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

This Paper has 47 answerable questions with 0 answered.
 C—4(BMS)Revised Syllabus Time Allowed : 3 Hours Full Marks : 100
 The figures in the margin on the right side indicate full marks. Notations and symbols have their usual meanings Section A ARITHMETIC (15 marks)Answer Question No. 1 (compulsory – 5 marks) and any one (10 marks) from the rest. Marks
1.(a)1 (0)
(b)2 (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
(a)  (0)
(b)  (0)
(c)  (0)
(d)  (0)
(e)  (0)
(f)  (0)
(g)  (0)
5.(a)5 (0)
(b)5 (0)
6.(a)5 (0)
(b)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) A path of 4 ft wide is to be laid outside round the square garden of 60ft by 60ft. Find the area of the path. (0) (b) Base radius of a conical tent is 5 m and its height is 10 m. Find the area of the canvas of the tent. (0) (c) If the total surface area of a cube is 54 sq ft, find its volume. (0) (d) Three solid gold spherical beads of radii 3, 4 and 5 cms respectively are melted to form another solid spherical bead. Find its radius. (0) (e) Find the equation of the straight line making an intercept 3 on the x–axis and passing through the point (1, 2). (0) (f) For the equation of the circle x2 + y2 + 2x – 4y = 11, find the coordinates of its center and also its radius. (0) (g) Find the vertex of the parabola y2 – 2y – 8x = 23. (0) (h) Find the eccentricity of the ellipse 8x2 + 9y2 = 288. (0) 9. (a) The perimeter of a right angled triangle is 30 cm and hypotenuse is 13 cm. Find the other two sides and the area of the triangle. 5 (0) (b) Volume of a right circular cylinder, whose base has a radius of 7 cm, is same as volume of a cube having an edge of 11 cm. Find the the altitude and the total surface area of the cylinder. 3+2 (0) 10. (a) A right pyrami9d stands on a square base having a side of 10 cm and its height is 12 cm. Find its total surface area and volume. 5 (0) (b) If the three points (x, y), (5, –2) and (3, –4) are collinear, prove that 3x + 4y – 7 = 0. 5 (0) 11. (a) Find the centres and radii of two circles x2 + y2 + 6x + 14y + 9 = 0 and x2 + y2 ’ 4x ’ 10y ’ 7 = 0 and hence show that they touch each other externally. 1½+1½+2 (0) (b) Find the coordinates of center, length of latus rectum, coordinates of foci of the hyperbola 3x2 – 4y2 – 12x – 8y – 4 = 0. 2+1+1+1 (0)
 Section D ELEMENTARY STATISTICS (30 marks) Answer Question No. 12 (compulsory – 6 marks) and any two (12 x 2 = 24 marks) from the rest.
12.Attempt any five of the following : 2x5
(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)
15.2+3+3+2 (0)