# CWA ICWA Foundation : Business Mathematics and Statistics Fundamentals - December 2006

 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)1 (0)
(c)1 (0)
(d)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) Express 2√2 as a surd of sixth order. (0) (b) Find the modulus of the complex number 3 + 4i. (0) (c) If x varies as y then show that x2 + y2 varies as x2 – y2. (0) (d) Find the logarithm of 125 to the base 5√5. (0) (e) Find the quadratic equation whose one root is 3 + √2. (0) (f) Prove that 10P10 x 22C12 = 22P10. (0) (g) If S be the set of all prime numbers and M = {0, 1, 2, 3}, find S ∩ M. (0) 5. (a) For what value of m, 4x2 – 10mx + 4 = 0 and 4x2 – 9x + 2 = 0 have a common root? 5 (0) (b) Out of 5 gentlemen and 3 ladies, a committee of 6 persons is to be selected. Find the number of committees to be formed (i) when there are 4 gents: (ii) when there is a majority of gents. 5 (0) 6. (a) Publisher of a book pays a lump sum plus an amount for every copy for every copy he sold, to the author. If 1000 copies were sold the author would receive Rs. 2,500 and if 2700 copies were sold the author would receive Rs. 5,900. How much the author would receive if 5000 copies were sold? 5 (0) (b) Construct a truth table for (p ∧ q) ∧ ∼ (p ∧ q). 5 (0) 7. (a) Determine the time period by which a sum of money would be three times of itself at 8% p.a. C.I. [Given log103 = 0.4771, log101.08 = 0.0334] 5 (0) (b) Solve: x(x + y + z) = 6; y(x + y + z) = 12; z(x + y + z) = 18. 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) For an isosceles right angled triangle with length 5 cm of one side adjacent to the right angle, find the length of the perimeter of the triangle. (0) (b) The circumference of a circle is 88 cm. Determine the length of the perimeter of its semi–circle. (0) (c) The diameter of the base of a cylindrical pillar is 7 m and its height is 18 m. Find the volume of the pillar. (0) (d) The external and internal radii of a hollow sphere are 6 cm and 3 cm respectively. Find the volume of the sphere. (0) (e) If the point (5, y) divides the line joining points (4, 2) and (7, 5) internally, find y. (0) (f) Find the gradient of the line having equal intercepts of the axes in the first quadrant of the coordinate system. (0) (g) Determine the equation of a circle with (2, 3) and (4, 5) as the extremeties of its diameter. (0) (h) Find the eccentries of the ellipse whose minor axis is half of its major axis. (0) 9. (a) A circle of diameter 14 meter is inscribed within a square touching the sides. Find the area of the fillets thus formed and the cost of developing one fillet at the rate of Rs. 200 per square meter. 5 (0) (b) Find the equations of the sides of a triangle ABC whose vertices are A (–1, 8), B(4, –2) and C(–5, –3). 5 (0) 10. (a) These base of a right pyramid is an equilateral triangle of side 10√3 cm each. The area of the total surface of the pyramid is 270√3 cm2. Find the height of the pyramid. 5 (0) (b) Show that the two circles x2 + y2 + 4x + 10y = 20 and x2 + y2 – 8x – 6y + 16 = 0 touch each other externally. Also determine the coordinates of the point of contact. 5 (0) 11. (a) A conical tent is required to accommodate 11 persons. Each person must have 4 sq.m of space on the ground and 20 cu.m of air to breathe. Find the vertical height. 5 (0) (b) Find the equation of the hyperbola whose focus is at (1, 2), directrix 2x + y = 1 and eccentricity √3. 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)
14.4+3+3 (0)
15.(a)5 (0)
(b)5 (0)  