Part 1 Memory based Question | CSIR NET July 2026

[00:00:00]Hello students. Welcome to the memory based questions solution of the CS net July 2026. This is a part one. Myself Dr. Harish Garg. You can follow and subscribe my YouTube channel.

[00:00:13]The question that I had received from one of my student is shown in your screen.

[00:00:24]First of all, make sure student this is a memory based question.

[00:00:30]You can send the right right question in the comment box. We'll upload the solution in a 15 second time period in four all of you.

[00:00:38]Question what I would say directional derivative. It's very simple. It's a very simple. You can find the gradient.

[00:00:45]Find the partial derivative with respect to x.

[00:00:48]2x - 4y squared and then with respect to y 8xy + 3y squared. And what is the definition of the directional derivative? Gradient dot unit vector.

[00:01:03]Fine. Now, the unit vector is given to you alpha i cap plus beta j cap. Find the gradient at the 1 {comma} 1. So that 1 2 - 4 is a minus of 2.

[00:01:14]And - 8 + 3 is a minus 5 dot unit vector of the alpha {comma} beta which comes to be 14 divided by 5.

[00:01:26]If you find the dot product, - 2 alpha - 5 beta is 14 over 5. Make sure it's a unit vector. The unit vector after you pass to alpha squared plus beta squared must be 1.

[00:01:40]Fine. Now, look at that second is in the direction of the 1 {comma} 2. Find the gradient at the 1 {comma} 2. It's a 2 find 0 and 0. 2 {comma} 0 alpha {comma} beta which is equal to 6 over 5. Can you find the value of the alpha? 2 alpha is equal to 6 over 5. Alpha is my 3 over 5.

[00:02:05]Is it fine? The ones the alpha is 3 by 5, I can substitute in the equation. You will get minus 5 beta is a minus 6 by 5. 20 by 5 is 4.

[00:02:17]Beta will be minus 4 over 5.

[00:02:21]Fine? And clearly say both are satisfied by unit condition. The alpha got the answer 4 over 5. 25 alpha minus beta 4 plus 3 7 over 5. So, get the answer over here.

[00:02:35]25 and 25 cancel. 49 is the right answer of the problem.

[00:02:41]Comment and tell me if you get the same answer. Answer you will get 3 over 5. If you like the video, like and share. If you have more questions on the memory based question, send me your questions in the comment box. I will upload the video for you in the next 15 minutes.

[00:02:58]Till then, you can subscribe to my YouTube channel and let me know your answers and your correct answer in the comment box. Best of luck, students.

[00:03:05]Happy learning.