" 2."[,(1+x)^(17),(1+x)^(19),(1+x)^(23)],[(1+x)^(23),(1+x)^(29),(1+x)^(34)],[(1+x)^(41),(1+x)^(43),(1+x)^(47)]|

If |{:((1+x)^(17),(1+x)^(19),(1+x)^(23)),((1+x)^(23),(1+x)^(29),(1+x)^(34)),((1+x)^(41),(1+x)^(43),(1+x)^(47)):}|=Ax^2+Bx+C then value of A = "........."

If f(x)=|((1+x)^(17),(a+x)^(19),(1+x)^(23)),((a+x)^(23),(a+x)^(29),(1+x)^(34)),((1+x)^(41),(1+x)^(43),(1+x)^(47))| =A+Bx+Cx^(2)+………. then A is equal to………….

If f(x)=|((1+x)^(17),(a+x)^(19),(1+x)^(23)),((a+x)^(23),(a+x)^(29),(1+x)^(34)),((1+x)^(41),(1+x)^(43),(1+x)^(47))| =A+Bx+Cx^(2)+………. then A is equal to………….

STATEMENT -1 : f(x) f(x)=|{:((1+x)^21,(1+x)^22,(1+x)^23),((1+x)^31,(1+x)^32,(1+x)^33),((1+x)^41,(1+x)^42,(1+x)^43):}| , then coefficient of x in f(x) is zero. STATEMENT - 2 If F(x) = A_0+A_1x+…+A_(n)x^n , then A_1=F'(0) dash denotes differential coefficient.

If x+ (1)/(x)=1 , find x^(23) + (1)/(x^(23))=

(1+x)17(1+x)19(1+x)23 If f(x)|(1+x)23c+x)29(1+x)341=A+Bx+Cr+..., then (1+x)41(1+x)43(1+x)47A

int_(-1)^(1) (17x^(5)-x^(4)+29 x^(3) -31 x +1)/(x^(2)+1)dx=

The series expansion of log[(1 + x)^((1 + x))(1-x)^(1-x)] is (1) 2[(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (2) [(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (3) 2[(x^(2))/(1.2) + (x^(4))/(2.3)+(x^(6))/(3.4)+...] (4) 2[(x^(2))/(1.2) -(x^(4))/(2.3)+(x^(6))/(3.4)-...]

The series expansion of log_(e) [(1 + x^((1 + x))(1-x)^(1-x)] is (1) 2[(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (2) [(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (3) 2[(x^(2))/(1.2) + (x^(4))/(2.3)+(x^(6))/(3.4)+...] (4) 2[(x^(2))/(1.2) -(x^(4))/(2.3)+(x^(6))/(3.4)-...]