x^2/(r^2-r-6)+y^2/(r^2-6r+5)=1 will repr...

`x^2/(r^2-r-6)+y^2/(r^2-6r+5)=1` will represent ellipse if r lies in the interval (a).(-`oo`,2) (b). (3,`oo`) (c). (5,`oo`) (d).(1,`oo`)

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(x^(2))/(r^(2)-r-6) +(y^(2))/(r^(2) - 6r + 5) = 1 will represents an ellipse if r lies in the interval _

If (y+3)/(2y+5)=sin^2x+2cosx+1, then the value of y lies in the interval (-oo,-8/3) (b) (-(12)/5,oo) (-8/3,-(12)/5) (d) (-8/3,oo)

f(x)=(x-2)|x-3| is monotonically increasing in (a) (-oo,5/2)uu(3,oo) (b) (5/2,oo) (c) (2,oo) (d) (-oo,3)

The equation ||x-2|+a|=4 can have four distinct real solutions for x if a belongs to the interval a) (-oo,-4) (b) (-oo,0) c) (4,oo) (d) none of these

If cos^2x-(c-1)cosx+2cgeq6 for every x in R , then the true set of values of c is (a) (2,oo) (b) (4,oo) (c) (-oo,-2) (d) (-oo,-4)

If the ellipse (x^2)/4+y^2=1 meets the ellipse x^2+(y^2)/(a^2)=1 at four distinct points and a=b^2-5b+7, then b does not lie in (a) [4,5] (b) (-oo,2)uu(3,oo) (c) (-oo,0) (d) [2,3]

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)

If the parabols y^(2) = 4kx (k gt 0) and y^(2) = 4 (x-1) do not have a common normal other than the axis of parabola, then k in (a) (0,1) (b) (2,oo) (c) (3,oo) (d) (0,oo)

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

The range of a for which the equation x^2+ax-4=0 has its smaller root in the interval (-1,2)i s a. (-oo,-3) b. (0,3) c. (0,oo) d. (-oo,-3)uu(0,oo)

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