ycliper

ะŸะพะฟัƒะปัั€ะฝะพะต

ะœัƒะทั‹ะบะฐ ะšะธะฝะพ ะธ ะะฝะธะผะฐั†ะธั ะะฒั‚ะพะผะพะฑะธะปะธ ะ–ะธะฒะพั‚ะฝั‹ะต ะกะฟะพั€ั‚ ะŸัƒั‚ะตัˆะตัั‚ะฒะธั ะ˜ะณั€ั‹ ะฎะผะพั€

ะ˜ะฝั‚ะตั€ะตัะฝั‹ะต ะฒะธะดะตะพ

2025 ะกะตั€ะธะฐะปั‹ ะขั€ะตะนะปะตั€ั‹ ะะพะฒะพัั‚ะธ ะšะฐะบ ัะดะตะปะฐั‚ัŒ ะ’ะธะดะตะพัƒั€ะพะบะธ Diy ัะฒะพะธะผะธ ั€ัƒะบะฐะผะธ

ะขะพะฟ ะทะฐะฟั€ะพัะพะฒ

ัะผะพั‚ั€ะตั‚ัŒ ะฐ4 schoolboy runaway ั‚ัƒั€ะตั†ะบะธะน ัะตั€ะธะฐะป ัะผะพั‚ั€ะตั‚ัŒ ะผัƒะปัŒั‚ั„ะธะปัŒะผั‹ ัะดะธัะพะฝ
ะกะบะฐั‡ะฐั‚ัŒ

๐๐š๐ฌ๐ข๐ฌ ๐š๐ง๐ ๐ƒ๐ข๐ฆ๐ž๐ง๐ฌ๐ข๐จ๐ง | ๐…๐จ๐ฎ๐ง๐๐š๐ญ๐ข๐จ๐ง ๐จ๐Ÿ ๐‹๐ข๐ง๐ž๐š๐ซ ๐€๐ฅ๐ ๐ž๐›๐ซ๐š | ๐‚๐’๐ˆ๐‘ ๐๐„๐“ ๐‰๐ฎ๐ง๐ž ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ” | ๐‹๐ž๐œ ๐Ÿ๐ŸŽ | ๐ˆ๐…๐€๐’

ะะฒั‚ะพั€: Mathematics - CSIR NET, GATE, SET & NBHM: IFAS

ะ—ะฐะณั€ัƒะถะตะฝะพ: 2026-01-05

ะŸั€ะพัะผะพั‚ั€ะพะฒ: 386

ะžะฟะธัะฐะฝะธะต: IFAS: India's No. 1 Institute for CSIR NET, GATE, SET & other PhD Mathematical Science Entrance Examinations!

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Points Cover in this Video -

00:00:00 Introduction
00:05:58 Basis of Vector Space
00:06:16 Dimension of Vector Space
00:13:36 Practice Questions
00:27:38 Some Basic Properties of Basis
00:39:15 Complementary Subspaces
00:42:47 Practice Questions

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ะะต ัƒะดะฐะตั‚ัั ะทะฐะณั€ัƒะทะธั‚ัŒ Youtube-ะฟะปะตะตั€. ะŸั€ะพะฒะตั€ัŒั‚ะต ะฑะปะพะบะธั€ะพะฒะบัƒ Youtube ะฒ ะฒะฐัˆะตะน ัะตั‚ะธ.
ะŸะพะฒั‚ะพั€ัะตะผ ะฟะพะฟั‹ั‚ะบัƒ...
๐๐š๐ฌ๐ข๐ฌ ๐š๐ง๐ ๐ƒ๐ข๐ฆ๐ž๐ง๐ฌ๐ข๐จ๐ง | ๐…๐จ๐ฎ๐ง๐๐š๐ญ๐ข๐จ๐ง ๐จ๐Ÿ ๐‹๐ข๐ง๐ž๐š๐ซ ๐€๐ฅ๐ ๐ž๐›๐ซ๐š | ๐‚๐’๐ˆ๐‘ ๐๐„๐“ ๐‰๐ฎ๐ง๐ž ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ” | ๐‹๐ž๐œ ๐Ÿ๐ŸŽ | ๐ˆ๐…๐€๐’

ะŸะพะดะตะปะธั‚ัŒัั ะฒ:

