The value of the determinant `|[x,x-1],[x-1,x]|` is (A) "1," (B) "-1," (C) "2," (D) "-2"

Value of the determinant |(x,1,1),(0,1+x, 1),(-y, 1+x, 1+y)| is (A) xy (B) xy(x+2) (C) x(x+1)(y+1) (D) xy(x+1)

For all real values of x, the minimum value of (1-x+x^2)/(1+x+x^2) is(A) 0 (B) 1 (C) 3 (D) 1/3

The value of the determinant |((a^x+a^-x)^2 ,(a^x-a^-x)^2 ,1), ((b^x+b^-x)^2 , (b^x-b^-x)^2 ,1) , ((c^x+c^-x)^2, (c^x-c^-x)^2 , 1)| (A) is 0 (B) is independent of a (C) depends on b only (D) depends on a,b,and c

For what value of x, matrix [[6-x,4],[3-x,1]] is a singular matrix ? A) 1 B) 2 C) -1 D) -2

The value of x satisfying the equation log_(2)(x^(2)-2x+5)=2 is "(a) 1 (b) 0 (c) -1 (d) 2 "

If a,b,c and d are the roots of the equation x^(4)+2x^(3)+4x^(2)+8x+16=0 the value of the determinant |{:(1+a,1,1,1),(1,1+b,1,1),(1,1,1+c,1),(1,1,1,1+d):}| is

Let f(x)=(1+b^2)x^2+2b x+1 and let m(b) the minimum value of f(x) as b varies, the range of m(b) is (A) [0,1] (B) (0,1/2] (C) [1/2,1] (D) (0,1]

The value of sin(cot^-1x)= (A) sqrt(1+x^2) (B) x (C) (1+x^2)^(-3/2) (D) (1+x^2)^(-1/2)

The value of the determinant of n^(t h) order, being given by |[x, 1, 1...], [1, x, 1...], [1, 1, x...],[... , ... , ...]| is a. (x-1)^(n-1)(x+n-1) b. (x-1)^n(x+n-1) c. (1-x)^(-1)(x+n-1) d. none of these

The value of lim_(x->1)(1-sqrt(x))/((cos^(-1)x)^2) is 4 (b) 1/2 (c) 2 (d) 1/4