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(""^(20)C(1))/(""^(20)C(0))+2.(""^(20)C(...

`(""^(20)C_(1))/(""^(20)C_(0))+2.(""^(20)C_(2))/(""^(20)C_(1))+3.(""^(20)C_(3))/(""^(20)C_(2)) +…20.(""^(20)C_(20))/(""^(20)C_(19)) =210`

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Prove that (""^20C_1)/(""^20C_0) + 2. (""^20C_2)/(""^20C_1) + 3. (""^20C_3)/(""^20C_2) + …..+20. (""^20C_20)/(""^20C_19) = 210

1.""^20C_1 - 2.""^20C_2 + 3.""^20C_3 - …..-20.""^20C_20 =

""^20C_0 + ""^20C_1 + ""^20C_2+…….+""^20C_10 =

""^20C_10.""^15C_0 + ""^20C_9.""^15C_1 + ""^20C_8.""^15C_2 + …..+""^20C_0.""^15C_10 =

The sum of the series ""^20C_0 - ""^20C_1 + ""^20C_2 - ""^20C_3 +…….""^20C_10 is

Observe the following statements : Statement - I : 1/2 . ""^10C_0 - ""^10C_1 + 2. ""^10C_2 - 2^2. ""^10C_3 + ……+ 2^9. ""^10C_10 = -1/2 Statement - II : ""^20C_1 - 2(""^20C_2) + 3.(""^20C_3)-…..-20.(""^20C_20) = 0 Then the false statements are :

Show that ""^(10)C_2+^(11)C_2+^(12)C_2+^(13)C_2+...+^(20)C_2=^(21)C_3-^(10)C_3 .

tan20^(0)+4 sin20^(0)=

(d ^(20))/(dx ^(20)) [ 2 cos x cos 3x]=