ะ”ะพัั‚ัƒะฟะฝั‹ะต ั„ะพั€ะผะฐั‚ั‹ ะดะปั ัะบะฐั‡ะธะฒะฐะฝะธั:

ะกะบะฐั‡ะฐั‚ัŒ ะฒะธะดะตะพ

  • ะ˜ะฝั„ะพั€ะผะฐั†ะธั ะฟะพ ะทะฐะณั€ัƒะทะบะต:

ะกะบะฐั‡ะฐั‚ัŒ ะฐัƒะดะธะพ

ะŸะพั…ะพะถะธะต ะฒะธะดะตะพ

๐‹.๐ˆ. & ๐‹.๐ƒ. ๐’๐ž๐ญ ๐จ๐Ÿ ๐•๐ž๐œ๐ญ๐จ๐ซ๐ฌ | ๐…๐จ๐ฎ๐ง๐๐š๐ญ๐ข๐จ๐ง ๐จ๐Ÿ ๐‹๐ข๐ง๐ž๐š๐ซ ๐€๐ฅ๐ ๐ž๐›๐ซ๐š | ๐‚๐’๐ˆ๐‘ ๐๐„๐“ ๐‰๐ฎ๐ง๐ž ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ” | ๐‹๐ž๐œ ๐ŸŽ๐Ÿ— | ๐ˆ๐…๐€๐’

๐‹.๐ˆ. & ๐‹.๐ƒ. ๐’๐ž๐ญ ๐จ๐Ÿ ๐•๐ž๐œ๐ญ๐จ๐ซ๐ฌ | ๐…๐จ๐ฎ๐ง๐๐š๐ญ๐ข๐จ๐ง ๐จ๐Ÿ ๐‹๐ข๐ง๐ž๐š๐ซ ๐€๐ฅ๐ ๐ž๐›๐ซ๐š | ๐‚๐’๐ˆ๐‘ ๐๐„๐“ ๐‰๐ฎ๐ง๐ž ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ” | ๐‹๐ž๐œ ๐ŸŽ๐Ÿ— | ๐ˆ๐…๐€๐’

Vector Subspace | Linear Algebra | By GP Sir

Vector Subspace | Linear Algebra | By GP Sir

๐๐ž๐ซ๐ฆ๐ฎ๐ญ๐š๐ญ๐ข๐จ๐ง ๐‹๐ข๐ง๐ž๐š๐ซ ๐“๐ซ๐š๐ง๐ฌ๐Ÿ๐จ๐ซ๐ฆ๐š๐ญ๐ข๐จ๐ง | ๐‹๐ข๐ง๐ž๐š๐ซ ๐€๐ฅ๐ ๐ž๐›๐ซ๐š | ๐‚๐’๐ˆ๐‘ ๐๐„๐“ ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ” | ๐‹๐ž๐œ ๐Ÿ๐Ÿ“ | ๐ˆ๐…๐€๐’

๐๐ž๐ซ๐ฆ๐ฎ๐ญ๐š๐ญ๐ข๐จ๐ง ๐‹๐ข๐ง๐ž๐š๐ซ ๐“๐ซ๐š๐ง๐ฌ๐Ÿ๐จ๐ซ๐ฆ๐š๐ญ๐ข๐จ๐ง | ๐‹๐ข๐ง๐ž๐š๐ซ ๐€๐ฅ๐ ๐ž๐›๐ซ๐š | ๐‚๐’๐ˆ๐‘ ๐๐„๐“ ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ” | ๐‹๐ž๐œ ๐Ÿ๐Ÿ“ | ๐ˆ๐…๐€๐’

๐‘๐š๐ง๐คโ€“๐๐ฎ๐ฅ๐ฅ๐ข๐ญ๐ฒ ๐“๐ก๐ž๐จ๐ซ๐ž๐ฆ | ๐…๐จ๐ฎ๐ง๐๐š๐ญ๐ข๐จ๐ง ๐จ๐Ÿ ๐‹๐ข๐ง๐ž๐š๐ซ ๐€๐ฅ๐ ๐ž๐›๐ซ๐š | ๐‚๐’๐ˆ๐‘ ๐๐„๐“ ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ” | ๐‹๐ž๐œ ๐Ÿ๐Ÿ‘ | ๐ˆ๐…๐€๐’

