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Newton's second law of motion is F = MA. Thus, Ft = mv - mu.
Now, when F = 0, then v = u. In the absence of force, the object continues to move with same velocity throughout.
Now, when F = 0 and u = 0, then v = 0. That is, an object at rest will remain at rest if no force is acting on it. Thus, Newton's first law is derived from second law.
Now, let us consider a system of 2 bodies 1 and 2, and consider that there is no external force acting. Now, let F12 be the force acting on 2 by 1 & F21 be the force acting on 1 by 2.
The rate of change of momentum of 1 = dp1/dt and rate of change of momentum of 2 = dp2/dt. Thus, according to Newton's second law of motion F12 = dp2/dt and F21 = dp1/dt
Adding both the above equations, we get
F12 + F21 = dp2/dt + dp1/dt = d(p2+p1)/dt
We know that, no force is applied. Thus, momentum change will also be 0 because no change in velocity occurs.
Thus, d(p1 + p2)/dt = 0
Therefore, F12 + F21 = 0
That is, F12 = - F21.
Thus, Newton's third law is proved with Newton's second law.

Hello Animesh,
You can appear for AIEEE. It provides admission to government colleges, which are cost-effective. I would also suggest you to appear for individual state examinations (OJEE in Odisha, EAMCET in Andhra Pradesh/ Telangana, COMEDK in Karnataka, etc.). These exams also guarantee you good colleges and serve as a backup in case things don't end up the way you've planned for IIT/ AIEEE.
Every state has its own share of good engineering colleges. So, don't underestimate or overlook them. They can prove to be vital. The more the entrance examinations you appear for, the more the options you will have for choosing colleges.
There are certain private colleges like SRM, KIIT - Odisha, GITAM - Vishakhapatnam and ITER - Odisha conduct their own entrance examinations. You can opt for these as well.
After the results of those entrance examinations are announced, if you have a valid score and rank, you can attend the counselling procedure for the respective entrance examination. During the counselling procedure, you can select a college of your choice and the branch of engineering.
I hope it helps. If so, kindly, upvote this answer. If you've any further questions, kindly revert.