(1) A polynomial of sixth degree f(x) satisfies f(x)=f(2-x) for all x belonging to R,if f(x)=0 has 4 distinct and two equal roots,then sum of the roots of f(x)=0 is? (2)the graphs y=2x^3-4x+2 and y=x^3+2x-1 intersect at exactly 3 distinct points.The slope of the line passing through two of these points is? (3)a horse runs along a circle with the speed of 20km/hr.A lantern is at the centre of the circle.A fence is there along the tangent to the circle at the point at which the horse starts.The speed with which the shadow of the horse moves along the fence at the momentwhen it covers 1/8 of the circle in km/hr is? options are,20,40,30,60 (4)Let f(x)=x^3-3x^2+2x.If the polynomial f(x)=k has exactly one positive and one negative solution,then the value of k is? (5)let f(x)=integration from lower limit sinx to upper limit cosx, e^(1+arcsint)^2dt((((read it as e to the power (1+arcsint) ka whole squared))))on the interval [0,pie/2],then choose the correct option (a)f" (c)=0 for all c belonging to (0,pie/2) (b)f" (c)=0 for some c belonging to (0,pie/2) (c)f' (c)=0 for all c belonging to (0,pie/2) (d)f(c) not equal to 0 for all c belonging to (0,pie/2)

 

(1) A polynomial of sixth degree f(x) satisfies f(x)=f(2-x) for all x belonging to R,if f(x)=0 has 4 distinct and two equal  roots,then sum of the roots of f(x)=0 is? 

 

(2)the graphs y=2x^3-4x+2 and y=x^3+2x-1 intersect at exactly 3 distinct points.The slope of the line passing through two of these points is?

 

(3)a horse runs along a circle with the speed of 20km/hr.A lantern is at the centre of the circle.A fence is there along the tangent to the circle at the point at which the horse starts.The speed with which the shadow of the horse moves along the fence at the momentwhen it covers 1/8 of the circle in km/hr is?

options are,20,40,30,60

 

(4)Let f(x)=x^3-3x^2+2x.If the polynomial f(x)=k has exactly one positive and one negative solution,then the value of k is?

 

(5)let f(x)=integration from lower limit sinx to upper limit cosx,  e^(1+arcsint)^2dt((((read it as e to the power (1+arcsint) ka whole squared))))on the interval [0,pie/2],then choose the correct option

(a)f" (c)=0 for all c belonging to (0,pie/2)

(b)f" (c)=0 for some c belonging to (0,pie/2)

(c)f' (c)=0 for all c belonging to (0,pie/2)

(d)f(c) not equal to 0 for all c belonging to (0,pie/2)