The complete set of values of a so that equation `sin^4 x+ a sin^2 x+ 4=0` has at least one real root is (A) `(- oo, -5]` (B) `(- oo , 4] uu [ 4, oo)` (C) `(-oo, -4]` (D) `[4, oo)`

The solution set of (x + 3)/(x - 2) le 2 is a) (-oo, oo) b) (-oo, 2] uu [7, oo) c) (-oo, 2) uu [7, oo) d) [7, oo)

[ Suppose a in R .The set of values of a for which the quadratic equation x^(2)-2(a+1)x+a^(2)-4a+3=0 has two negative roots is [ (a) (-oo,-1), (b) (1,3) (c) (-oo,1)uu(3,oo), (d) phi]]

The solution of system of linear inequalities in x represented on line as (i) x in ( - oo,-4) cup [3,oo) (ii) x in (- oo, -4] cup (5,oo) (iii) x in (- oo , -3) cup (5,oo) (iv) x in (-oo , -4) cup [ 5,oo)

The set of all values of m for which both the roots of the equation x^2-(m+1)x+m+4=0 are real and negative is (a) (-oo,-3]uu[5,oo) (b) [-3,5] (c) (-4,-3] (d) (-3,-1]

The value of a for which the function f(x)=(4a-3)(x+log5)+2(a-7)cotx/2sin^2x/2 does not possess critical points is (a) (-oo,-4/3) (b) (-oo,-1) (c) [1,oo) (d) (2,oo)

For x^2-(a+3)|x|-4=0 to have real solutions, the range of a is a) (-oo,-7]uu[1,oo) b) (-3,oo) c) (-oo,-7] d) [1,oo)

For x^2-(a+3)|x|=4=0 to have real solutions, the range of a is a (-oo,-7]uu[1,oo) b (-3,oo) c (-oo,-7] d [1,oo)

The real values of lambda for which the equation,4x^(3)+3x^(2)-6x+lambda=0 has two distinct real roots in [0,1] lie in the interval (A)(0,oo)(B)(3,oo)(C)(-5,(7)/(4))(D)[0,(7)/(4))

If b gt a , then the equation (x-a)(x-b)-1=0 has (a) Both roots in (a, b) " " (b) Both roots in (-oo, a) (c) Both roots in (b, +oo) " " (d) One root in (-oo, a) and the other in (b, +oo)