any good backlinks *(used a few checkers!). Also, I don't think that you could easily rank for such keywords (better optimize your website for a few long-tail keywords...)