๐‘๐š๐ง๐คโ€“๐๐ฎ๐ฅ๐ฅ๐ข๐ญ๐ฒ ๐“๐ก๐ž๐จ๐ซ๐ž๐ฆ | ๐…๐จ๐ฎ๐ง๐๐š๐ญ๐ข๐จ๐ง ๐จ๐Ÿ ๐‹๐ข๐ง๐ž๐š๐ซ ๐€๐ฅ๐ ๐ž๐›๐ซ๐š | ๐‚๐’๐ˆ๐‘ ๐๐„๐“ ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ” | ๐‹๐ž๐œ ๐Ÿ๐Ÿ‘ | ๐ˆ๐…๐€๐’

๐…๐จ๐ฎ๐ง๐๐š๐ญ๐ข๐จ๐ง ๐จ๐Ÿ ๐‹๐ข๐ง๐ž๐š๐ซ ๐€๐ฅ๐ ๐ž๐›๐ซ๐š | ๐Œ๐š๐ญ๐ซ๐ข๐ฑ ๐‘๐ž๐ฉ๐ซ๐ž๐ฌ๐ž๐ง๐ญ๐š๐ญ๐ข๐จ๐ง ๐จ๐Ÿ ๐‹๐ข๐ง๐ž๐š๐ซ ๐“๐ซ๐š๐ง๐ฌ๐Ÿ๐จ๐ซ๐ฆ๐š๐ญ๐ข๐จ๐ง | ๐‚๐’๐ˆ๐‘ ๐๐„๐“ ๐‰๐ฎ๐ง๐ž ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ”

๐…๐จ๐ฎ๐ง๐๐š๐ญ๐ข๐จ๐ง ๐จ๐Ÿ ๐‹๐ข๐ง๐ž๐š๐ซ ๐€๐ฅ๐ ๐ž๐›๐ซ๐š | ๐Œ๐š๐ญ๐ซ๐ข๐ฑ ๐‘๐ž๐ฉ๐ซ๐ž๐ฌ๐ž๐ง๐ญ๐š๐ญ๐ข๐จ๐ง ๐จ๐Ÿ ๐‹๐ข๐ง๐ž๐š๐ซ ๐“๐ซ๐š๐ง๐ฌ๐Ÿ๐จ๐ซ๐ฆ๐š๐ญ๐ข๐จ๐ง | ๐‚๐’๐ˆ๐‘ ๐๐„๐“ ๐‰๐ฎ๐ง๐ž ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ”

ะะตะฟั€ะตั€ั‹ะฒะฝะพัั‚ัŒ vs ะ ะฐะฒะฝะพะผะตั€ะฝะฐั ะฝะตะฟั€ะตั€ั‹ะฒะฝะพัั‚ัŒ

ะะตะฟั€ะตั€ั‹ะฒะฝะพัั‚ัŒ vs ะ ะฐะฒะฝะพะผะตั€ะฝะฐั ะฝะตะฟั€ะตั€ั‹ะฒะฝะพัั‚ัŒ

TIFR 2025 Linear Algebra Previous Year Questions | 2014-23 PYQs | L1

TIFR 2025 Linear Algebra Previous Year Questions | 2014-23 PYQs | L1

ะ›ะ•ะšะฆะ˜ะฏ ะŸะ ะž ะะะ”ะะ–ะะซะ• ะจะ˜ะคะ ะซ ะะ ะšะžะะคะ•ะ ะ•ะะฆะ˜ะ˜ ะ‘ะะ—ะžะ’ะซะฅ ะจะšะžะ› ะ ะะ ะ’ ะขะ ะžะ˜ะฆะšะ•

ะ›ะ•ะšะฆะ˜ะฏ ะŸะ ะž ะะะ”ะะ–ะะซะ• ะจะ˜ะคะ ะซ ะะ ะšะžะะคะ•ะ ะ•ะะฆะ˜ะ˜ ะ‘ะะ—ะžะ’ะซะฅ ะจะšะžะ› ะ ะะ ะ’ ะขะ ะžะ˜ะฆะšะ•

ะ’ั‹ ะฝะธะบะพะณะดะฐ ะฝะต ะดะพะปะถะฝั‹ ะฑั‹ะปะธ ัƒะทะฝะฐั‚ัŒ ัั‚ะพโ€ฆ ะขะฐะนะฝะฐ ะ‘ะตั…ั‚ะตั€ะตะฒะฐ, ะบะพั‚ะพั€ะฐั ะพะฑัŠััะฝัะตั‚ ะ‘ะพะณะฐ ะธ ะถะธะทะฝัŒ

