If y then find dy/dx
Compute d/dx If sqrt(3) i r (cos 8 i sin then find r and 8.
Evaluate
integral SinX dx) State True or False, for each of the following:

(iii)

where absolute value of x. R R and R R are two functions such that

f(x) and 2x 3. Find fog and gof. Evaluate the following:

<br><br> <img src='./qimages/9464-1g.jpg'> Solve the following system of linear equations:

2x 3y 8
3x 4y 11
For each of the following, state whether it is true or false; where A. C are sets and U and n denote set union and set intersection respectively: A n B B n A

(ii) A n B B U A

(iii) A U 41 41, where 41 denotes an empty set Find the area of the region bounded by x and y =6. Obtain the conjugate of the following complex numbers 4 6i

(ii) 5

(iii) 7i

where Find the value of the following determinant:

1 1
2 2

(m) Determine the equation of a straight line passing through the point and the point 2). Find the equation of a sphere with centre and radius as 7 units. Evaluate <img src='./qimages/9464-1o.jpg'>

2.(a) Find dy/dx, if y =sin x sin 2x sin 3x.
Find the equation of a straight line in the three-dimensional space joining the points and 4).
Find the value of the determinant

x x 4y
7y 13y


3.(a) Using Trapezoidal rule or Simpson's 1/3 rule and taking four subdivisions of the interval find the approximate value of
<img src='./qimages/9464-3a.jpg'>
Find the area of the surface of the solid obtained by revolving the line y 3 about the x-axis that lies between x 1 and x 4.
If 1 2 3 ] and B -1 1
2 -1 5 3 5 -2

find Let S 12t — 3t^2. Find d^2S dt^2.

(b) Find the equation of the tangent to the curve y x^2 4x l at the point, where x 3.
The following pie chart represents the number of valid votes obtained by four students who contested for school leadership. The total number of valid votes polled was 720. What is the minimum number of votes obtained by any candidate? <img src='./qimages/9464-4c.jpg'>

5.(a) The function is defined as

<br><br> <img src='./qimages/9464-5a.jpg'>

Examine whether is continuous at x 1.

(b) If x^y prove that dy/dx logex/(1 logex)^2
If y (sec x tan find dy/dx

6.(a) The mean of 200 items was 50. Later on, it was discovered that two items were misread as 92 and 8 instead of 192 and 88. Find the correct mean.
Find the vertex, focus and directrix of the parabola given by the following equation 4y^2 12x 12y 39 0.
One end of a diameter of the circle x^2 y^2 3x 5y 4 0 is 1). Find the co-ordinates of the other end.