Ncert Solutions Maths class 11th

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A
alok kumar singh

Contributor-Level 10

3, A? , A? , A? , .A? , 243
d = (243-3)/ (m+1) = 240/ (m+1)
3, G? , G? , G? , 243
r = (243/3)¹/ (³? ¹) = (81)¹/? = 3
G? = A?
=> 3 (3)² = 3 + 4 (240/ (m+1)
=> 27 = 3 + 960/ (m+1)
=> m+1 = 40
=> m=39

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alok kumar singh

Contributor-Level 10

Let xyz be the three digit number
x+y+z=10, x≥1, y≥0, z≥0
x-1=t => x=1+t, x-1≥0
t≥0
t+y+z = 10-1
t+y+z=9, 0≤t, y, z≤9
total number of non negative integral solution =? ³? ¹C? = ¹¹C? = (11*10)/2 = 55
But for t=9, x=10, so required number or integers = 55-1=54

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alok kumar singh

Contributor-Level 10

lim? →? (1/3 (a+2x)? ²/³2 - 1/3 (3x)? ²/³3) / (1/3 (3a+x)? ²/³1 - 1/3 (4x)? ²/³4)
= (1/3 (3a)? ²/³ (2-3) / (1/3 (4a)? ²/³ (1-4) = (3? ²/³)/ (4? ²/³) * 1/3
= (2? /³)/ (9¹/³) * 1/3 * 2/3 (1/9)¹/³

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