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Find the point on the terminal side of θ = negative three pi divided by four that has an x coordinate of -1.
The point P(21, 28) is on the terminal side of θ. Evaluate sin θ.
If the normal at one extremity of latus rectum of an ellipse passes through one extremity of the minor axis, prove that the eccentricity e is given by e⁴+e²-1=0
Let S≡4x²−9y²−36=0 and S'≡y²−4x=0 be two conics. Under what conditions on k, will the conic S+kS'= 0 represent: i) an ellipse? ii) a hyperbola?
How to prove that the path traced by the foot of the perpendicular from the focus of a parabola on any tangent to the parabola is the tangent at its vertex.
To find the equation of the right circular cone whose vertex is (1,-1,2), the axis is
x-1/2 = y+1/1 = z-2/-2
and the semi-vertical angle is 45º
A box contains a certain no. of balls, on each of 60% balls A is marked and on each of 30% balls letter B is marked and on each of the remaining balls letter C idols marked . A ball is drawn at random, find the probability that the ball drawn is (1)marked C
(2)marked A or B
(3)marked neither B nor C
Obtain the Fourier cosine series for the following function:

F(x)= 1 for (0 less than equal to x< 1)

0 for (1 less than equal to x < 4 )
Solve the heat conduction equation:
for the following boundary and initial conditions:
8(d^2u/dt^2)=(du/dt), for 0<X< 5 and t> 0,
u(0,t) = u(5,t) = 0,
u(x,0) =2sin(πx)− 4sin(2πx)
(3.26) From a box containing 4 black balls and 2 green balls, 3 balls are drawn in succession, each ball being replaced in the box before the next draw is made.
a) Find the Probability Distribution for X, the number of green balls. Explain your answer.
b) Calculate the expected number of green balls.
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