" (b) "2x^(2)-(5)/(6)x+(1)/(12)

[" The area that is enclosed in the "],[" circle "x^(2)+y^(2)=2" which is not "],[" common area enclosed by "],[y=x&y^(2)=x" is "],[[" (A) "(1)/(12)(2 pi-1)," (b) "],[" (B) "(1)/(6)(12 pi-1),(1)/(12)(6 pi-1)],[" (D) "(1)/(12)(12 pi-1)]]

Let 2sin^2x+3sinx-2>0 andx^2-x-2<0(x is measured in radians). Then x lies in the interval (a) (pi/6,(5pi)/6) (b) (-1,(5pi)/6) (c) (-1,2) (d) (pi/6,2)

If f_(k)(x)=(1)/(k)(sin^(k)x+cos^(k)x) then f_(4)(x)-f_(6)(x)=(A)(1)/(12) (B) (5)/(12) (C) (-1)/(12) (D) -(5)/(12)

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)-...]

Factorise: 2x^2-5/6x+1/12

If (1+x-2x^(2))^(6)=1+a_(1)x+a_(2)x^(12)+...+a_(12)x^(12) then find the value of a_(2)+a_(4)+a_(6)+...+a_(12)