ะ’ั‹ ะฝะธะบะพะณะดะฐ ะฝะต ะดะพะปะถะฝั‹ ะฑั‹ะปะธ ัƒะทะฝะฐั‚ัŒ ัั‚ะพโ€ฆ ะขะฐะนะฝะฐ ะ‘ะตั…ั‚ะตั€ะตะฒะฐ, ะบะพั‚ะพั€ะฐั ะพะฑัŠััะฝัะตั‚ ะ‘ะพะณะฐ ะธ ะถะธะทะฝัŒ

ะžะฝะตะผะตะฝะธะต ะฟะฐะปัŒั†ะตะฒ ั€ัƒะบ. ะšะฐะบ ะฑั‹ัั‚ั€ะพ ัƒะฑั€ะฐั‚ัŒ ะทะฐ 2 ะผะธะฝัƒั‚ั‹. ะŸะพั‡ะตะผัƒ ะฟะพัะฒะปัะตั‚ัั? ะงะตะผ ะพะฟะฐัะฝะพ?

ะžะฝะตะผะตะฝะธะต ะฟะฐะปัŒั†ะตะฒ ั€ัƒะบ. ะšะฐะบ ะฑั‹ัั‚ั€ะพ ัƒะฑั€ะฐั‚ัŒ ะทะฐ 2 ะผะธะฝัƒั‚ั‹. ะŸะพั‡ะตะผัƒ ะฟะพัะฒะปัะตั‚ัั? ะงะตะผ ะพะฟะฐัะฝะพ?

๐Œ๐š๐ญ๐ซ๐ข๐œ๐ž๐ฌ ๐š๐ง๐ ๐“๐ก๐ž๐ข๐ซ ๐๐ซ๐จ๐ฉ๐ž๐ซ๐ญ๐ข๐ž๐ฌ | ๐‹๐ข๐ง๐ž๐š๐ซ ๐€๐ฅ๐ ๐ž๐›๐ซ๐š | ๐‚๐’๐ˆ๐‘ ๐๐„๐“ ๐Œ๐š๐ญ๐ก๐ž๐ฆ๐š๐ญ๐ข๐œ๐ฌ | ๐‹๐ž๐œ ๐ŸŽ๐Ÿ | ๐ˆ๐…๐€๐’

๐Œ๐š๐ญ๐ซ๐ข๐œ๐ž๐ฌ ๐š๐ง๐ ๐“๐ก๐ž๐ข๐ซ ๐๐ซ๐จ๐ฉ๐ž๐ซ๐ญ๐ข๐ž๐ฌ | ๐‹๐ข๐ง๐ž๐š๐ซ ๐€๐ฅ๐ ๐ž๐›๐ซ๐š | ๐‚๐’๐ˆ๐‘ ๐๐„๐“ ๐Œ๐š๐ญ๐ก๐ž๐ฆ๐š๐ญ๐ข๐œ๐ฌ | ๐‹๐ž๐œ ๐ŸŽ๐Ÿ | ๐ˆ๐…๐€๐’

๐Œ๐š๐ญ๐ซ๐ข๐ฑ ๐‹๐ข๐ง๐ž๐š๐ซ ๐“๐ซ๐š๐ง๐ฌ๐Ÿ๐จ๐ซ๐ฆ๐š๐ญ๐ข๐จ๐ง | ๐‹๐ข๐ง๐ž๐š๐ซ ๐€๐ฅ๐ ๐ž๐›๐ซ๐š | ๐‚๐’๐ˆ๐‘ ๐๐„๐“ ๐‰๐ฎ๐ง๐ž ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ” | ๐‹๐ž๐œ ๐Ÿ๐Ÿ’ | ๐ˆ๐…๐€๐’

๐Œ๐š๐ญ๐ซ๐ข๐ฑ ๐‹๐ข๐ง๐ž๐š๐ซ ๐“๐ซ๐š๐ง๐ฌ๐Ÿ๐จ๐ซ๐ฆ๐š๐ญ๐ข๐จ๐ง | ๐‹๐ข๐ง๐ž๐š๐ซ ๐€๐ฅ๐ ๐ž๐›๐ซ๐š | ๐‚๐’๐ˆ๐‘ ๐๐„๐“ ๐‰๐ฎ๐ง๐ž ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ” | ๐‹๐ž๐œ ๐Ÿ๐Ÿ’ | ๐ˆ๐…๐€๐’

