The set of values of a for which `x^2+ax+sin^-1 (x^2-4x+5) +cos^-1 (x^2-4x+5)=0` has at least one solution is (A) `(-oo, -sqrt(2pi)] cup[sqrt[(2pi, oo]` (B) `(-oo, -sqrt(2pi)] cup[sqrt((2pi, oo)` (C) R (D) none of these

The exhaustive set of values of a such that, x^2+a x+sin^(-1)(x^2-4x+5)+cos^(-1)(x^2-4x+5)=0 (A) {-2-pi/4} (B) {-oo,-2-pi/4} (C) {-oo,-2-pi/4} (D) none of these

The exhaustive set of values of a such that, x^2+a x+sin^(-1)(x^2-4x+5)+cos^(-1)(x^2-4x+5)=0 (A) {-2-pi/4} (B) {-oo,-2-pi/4} (C) {-oo,-2-pi/4} (D) none of these

Set of value of m for which a chord of slope m of the circle x^2+y^2=4 touches parabola y^2=4x is (A) (-oo , -sqrt((sqrt2 -1)/2)] uu [sqrt((sqrt2 -1)/2) , oo) (B) (-oo , -1) uu (1, oo ) (C) (-1,1) (D) (-oo , oo)

Let f:R rarr(0,(pi)/(2)) be a function defined by f(x)=cot^(-1)(x^(2)+4x+alpha^(2)-alpha), complete set of valuesof alpha for which f(x) is onto,is (A) [(1-sqrt(17))/(2),(1+sqrt(17))/(2)] (B) (-oo,(1-sqrt(17))/(2)]uu[(1+sqrt(17))/(2),oo)(C)((1-sqrt(17))/(2),(1+sqrt(17))/(2))( D) none of these

If |x-2| (A) x in R , (B) x in[0,oo)] , (C) x in(-oo,(4-sqrt(2))/(2)]uu[(5)/(2),oo), (D) x in(-oo,(4-sqrt(2))/(2)]uu[(5+sqrt(3))/(2),oo]

Set of value of m for which a chord of slope m of the circle x^(2)+y^(2)=4 touches parabola y^(2)=4x is (A)(-oo,-sqrt((sqrt(2)-1)/(2))]uu[sqrt((sqrt(2)-1)/(2)),oo)(B)(-oo,-1)uu(1,oo)(C)(-1,1)(D)(-oo,oo)

The set of all real numbers x for which x^2-|x+2|+x >0 is (a)(-oo,-2)uu(2,oo) (b) (-oo,-sqrt(2))uu(sqrt(2),oo) (c)(-oo,-1)uu(1,oo) (d) (sqrt(2),oo)

int_0^oo(x dx)/((1+x)(1+x^2)) is equal to (A) pi/4 (B) pi/2 (C) pi (D) none of these"

int_0^oo(x dx)/((1+x)(1+x^2)) is equal to (A) pi/4 (B) pi/2 (C) pi (D) none of these"

int_0^oo(x dx)/((1+x)(1+x^2)) is equal to (A) pi/4 (B) pi/2 (C) pi (D) none of these"