BACHELOR IN COMPUTER APPLICATIONS
Term-End Examination
June, 2010
CS-60: FOUNDATION COURSE IN
MATHEMATICS IN COMPUTING
Time : 3 hours Maximum Marks : 75
Note: Question No. 1 is compulsory. Attempt any three questions from questions No. 2 to 6. Use of calculator is permitted.1.
(a) Show that the function f (x) = 3x —1 ; 15x3=45
Is one-one and onto. (b) Tell for each whether the statement is true or false :
(i) R, the set of Real Numbers, is closed under addition operation.
(ii) In R, the operation of multiplication is not commutative
(iii) The relation '>' of 'greater than in R is transitive.
(c) The function:
Is one-one
(d) Find 
(e) Evaluate 
(f) Prove that the points 
and 
are the vertices of an isosceles triangle.
and are the vertices of an isosceles triangle.(g) Find the equation of a straight line which passes through the points 
(h) Find the equation of a straight line which meets x-axis in (5,0) and y-axis in (0,-3).
(i) Find the equation of the parabola whose focus is the point (3,4) and directrix is the straight line 2x-3y+5=0.
(j) Find the equation of a circle with radius 5 units and centre as (2, -3).
(k) Find the coordinates of the vertices and the foci and the length of the latus rectum of the hyperbola
.
.(l) Solve the system of simultaneous equations:
(m) If 
Find 
(n) Evaluate
(o) Obtain
in the form of
.
in the form of
.2.
(a) Evaluate the integral 3+4+3
(b) Evaluate the integral
(c) Find the area of the region bounded by the curve 
And lying above the x-axis.3. 4+3+3
(a) Find the equation of the circle circumscribing the triangle with vertices 
(b) Find the equation of parabola with focus 
and directrix 
Find the equation of the axis.
and directrix Find the equation of the axis.(c) Find the standard equation of the hyperbola with eccentricity 
4. 4+3+3
(a) Find the equation of the plane which is perpendicular to the plane 
and which is contains the line of intersection of the planes 
and which is contains the line of intersection of the planes (b) Find the equation to the sphere through the circle
and the point
.(c) Find the equation to the cone whose vertex is origin and which passes through the curve given by
5. 3+3+4
(a) Prove that 
.
.(b) Solve the equation 
(c) Expand 
in terms of the cosines of multiples of
.
in terms of the cosines of multiples of.6. 4+3+3
(a) Find the maxima and minima of the following faction
(b) Find the equations of the tangents and the normal to the following faction
(c) Trace the curve
.
.
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