ะ—ะฐะดะฐั‡ะฐ ะธะท ะฒัั‚ัƒะฟะธั‚ะตะปัŒะฝั‹ั… ะกั‚ัะฝั„ะพั€ะดะฐ

ะ—ะฐะดะฐั‡ะฐ ะธะท ะฒัั‚ัƒะฟะธั‚ะตะปัŒะฝั‹ั… ะกั‚ัะฝั„ะพั€ะดะฐ

ะŸะพั‡ะตะผัƒ ะกะขะะ ะฆะซ ะ‘ะžะฏะ›ะ˜ะกะฌ ะกะ’ะฏะขะžะš ะฑะพะปัŒัˆะต, ั‡ะตะผ ะดั€ัƒะณะธั… ะดะฝะตะน

ะŸะพั‡ะตะผัƒ ะกะขะะ ะฆะซ ะ‘ะžะฏะ›ะ˜ะกะฌ ะกะ’ะฏะขะžะš ะฑะพะปัŒัˆะต, ั‡ะตะผ ะดั€ัƒะณะธั… ะดะฝะตะน

Heat , Wave & Laplace Equation | JRF Express | Crack From Crash Within 45 Days | CSIR NET | L14

Heat , Wave & Laplace Equation | JRF Express | Crack From Crash Within 45 Days | CSIR NET | L14

Maximal Ideals | Ring Theory | CSIR NET Mathematics 2024 | IFAS | Lec 2

Maximal Ideals | Ring Theory | CSIR NET Mathematics 2024 | IFAS | Lec 2

Mass Spectrometry || By Hitesh Sir || CSIR NET DEC 2025

Mass Spectrometry || By Hitesh Sir || CSIR NET DEC 2025

๐‚๐‹๐Ž๐‚๐Š | ๐“๐š๐ซ๐ ๐ž๐ญ ๐‚๐’๐ˆ๐‘ ๐๐„๐“ ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ“ | ๐„๐Œ๐Ž๐“๐ˆ๐Ž๐ ๐Ÿ.๐ŸŽ | ๐‹๐ž๐œ ๐Ÿ๐Ÿ• | IFAS

๐‚๐‹๐Ž๐‚๐Š | ๐“๐š๐ซ๐ ๐ž๐ญ ๐‚๐’๐ˆ๐‘ ๐๐„๐“ ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ“ | ๐„๐Œ๐Ž๐“๐ˆ๐Ž๐ ๐Ÿ.๐ŸŽ | ๐‹๐ž๐œ ๐Ÿ๐Ÿ• | IFAS

NotebookLM: ะฑะพะปัŒัˆะพะน ั€ะฐะทะฑะพั€ ะธะฝัั‚ั€ัƒะผะตะฝั‚ะฐ (12 ัั†ะตะฝะฐั€ะธะตะฒ ะฟั€ะธะผะตะฝะตะฝะธั)

NotebookLM: ะฑะพะปัŒัˆะพะน ั€ะฐะทะฑะพั€ ะธะฝัั‚ั€ัƒะผะตะฝั‚ะฐ (12 ัั†ะตะฝะฐั€ะธะตะฒ ะฟั€ะธะผะตะฝะตะฝะธั)

ะšะฐะบ ะฝะฐะฑั€ะฐั‚ัŒ 15/15 ะฑะฐะปะปะพะฒ ะฟะพ ะฐั‚ั‚ะตัั‚ะฐั‚ัƒ GATE 2026 | ะ’ัะต ะพั‚ั€ะฐัะปะธ

ะšะฐะบ ะฝะฐะฑั€ะฐั‚ัŒ 15/15 ะฑะฐะปะปะพะฒ ะฟะพ ะฐั‚ั‚ะตัั‚ะฐั‚ัƒ GATE 2026 | ะ’ัะต ะพั‚ั€ะฐัะปะธ

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ะšะพะฝั‚ะฐะบั‚ั‹ ะดะปั ะฟั€ะฐะฒะพะพะฑะปะฐะดะฐั‚ะตะปะตะน: [email protected]