A student wrote `(1-x)^-2=1+2x+3x^2+4x^3+…….for -2ltxlt2` and got zero marks because
(A) x was allowed to be 0
(B) x was allowed to be -ve
(C) x was allowed to have negative as well as positive values
(D) `|x|` was greater than 1 for some values of x

If 1+2x+3x^2+4x^3+oogeq4 , then a) least value of x is 1//2 ; b) greatest value of x is 4/3; c) least value of x is 2/3 ; d) greatest value of x does not exists

If |(x^2+4x, x-1, x+3),(2x, 3x-1, 5x-1),(6x-1, 4x, 8x-2)|=ax^4+bx^3+cx^2+dx+k be an identity in x and f(x) is a continuous function which attains ony rational values and f(0)=a, then f(x)=4 (A) for no value of x (B) for all values of x (C) ony for finite number of values of x (D) ony for all non zero values of x

If f(x)=x^3+2x^2+3x+4 and g(x) is the inverse of f(x) then g^(prime)(4) is equal to- 1/4 (b) 0 (c) 1/3 (d) 4

If f(x)=x^3+2x^2+3x+4 and g(x) is the inverse of f(x) then g^(prime)(4) is equal to- 1/4 (b) 0 (c) 1/3 (d) 4

Let x<1, then value of |(x^2+2, 2x+1,1), (2x+1, x+2, 1), (3, 3 ,1)| is a. none-negative b. none-positive c. negative d. positive

If int _(0)^(2)(3x ^(2) -3x +1) cos (x ^(3) -3x ^(2)+4x -2) dx = a sin (b), where a and b are positive integers. Find the value of (a+b).

If the expression [m x-1+(1//x)] is non-negative for all positive real x , then the minimum value of m must be -1//2 b. 0 c. 1//4 d. 1//2

let f(x)=-x^3+(b^3-b^2+b-1)/(b^2+3b+2) if x is 0 to 1 and f(x)=2x-3 if x if 1 to 3 .All possible real values of b such that f (x) has the smallest value at x=1 are

Show that (a) x^(2)-3x+6 gt 0 for all x, (b) 4x-x^(2)-6 lt 0 for all x. (c) 2x^(2)-4x+7 is always +ve. (d) -2x^(2)+3x-4 is always -ve. (e) -x^(2)+3x-3 is always -ve.

If x=1 and x=2 are solutions of equations x^3+a x^2+b x+c=0 and a+b=1, then find the value of bdot