# CWA ICWA Foundation : Business Mathematics and Statistics Fundamentals - June 2005

 C—4(BMS)Revised Syllabus Time Allowed : 3 Hours Full Marks : 100
 The figures in the margin on the right side indicate full marks. Section A ARITHMETIC (15 marks)Answer Question No. 1 (compulsory – 5 marks) and any one (10 marks) from the rest. Marks
1.(a)2 (0)
(b)1 (0)
(c)2 (0)
2.(a)5 (0)
(b)5 (0)
3.(a)5 (0)
(b)5 (0)
 Section B ALGEBRA (25 marks) Answer Question No.4 (compulsory – 5 marks) and any two (10 x 2 = 20 marks) from the rest.
4.Answer any five of the following : 1x5=5
(a)  (0)
(b)  (0)
(c)  (0)
(d)  (0)
(e)  (0)
(f)  (0)
(g)  (0)
5.(a)5 (0)
(b)5 (0)
6.(a)3 (0)
(b)2 (0)
(c)5 (0)
7.(a)5 (0)
(b)5 (0)
 Section C MENSURATION (30 marks) Answer Question No.8 (compulsory – 10 marks) and any two (10 x 2 = 20 marks) from the rest.
 8. Answer any five of the following : 2x5=10 (a) The side of rhombus PQRS is 12 cm and one of the diagonals PR is 8 cm. Find the other diagonal and hence its area. (0) (b) The perimeter of an isosceles triangle is 544 cm. and each equal side is 5/6 of the base. Find its area. (0) (c) A bicycle wheel makes 5000 revolutions in moving 11 km. Find the diameter of the wheel. (0) (d) The altitude of a pyramid having square base is 6 ft. Each side of base is 4 ft. Find the volume. (0) (e) The diameter of a sphere is 5 cm. Find the surface area of its hemisphere. (0) (f) Find the slope of the line perpendicular to the line joining the points (4, –3), (2, 1). (0) (g) Find the coordinate of the point which divide the line segment joining the points (5, 8) and (6, 3) in the ratio 2 : 3 externally. (0) (h) Find the centre and radius of the circle x2 + Y2 – 4x – 6y – 12 = 0. (0) 9. (a) A path of 100 cm. wide is formed round a rectangular garden of 600 cm. by 500cm. in its inner side. Find the area of the path. If the construction of the path is at the rate of Rs. 3 per sq. cm., find the cost to construct the path. 5 (0) (b) For the equation of the parabola y2 – 6y – 12x – 3 = 0, find the focus, directrix and the length of latus rectum. 5 (0) 10. (a) A conical tent is required to accommodate 11 people, each person must have 14 sq. fit. of space on the ground and 140 cubic ft. of air to breathe. Give the vertical height, slant height and the width of the tent. 5 (0) (b) Find the equations of the diagonals of the rectangle formed by the lines x = 2, x = 5, y = 2 and y = 5. 5 (0) 11. (a) A point p(x, y) moves in such a way that the differences of its distances from A (1, 4) and B (1, –4) is always equal to 6. Find the equation of the locus of P. 5 (0) (b) The ellipse px2 + 4y2 = 1 passes through the points (±1, 0). Find the value of p and hence find the lengths of its major and minor axes. 5 (0)
 Section D ELEMENTARY STATISTICS (30 marks) Answer Question No. 12 (compulsory – 10 marks) and any two (10 x 2 = 20 marks) from the rest.
12.Answer any five of the following : 2x5=10
(a)  (0)
(b)  (0)
(c)  (0)
(d)  (0)
(e)  (0)
(f)  (0)
(g)  (0)
(h)  (0)
13.(a)5 (0)
(b)5 (0)
14.(a)5 (0)
(b)5 (0)
15.(a)5 (0)
(b)5 (0)