`(x-1)^4+4(x-1)^3+6(x-1)^2+4 (x-1)+1` = ?

(3x^(2)+x+1)/(x-1)^(4)=a/(x-1)+b/(x-1)^(2)+c/(x-1)^(3)+d/(x-1)^(4) rArr [{:(a,b), (c, d):}]=

Solve for x : (x-1)/(x-2)+(x-3)/(x-4)=3 1/3;\ \ x!=2,\ 4

e^{(x-1)-1/2(x-1)^2+((x-1)^3)/3-(x-1)^(4)/4+......} is eqaul to

Simplify: {4^(-1)"x"\ 3^(-1)}^2 (ii) \ \ \ {5^(-1)-:6^(-1)}^3 (iii) (2^(-1)+\ 3^(-1))^(-1) (iv) {3^(-1)"x"\ 4^(-1)}^(-1)\ "x"\ 5^(-1) (4^(-1)-\ 5^(-1))-:3^(-1)

The equation (2x^(2))/(x-1)-(2x +7)/(3) +(4-6x)/(x-1) +1=0 has the roots-

intdx/((x-1)^(3/4)(x+2)^(5/4))= (A) 4/3((x-1)/(x+2))^(1/4)+c (B) 4/3sqrt((x-1)/(x+2))+c (C) 4/3((x+2)/(x-1))^(1/4)+c (D) none of these

Without expanding, show that the value of each of the determinants is zero: |[(2^x+2^(-x))^2, (2^x-2^(-1))^2, 1] , [(3^x+3^(-1))^2, (3^x-3^(-x))^2, 1] , [(4^x+4^(-x))^2, (4^x-4^(-x))^2, 1]|

The term independent of x in expansion of ((x+1)/(x^(2/3)-x^(1/3)+1)-(x-1)/(x-x^(1/2)))^10 is (1) 120 (2) 210 (3) 310 (4) 4

The term independent of x in expansion of ((x+1)/(x^(2/3)-x^(1/3)+1)-(x-1)/(x-x^(1/2)))^10 is (1) 120 (2) 210 (3) 310 (4) 4

Solve the equation (12x-1)(6x-1)(4x-1)(3x-1)=5