CBSE 2026 Maths Exam: Top 15 Repeated Proof Questions Revealed #Class10 #Maths

Added: 2026-05-12

[00:00:01]All the students that are going to appear for their second board examinations of mathematics, this video is super important for you.

[00:00:09]Not because I'm going to impart any extra knowledge. Nahi. This video is just to cross-check whether you have done these ultimate proofs or not.

[00:00:17]Because guys, believe me, I have analyzed 10 years papers of CBSE board examination mathematics, and I have found that these 15 proofs, they almost appear every year. So, this year also, for sure, one of these proofs might appear in your board examinations. Okay?

[00:00:37]So, let's go through them one by one.

[00:00:40]Starting from real numbers, guys. Okay.

[00:00:42]So, almost every year, you either get a question ki prove that under root of root two, ya root three, ya root five, ya root seven is irrational. Or or you get question like this ki prove that three plus two root five, or one by root three, or two minus root say root three, these are irrational. So, these are the two types of questions that you cannot miss. I hope you have remembered all the steps of these proofs. Next, guys, for triangles. So, guys, everybody will tell you, I'll also tell you, this is like a no-brainer, that you have to memorize each and every step of basic proportionality theorem or Thales' theorem. Theek hai? So, Thales' theorem is another name for BPT. Also, guys, you should remember the statement also, because a lot of time they ask you to write the statement. Achha. Similarly, converse of basic proportionality theorem is super important. Also, mug up its statement and the proof. Okay? Next, guys, we have these problems of trapezium. Okay? So, again, very commonly asked questions ki in a trapezium with AB parallel to DC, if the diagonals intersect each other at point O, then prove that the proportional relationships of the segments is true.

[00:01:52]That means AO by BO is equals to CO by DO. Guys, very commonly asked question.

[00:01:57]Very commonly asked. Okay, next guys, the median wala question.

[00:02:01]Where the medians of two triangles are given and the triangles are given similar to each other. Okay, and the ratio of corresponding side is given equal to the ratio of corresponding medians. So, you have to prove that the third remaining sides, you know, their ratio is equal to the ratio of the median. Right? AB by PQ is equals to AD by PM. Very commonly asked proof question from triangle chapter. Make sure you do that proof. Okay, next up guys, next up. We have uh yes, so we have circles guys. So, in circles, first of all, the two core theorems, they are super important. You have to mug up their proofs, right? So, tangent and radius wala theorem and external tangents wala theorem. Both of them are super easy to prove. Make sure you do their proof. Okay, next guys, again, for circles, these are very commonly asked questions. Key have to prove that the tangents drawn at the ends of a diameter are parallel to each other. Next, prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the point of contacts at the center. So, you should know how to form the figure, what the question is asking you to prove. Okay, and again guys, very commonly asked question, very commonly asked proof. Okay, next guys, we have quadrilateral properties uh proofs that are very common. For example, prove that a parallelogram circumscribing a circle is a rhombus.

[00:03:31]And there are different variations of this problem. So, make sure you do all the variations of the proofs. Okay, next we have prove that the opposite sides of a quadrilateral circumscribing a circle subtend supplementary angle at the center of the circle. Again guys, these are all NCERT based proofs and they are asked regularly. Okay? Now, guys, next up for trigonometry, guys. Okay? So, all of you must have seen this question. sin - cos + 1 over sin + cos - 1 is equals to 1 over sec - tan or they could ask you to prove this equals to sec + tan.

[00:04:10]Right? So, here everyone knows the very first step, you have to divide by cos.

[00:04:14]Right? So, very important, and again, this is a proof where you should know what the first step is, otherwise confused. Okay? Next, guys, this problem here. Under root of 1 + sin over 1 - sin is equals to sec + tan. Very commonly asked proof, guys. Very commonly asked proof. Okay? Next, guys, prove that the trigonometric identity involving this expansion of squares So, this is a question you must have all seen, and I'm sure you must have all done, also. Right? Other than that, you know, in these years, what I have seen is CBSE is also asking you to figure out the value of, let's say, tan 45° or, you know, tan 60° geometrically. Geometrically, figure out the values. Okay? So, this also is a commonly asked question from trigonometry. These years, you can see.

[00:05:04]Okay? So, yes, guys, that was all for the proof wala part. Is there any proof that I have missed that you think might come in this exam? Comment that. And, guys, all the very best for your board examinations. Thank you very much.

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