`|[(x-2)^(2), (x-1)^(2), x^(2)], [(x-1)^(2), x^(2), (x+1)^(2)],[x^(2), (x+1)^(2), (x+2)^(2)]|+P^(3)=0 `the value of `P` is

If f(x)=|[x-2, (x-1)^2, x^3] , [(x-1), x^2, (x+1)^3] , [x,(x+1)^2, (x+2)^3]| then coefficient of x in f(x) is

IF ax^3+bx^2+cx+d = |(x^2,(x-1)^2, (x-2)^2) ,((x-1)^2, (x-2)^2, (x-3)^2), ((x-2)^2, (x-3)^2, (x-4)^2)| , then d= (A) 1 (B) -8 (C) 0 (D) none of these

(4) If p(x)=x^(3)-2x^(2)-x+2=(x+1)(x-2)(x-d) then what is the value of d?

Let (1 + x^(2))^(2) (1 + x)^(n) = a_(0) + a_(1) x + a_(2) x^(2) + … if a_(1),a_(2) " and " a_(3) are in A.P , the value of n is

If (x^(2)+x+2)/(x^(2)+2x+1)=A+(B)/(x+1)+(C)/((x+1)^(2)) , then find the value of A+B+C .

lim_(xrarr1) [(x-2)/(x^(2)-x)-(1)/(x^(3)-3x^(2)+2x)]

If x,y,zepsilonR then the value of |((2x^(x)+2^(-x))^(2),(2^(x)-2^(-x))^(2),1),((3x^(x)+3^(-x))^(2),(3^(x)-3^(-x))^(2),1),((4^(x)+4^(-x))^(2),(4^(x)-4^(-x))^(2),1)| is

int((1-x^(- 2))/(x^(1//2)-x^(-1//2))-2/(x^(3//2))+(x^(- 2)-x)/(x^(1//2)-x^(-1//2)))dx

Check whether the following are quadratic equation (i) (x+1)^2=2(x-3) (ii) x^2-2x=(-2)(3-x) (iii) (x-2)(x+1)=(x-1)(x+3) (iv) (x-3)(2x+1)=x(x+5) (v) (2x-1)(x-3)=(x+5)(x-1) (vi) x^2+3x+1=(x-2)^2 (vii) (x+2)^3=2x(x^2-1) (viii) x^3-4x^2 – x + 1 = (x – 2)^3

If (ax-1)/((1-x+x^(2))(2+x))=(x)/(1-x+x^(2))-(1)/(2+x) then a=