`|{:(3x^2,3x,1),(x^2+2x,2x+1,1),(2x+1,x+2,1):}|=(x-1)^3`

The equation |((1+x)^2,(1-x)^2,-(2+x^2)),(2x+1,3x,1-5x),(x+1,2x,2-3x)|+|((1+x)^2,2x+1,x+1),((1-x)^2,3x,2x),(1-2x,3x-2,2x-3)|=0 has (a) no real solution (b) 4 real solutions (c) two real and two non-real solutions (d) infinite number of solutions, real or non-real

By using properties of determinants , show that : {:|( 1,x,x^(2) ),( x^(2) ,1,x) ,( x,x^(2), 1) |:} =( 1-x^(3)) ^(2)

If f(x)= |{:(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(x-1),x(x-1)(x-2),x(x+1)(x-1)):}| then find f(200) .

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) "_____"

|(x, 3x+2,2x-1),(2x-1,4x,3x+1),(7x-2,17x+6,12x-1)|=0 is true for

If f(x)=|(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(x-1),x(x-1)(x-2),x(x-1)(x+1))| then the value of f(11) is -

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))| The f(100) is equal to

|{:(x-1," "1),(" "x^3," "x^2+x+1):}|

3x-2 lt 2x+1

If f(x)={(x^2+2,,,xge2),(1-x ,,,xlt2):} ; g(x)={(2x,,,xgt1),(3-x ,,,xle1):} then the value of lim_(x->1) f(g(x)) is