# CWA ICWA question papers Foundation

## Business Mathematics and Statistics Fundamentals June 2011

P—4(BMS)
Syllabus 2008
Time Allowed : 3 Hours Full Marks : 100
The figures in the margin on the right side indicate full marks.
Notations and symbol have usual meanings
SECTION I (Arithmetic — 10 marks)
Marks
1. Answer any two of the following:
Choose the correct option showing the proper reasons/calculations. 3×2
(a) If 2 – x, 3 – x, 5 – x and 7 – x are in proporation,then the value of X is
(i) 1, (ii) –1, (iii) 2, (iv) none of these
(0)
(b) The average of 10 numbers is 21. If an additional number is included the average becomes 20. The additional number is
(i) 10, (ii) 5 (iii) 3 (iv) none of them
(0)
(c) True discount of a bill value due in 2 years at 4% per annum. Simple interest is Rs.40. Then bill value is
(i) Rs. 540, (ii) Rs. 500, (iii) Rs. 460, (iv) none of them
(0)
2. Answer any one of the following. 4×1
(a) Due to fall in rate of interest from 12% to 10% per annum in 4 years, home loan amount of a person decreases by Rs. 4800. Find the home loan he took first. (0)
(b) At what ratio sugar at Rs. 30 per kg be mixed with sugar at Rs. 35 per kg to produce a mixture making profit 25% when sold at Rs. 40 per kg? (0)
SECTION II (Algebra — 15 marks)
Marks
3. Answer any three of the following:
Choose the correct option showing necessary reasons/calculations. 3×3
(a) The number of ways in which 9 different things can be divided into 3 groups containing 2, 3 and 4 things respectively is
(i) 15120, (ii) 1260 (iii) 630 (iv) none of these.
(0)
(b)
If x + iy =
1
3 + 2i
the value of x – y is
(i)
1
13
, (ii)
1
√14
, (iii)
1
5
(iv) none of these.
(0)
(c) If c varies directly as x + b, c = 8 when b = 2 and c = 10 when b = 3 then value of x is
(i) 0, (ii) 1, (iii) 2, (iv) none of these.
(0)
(d)
The logarithm of 324 to the base
1
3√2
is
(i) – 4, (ii) –2, (iii) 4 (iv) none of these.
(0)
(e) Let p be ” the student is a girl ” and q be ” the student is studious”. Then the symbolic form of the statement ” the student is a boy but he is not studious ” is
(i) p ∧ ∼ q, (ii) ∼ p ∧ q, (iii) ∼ p ∧ ∼ q, (iv) none of these
(0)
4. Answer any two of the following: 3×2
(a) In a class of students 20 passed in Statistics, 25 passed in Mathematics and 10 passed in Statistics but not in Mathematics. Find the number of students who passed inMathematics but not in Statistics. (0)
(b) Solve : 2x + 1 + 2x – 1 = 160 (0)
(c)
Simplify:
√5 + √2
√5 – √2

√5 – √2
√5 + √2
(0)
SECTION III (Mensuration — 15 marks)
Marks
5. Answer any three of the following:
Choose the correct option showing necessary reasons/calculations. 3×3
(a) The perimeter of a rectangale, having area 18 sq cm and its length being twice its breadth, is
(i) 9 cm, (ii) 18 cm, (iii) 24 cm, (iv) none of these
(0)
(b)
If the perimeter of a semicircle is 36 cm then area of the semicircle is (Take π =
22
7
)
i) 77 sq.cm, (ii) 154 sq.cm, (iii) 38.5 sq.cm (iv) none of these
(0)
(c) If the diameter of the base of a cylinder is equal to its height and its volume is 2156 cc,
its whole surface is (Take π =
22
7
)
(i) 920 sq.cm, (ii) 900 sq.cm, (iii) 924 sq.cm (iv) none of these
(0)
(d) The radius of a sphere is 3 cm. It is melted and drawn into a wire of diameter 0.2 cm. Then length of the wire (in cm) is
(i) 3400, (ii) 3500, (iii) 3600, (iv) none of these.
(0)
(e) Three sides of a cuboid are 18, 37.5 and 40 cm. Then the edge of that cube whose volume is equal to this cuboid is
(i) 30 cm, (ii) 35 cm, (iii) 40 cm, (iv) none of these
(0)
6. Answer any two of the following: 3×2
(a) If the area of an equilateral triangle is √3 sq cm then find the perimeter of the triangle. (0)
(b)
The height of a right circular cone is 42cm and its slant height is 45.5 cm. Find the cost of painting of
its total surface at the rate of Re. 1 per sq cm.(Take π =
22
7
).
(0)
(c) A right pyramid stands on a base 12 cm square and its height is 8 cm. Find the slant surface area of it. (0)
SECTION IV (Co–ordinate Geometry — 10 marks)
Marks
7. Answer any two of the following:
Choose the correct option showing proper reasons/calculations. 3×2
(a) If x (2,a), y (3,–1) and z(4,–5) are collinear then a is
(i) 1, (ii) 2, (iii) 3, (iv) none of these.
(0)
(b) A line passing through (1,3) and perpendicular to the line 2x – 3y = 7 is
(i) 2y +3x = 11, (ii) 3y = 2x + 7, (iii) 2y +3x = 9, (iv) none of these.
(0)
(c) The length of intercept of the circle x 2 + y2 – 2x – 10y + 22 = 0 on the line x = 1 is
(i) 2 units, (ii) 4 units, (iii) 6 units, (iv) none of these
(0)
(d) For the parabola y2 = 4x intersecting the line y + 4 = 2x, the length of the chord thus formed is
(i) √5 unit, (ii) 2√5 unit, (iii) 3√5 unit, (iv) none of these
(0)
8. Answer any one of the following: 4×1
(a) In the hyperbola 25 y2 – 16 x2 = 400, find the equation of latus rectum and length of the axes. (0)
(b) Find the equation of the ellipse whose focii are (2,0), (–2,0) and eccentricity is ⅓ (0)
SECTION V (Calculus — 15 marks)
Marks
9. Answer any three of the following:
Choose the correct option showing proper reasons/calculations. 3×3
(a)
If y = f(x) =
ax + b
cx – a
then for x ≠
a
c
,f(y) is
(i) x, (ii) –x, (iii)
1
x
, (iv) none of these
(0)
(b)
The value of lim
x→ ∝
4×2 + 3x – 1
2×2 + 7x + 5
is
(i) 2, (ii)
1
2
(iii) does not exist, (iv) none of these.
(0)
(c)
If y = xx then
dy
dx
is
(i) x log x, (ii) x (1 + log x), (iii) xx (1 + log x), (iv) none of these
(0)
(d)
The value of 1

