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.
 
1. (a) An article was marked to sale for Rs. 1240. But it was sold at a discount 22.5%. Compute its selling price 2
(b)
If
4x − 3z
4c
 =
4z − 3y
3b
 =
4y − 3z
2a
, show that each ratio is equal to
x + y + z
2a + 3b + 4c
.
 5
(c) The simple interest on Rs. 300 at the rate of 4% per annum with that on Rs. 500 at the rate of 3% per annum, both for the same period, is Rs. 162. Find the time period. 2
2. (a) The average score of girls in HSC examination is 75 and that of boys is 70. The average score of all the candidates in the examination is 72. Find the ratio of number of girls and boys that appeared in the examination. 5
(b) A person drove is car for 20 km. at an average speed of 25 km. per hour. At what average speed must be drive for the next 20 km., if his average speed for the whole distance is to be 30 km. per hour? 5
3. (a) At what simple interest rate percent per annum a sum of money will be doubled of itself in 25 years? 5
(b) A dealer mixes 90 liters of wine containing 10% of water with 60 litres of another wine containing 20% of water. What is the percentage of water in the mixture? If 50 litres pure water is added to the mixture, find the percentage of water in the final mixture. 5

  SECTION B(Algebra — 25 marks)
Answer Question No. 4 (compulsory — 5 marks) and any two (10x2=20 marks) from the rest.
 
4. Answer any five of the following :
(a)Find p if (p)p√p = (p√p)p
(b)Solve: x2 + 9 = 0.
(c)If n(s) = 12, n(T) = 20 and S ⊂ T, find n (SUT).
(d)If a varies as b prove that a + b varies as a — b.
(e)If the roots of a quadratic equation be 3 and 5, find the quadratic equation.
(f)Find the logarithm of 125 to the base 5√5.
(g)If rC12 = rC8, find 22Cr.
1x5=5
5. (a) Solve by Cramer's rule 5
x + y + z =6, 2x — y + 3z = 9, x + 3y — 2z = 1.
(b)
Prove that
4x log √27 + log8 + log √1000
log 14400
 =
3
4
 5
6. (a) Prove that "CALCUTTA" is twice of "AMERICA" in respect of number of arrangements of letters. 3
(b) If S is the set of all prime numbers, M = {x|0 ≤ x ≤ 9}, exhibit.
(i)M − (S∩M)(ii)M∪N where N = {o, 1, 2, ............... 20}.
 5
(c) Show by the truth table: P ⇒ q =~ q ⇒~ P. 5
7. (a) Out of 6 ladies and 3 gentlemen, a committee of six is to be selected. In how many ways can this committee containing at least 4 ladies be formed? 5
(b) If the roots of the equation ax2 + bx + c = 0 be in the ratio 2 : 3 then show that 6b2 = 25 ca. 5
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C-4(BMS)
Revised syllabus		 Marks
SECTION C(Mensuration — 30 marks)
Answer Question No. 8 (compulsory — 10 marks) and any two (10x2=20 marks) from the rest.
 
8. Answer any five of the following :
(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.
(b)The perimeter of an isosceles triangle is 544 cm. and each equal side is 5/6 of the base. Find its area.
(c)A bicycle wheel makes 5000 revolutions in moving 11 km. Find the diameter of the wheel.
(d)The altitude of a pyramid having square base is 6 ft. Each side of base is 4 ft. Find the volume.
(e)The diameter of a sphere is 5 cm. Find the surface area of its hemisphere.
(f)Find the slope of the line perpendicular to the line joining the points (4, —3), (2, 1).
(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.
(h)Find the centre and radius of the circle x2 + Y2 — 4x — 6y — 12 = 0.
 2x5=10
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
(b) For the equation of the parabola y2 — 6y — 12x — 3 = 0, find the focus, directrix and the length of latus rectum. 5
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
(b) Find the equations of the diagonals of the rectangle formed by the lines x = 2, x = 5, y = 2 and y = 5. 5
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
(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
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C-4(BMS)
Revised Syllabus

SECTION D(Elementary Statistics — 30 marks)
Answer Question No. 12 (compulsory — 10 marks) and any two (10x2=20 marks) from the rest.
12. Answer any five of the following : 2x5=10
(a) If a variable x takes 10 values 1, 2, 3, ........, 10 with frequencies as its values in each case, then find the arithmetic mean of x.
(b) If 2u = 5x is the relation between two variables x and u and harmonic mean of x is 0.4 find the harmonic mean of u.
(c)For a group of 10 items 10
Σ
i=1		 (xi − 2) = 40 and 10
Σ
i=1		 xi2 = 495. Then find the variance of this group.
(d) If first of two groups has 100 items and mean 4 and combined group has 250 items and mean 51, find the mean of the second group.
(e) Find the median of the following distribution :
Weight (in. Kg.)
No of students		 :
:		 65
5		 66
15		 67
17		 68
4
(f) Calculate the mode of the following distribution: 7, 4, 3, 5, 6, 6, 6, 2, 4, 3, 4, 3, 3, 4, 4, 2, 3.
(g) If the relation between two variables x and u is x — 10 =2u and mean deviation of x about its mean is 10 find the mean deviation of u about its mean.
(h) Which group is more skewed?
(i) Group I: A.M=22, mode=27, s.d.=10, (ii) Group II: A.M.=20, mode=26,     s.d.=9?
13. (a) Draw a line diagram from the following data of number of students in a class of a college: 5
Year
No of students		 :
:		 1990
20		 1991
25		 1992
24		 1993
30		 1994
35		 1995
38
(b) Draw a histogram from the following data of a factory: 5
Wages per hour (Rs.)
No. of workers		 :
:		 4-6
6		 6-8
12		 8-10
18		 10-12
10		 12-14
4
14. (a) From the following cumulative frequency distribution of marks of 22 students in Accountancy, calculate mode: 5
Marks
No. of students		 :
:		 Below 20
3		 Below 40
8		 Below 60
17		 Below 80
20		 Below 100
22
(b) Prove that the standard deviation of two values of a variable is equal to half of the range. 5
15. (a) Find the coefficient of variation for the following data: 5
Marks (x)
No. of students (f)		 :
:		 10
18		 20
12		 30
20		 40
10		 50
7		 60
3
(b) For a group containing 100 observations the arithmetic mean and standard deviation are 8 and 10.5 respectively. For 50 observations selected from these 100 observations, the arithmetic mean and standard deviation are 10 and 2 respectively. Find the arithmetic mean and standard deviation of other 50 observations. 5

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