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[mathjax] Question 1 उस बिन्दु का नियामक निकाले (2,4) तथा (6,8) को मिलाने वाली रेखाखण्ड को 1 : 3 के अनुपात मे अतः विभाजित तथा बहिंविभाजित करता है। [Find the coordinates of the point which divides the...
[mathjax] Question 1 निम्नलिखित बिन्दुओ के बीच की दूरी निकाले [Find the distance between the following pair of points] (i) (0,0),(-5,12) Sol : दूरी सुत्रः...
[mathjax] निम्नलिखित कोे सिद्ध कीजिए (Prove the following) Question 1 $\log _{e} 2-\frac{1}{2}=\frac{1}{1 \cdot 2 \cdot 3}+\frac{1}{3 \cdot 4 \cdot 5}+\ldots$ to $\infty$ Sol : $\log _{e}...
[mathjax] Question 1 (i) $\frac{e^{2 x}+1}{2 e^{x}}$ Sol : $=\frac{1}{2}\left[\frac{e^{2 x}+1}{e^{x}}\right]$ $=\frac{1}{2}\left[\frac{e^{2 x}}{e^{x}}+\frac{1}{e^{2}}\right]$...
[mathjax] Question 2 यदि (if) |x|<1 तो साबित कीजिए कि (show that) $(1+x)^{-\frac{1}{5}}=1-\frac{x}{5}+\frac{3x^2}{25}-\frac{11x^3}{125}+...to~ \infty$ Sol : L.H.S...
[mathjax] Question 1 किसी अनुक्रम के n पदो का जोड़ 2n 2 +4 है तो इसका n वाँ पद निकालिए । क्या यह अनुक्रम A.P मे है? Sol : S n =2n 2 +4 S n+1 =2(n-1) 2 +4 =2(n 2 -2n+1 2 ) 2 +4 =2n 2 -4n+2+4 S n+1 =2n...
[mathjax] Question 1 2 और 162 के बीच 7 G.M's राखिए। Sol : माना 2 और 162 के बीच 7 G.M's G 1 ,G 2 ,G 3 ... G है। 2,G 1 ,G 2 ,G 3 ,...G 7 ,162 G.P मे है। a=2 ,b=162, n=7...
[mathjax] Question 1 निम्नांकित गुणोत्तर श्रेढ़ी का योगफल निर्दिष्ट पदो तक ज्ञात कीजिए [Find the sum indicated terms of the following geometric progressions] (i) 1,2,4,8...12 पदो तक (to 12 terms) Sol...
[mathjax] एक अनुक्रम का n वाँ पद 2 3n (-5) n है। क्या यह अनुक्रम G.P मे है? यदि है तो इस G.P का सर्व अनुपात ज्ञात कीजिए। Sol : a n =2 3n (-5) n n=1,2,3 पर,...
[mathjax] Question 1 (i) 5 और 32 के बीच 8 A.M's रखिए। [Insert 8 A.M's between 5 and 32] Sol : 5 और 32 के बीच 8 AM: 5,A 1 ,A 2 ,A 3 ...A,32..A.P मे है। a=5 ,b=32 ,n=8...
[mathjax] श्रेणी 15+12+9+... के कितने पदो को लेने से उनका योगफल 15 मिलेगा? दो उत्तरो की व्याख्या कीजिए। श्रेणी: 15+12+9+... -3n 2 +33n-30=0 -3(n 2 -11n+10=0) n 2 -11n+10=0 n 2 -10n-n+10=0...
[mathjax] Question 1 अनुक्रम 10,5,0,-5,-10 ..का 10वाँ पद ज्ञात कीजिए। [Find the 10th term of the sequence 10,5,0,-5,-10,...] Sol : a=10, d=5-10=-5 a 10 =a+9d =10+9(-5) =10-45 =-35 Question 2 (i) कोई...