If `|x|<1,` then find the coefficient of `x^n` in the expansion of `(1+x+x^2+x^3+....)^2dot`

If |(x-4,2x,2x),(2x,x-4,2x),(2x,2x,x-4)|=(A+Bx)(x-A)^2 then the ordered pair (A,B) is equal to

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

Solve the following : (i) |x-2|=(x-2) " (ii) " |x+3| = -x-3 (iii) |x^(2)-x|=x^(2)-x " (iv) " |x^(2)-x-2| =2+x-x^(2)

If f(x)= |1x x+1 2x x(x-1)(x+1) x3 x(x-1) x(x-1)(x-2) (x+1)x(x-1)| then f(500) is equal to 0 b. 1 c. 500 d. -500

If f(x)= ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ​ 1 2x 3x(x−1) ​ x x(x−1) x(x−1)(x−2) ​ x+1 (x+1)x (x+1)x(x−1) ​ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ​ Then f(100) is equal to

If f(x)= |{:(1,,x,,x+1),(2x,,x(x-1),,(x+1)x),(3x(x-1),,x(x-1)(x-2),,(x+1)x(x-1)):}| then the value of f(500) "_____"

Let x_(1), x_(2), …… , x_(n) be in an A.P. If x_(1) + x_(4) + x_(9) + x_(11) + x_(20) + x_(22) + x_(27) + x_(30) = 272 , then x_(1) + x_(2) + x_(3) + ...... + x_(30) is equal to

If |[1 , x, x^2],[ x , x^2 , 1],[ x^2 , 1 , x]|=3 , then the value of |[x^(3)-1, 0 , x-x^4],[ 0, x-x^(4) , x^(3)-1],[ x-x^(4) , x^(3)-1 , 0]|

If |[1,x,x^2] , [x,x^2,1] , [x^2,1,x]|=3 then find the value of |[x^3-1, 0, x-x^4] , [0,x-x^4, x^3-1] , [x-x^4, x^3-1, 0]|

If f (x) = |(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0)| then