0
dy
x+√x
is
(i) loge2, (ii) 2 loge2, (iii) – loge2, (iv) none of these
(0)
(e) If u = x2y + y2z + z2 x then u x + uy + uz is
(i) (x + y + z), (ii) (x + y + z)2, (iii) (x2 + y2 + z2), (iv) none of these
(0)
10. Answer any two of the following: 3×2
(a)
A firm produces x tons valuable metal per month at total cost ‘C’ given by
C = Rs. (
1
3
x3 – 5×2 + 75x + 10)
Then at what level of output, the marginal cost attains its minimum?
(0)
(b)
If xy = ax2 +
c
x
show that x2y2 + 2(xy1 – y) = 0
(0)
(c)
Evaluate ∫ x log (1 + x) dx.
(0)
SECTION VI (Statistical Methods — 35 marks)
Marks
11. Answer any seven of the following:
Choose the correct option showing proper reasons/calculations. 3×7
(a) If 1 , 2 , 3 , 4 occur with respective frequencies 1 , 2 , 3 , 4 then their arithmetic mean is
(i) 7.5, (ii) 2.5, (iii) 3, (iv) none of these
(0)
(b) In a group of 150 observations the arithmetic mean is 60 and arithmetic mean of first 100 observations of the group is 50. Then arithmetic mean of the remaining observations of the group is
(i) 80, (ii) 60, (iii) 50, (iv) none of these
(0)
(c) If the observations 2,4,8 and 16 occur 8 , 6 , 4 and 2 times respectively then the geometric mean of the observations is
(i) 8, (ii) 4√2, (iii) 4, (iv) none of these
(0)
(d) If the arithmetic mean of 10 observations x1, x2 , …..x10 is 20 then harmonic mean of 10
observations
10
x1
,
10
x2
,…….
10
x10
is
(i) 2 (ii)
1
2
, (iii)
1
20
, (iv) none of these
(0)
(e) If the Variables x and y are related by 3x – 2y + 6 = 0 and the range of x is 10 then range of y is
(i) 18, (ii) 15, , (iii) 12, , (iv) none of these
(0)
(f) If sum of deviations of 4 values about 2 is 4and standard deviation of those 4 values is 2 then sum of squares of the 4 observations is
(i) 52, (ii) 40, (iii) 20, (iv) none of these
(0)
(g) Mean deviation about mean of first 6 positive integers is
(i) 3.5, (ii) 2.5, (iii) 1.5, (iv) none of these
(0)
(h) The median of the following distribution
x
frequency :
: 1
7 2
12 3
18 4
4 is
(i) 2, (ii) 3, (iii) 4, (iv) none of these
(0)
(i) If the mean and coefficient of variation of x are 10 and 50% respectively, then the standard deviation of 3 – 2x is
(i) 100, (ii) 50, (iii) 10, (iv) none of these
(0)
(j) If the coefficient of skewness,mean and variance of a set of values are –3 , 40 and 4 respectively then median of the values is
(i) 46, (ii) 42, (iii) 41, (iv) none of these
(0)
12. (a) Answer any two of the following: 5×2
(i) Tabulate the following data in a suitable tabular form “2000 men and 1600 women participated in a poll on the opinion about a certain measure. 1200 persons of whom 800 were male, voted against the measure. In all 1800 persons voted for the measure and 300 women were in different. ” Find percentage of women voted against the measure. (0)
(ii) Find mean and median of the following frequency distribution. Then calculate the mode using the empirical relation between them.
Class limits
f :
: 130 – 134
5 135 – 139
15 140 – 144
28 145 – 149
24 150 – 154
17 155 – 159
10 160 – 164
1
(0)
(iii) For a group containing 90 observations the mean and standard deviation are 59 and 9 respectively. For 40 observations of them mean and standard deviation are 54 and 6 respectively. Find the mean and standard deviation of the remaining 50 observations. (0)
(b) Write short note on any one of the following: 4×1
(i) Pie Chart, (0)
(ii) Dispersion of data. (0)