(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)

vineet chatterjee, 7 years ago

Grade:12

1 Answers

Ravi

askIITians Faculty 69 Points

7 years ago

Answer 3
Draw the figure. find the angle subtend by the arc length given. Calculate the projected distance at the fence i.e. the distance travelled by the shadow across the fence. Calculate the time using the distance travelled by the horse along the circle(2 pi r/8) and the speed with which it is running. Use this time and the distance travelled by the shadow along the fence(which can be calculated by the triangle formed and the angle subtend at the lantern) to get thye net distance covered and the time taken to get the speed of the shadow of the horse along the fence.

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