best optional for UPSC 2021

Free UPSC Mathematics Optional Paper-1 2021 Solutions: View Online | UPSC Maths Solution | IAS Maths Solution

1.(a) यदि A = [ 1 − 1 1 2 − 1 0 1 0 0 ] A = 1 − 1 1 2 − 1 0 1 0 0 A=[[1,-1,1],[2,-1,0],[1,0,0]]A=left[begin{array}{ccc}1 & -1 & 1 \ 2 & -1 & 0 \ 1 & 0 & 0end{array}right]A=[1−112−10100] है, तो A − 1 A − 1

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Free UPSC Mathematics Optional Paper-1 2020 Solutions: View Online | UPSC Maths Solution | IAS Maths Solution

UPSC M2020-1 WS खण्ड-A / SECTION-A (a) माना समुच्चय V V VVV में सभी n × n n × n n xx nn times nn×n के वास्तविक मैजिक वर्ग हैं। दिखाइए कि समुच्चय V , R V , R V,RV, RV,R पर एक सदिश समष्टि है। दो भिन्न-भिन्न 2 × 2 2 × 2 2xx22

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Free UPSC Mathematics Optional Paper-1 2019 Solutions: View Online | UPSC Maths Solution | IAS Maths Solution

खण्ड-A / SECTION-A (a) माना कि f : [ 0 , π 2 ] → R f : 0 , π 2 → R f:[0,(pi)/(2)]rarrRf:left[0, frac{pi}{2}right] rightarrow mathbb{R}f:[0,π2]→R एक संतत फलन है, जैसा कि f ( x ) = cos 2 ⁡ x 4 x 2 − π 2 , 0 ≤ x < π

Civil Services Maths

Free UPSC Mathematics Optional Paper-1 2018 Solutions: View Online | UPSC Maths Solution | IAS Maths Solution

खण्ड-A / SECTION-A (a) मान लीजिये कि A A AAA एक 3 × 2 3 × 2 3xx23 times 23×2 आव्यूह है और B B BBB एक 2 × 3 2 × 3 2xx32 times 32×3 आव्यूह है। दर्शाइये कि C = A ⋅ B C = A ⋅ B C=A*BC=A cdot BC=A⋅B एक अव्युत्क्रमणणीय

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