This Paper has 49 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) | If the mean proportional between x and 2 is 4, find x. | 1 | (0) |
| | (b) | The mean of 4 numbers is 9. If one number is excluded the mean becomes 8. Find the excluded number. | 1 | (0) |
| | (c) | Compute the simple interest on Rs. 5,700 for 2 years at 2.5% p.a. | 1 | (0) |
| | (d) | | A number is increased by 33 | | %. If the number thus obtained is 600, find the number |
| 2 | (0) |
| 2. | (a) | | 5 | (0) |
| | (b) | The prime cost of an article was three times the value of the materials used. The cost of raw materials was increased in the ratio 3:4 and the productive wage was increased in the ratio 4:5. Find the present prime cost of an article, which could formerly be made for Rs. 180. | 5 | (0) |
| 3. | (a) | A dealer of radio offers radio for Rs. 2,720 cash down or for Rs. 720 cash down and 24 monthly installments of Rs. 100 each. Find the rate of simple interest charged per annum. | 5 | (0) |
| | (b) | If the Banker’s gain on a sum due in 6 months at 4% per annum is Rs. 100, find the amount of bill. | 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) | Simplify: 3√48 – 4√75 + √192. | | (0) |
| | (c) | Find the conjugate of 3 + 2i. | | (0) |
| | (d) | If a + b varies as a – b, prove that a ∝ b. | | (0) |
| | (e) | Find the roots of the equation 2x2 – 5x + 3 = 0. | | (0) |
| | (f) | In XOY plane draw the graph of x = 2. | | (0) |
| | (g) | Find the value of log2 log3 81. | | (0) |
| 5. | (a) | | 5 | (0) |
| | (b) | A question paper of an examination is divided into 3 groups A, B and C containing 4, 5 and 3 questions respectively. In how many ways an examinee can answer 6 questions taking at least 2 from group A, at least 2 from group B and at least 1 from group C? | 5 | (0) |
| 6. | (a) | Prove that the proposition pv ~ (p ∧ q) is tautology. | 5 | (0) |
| | (b) | One of the roots of x2 + ax + 8 = 0 is 2 and roots of x2 + ax + b = 0 are equal. Find b. | 5 | (0) |
| 7. | (a) | Determine the time period during which a sum of Rs. 1,234 amounts to Rs. 5,678 at 8% p.a. compound interest, payable quarterly. [Given: log 1234 = 3.0913, log 5678 = 3.7542 and log 1.02 = 0.0086] | 5 | (0) |
| | (b) | | If | | = | | = | | ,show that bccb = caac = abba. |
| 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 sides of a right angled triangle are 3, 4, 5 cm respectively. Find the length of the perpendicular on the largest side from the vertex of the greatest angle. | | (0) |
| | (b) | A bicycle wheel makes 1000 revolutions in moving 4.4 kilometre. Find the radius of the wheel. | | (0) |
| | (c) | A solid cube has volume 125 cu.cm. Find the surface area of the cube. | | (0) |
| | (d) | The circumference of the base of the cylinder is 66 cm and its height is 10 cm. Find the volume of the cylinder. | | (0) |
| | (e) | If the x–intercept of a line is 2 and it passes through the point (1, 3), find the line. | | (0) |
| | (f) | Find the centre and radius of the circle x2 + y2 – 6y = 0. | | (0) |
| | (g) | Find the focus and length of the latus rectum of the parabola y2 = 4ax which passes through the point (–1, 3). | | (0) |
| | (h) | | Determine the eccentricity of the hyperbola | | – | | = 1. |
| | (0) |
| 9. | (a) | Find the area of the road which is 7 metre wide and is around but outside a circular park, whose circumference is 88 metre. What would be the total cost to develop the road at the rate of Rs. 100 per sq. metre and to develop the park at the rate of Rs. 150 per sq. metre? | 5 | (0) |
| | (b) | A (1, 2) and B (5, –2) are two given points on the xy–plane on which C is a moving point such that the value of area of the triangle ABC is 12 sq. units. Find the equation to the locus of C. | 5 | (0) |
| 10. | (a) | How many solid cylindrical iron rods of 3.5 cm radius and 1.6 dcm length may be moulded by melting three solid iron spheres of 14 cm diameter? | 5 | (0) |
| | (b) | Find the equation of an ellipse whose principal axes are long the coordinate axes, whose eccentricity is | √ | | and length of latus rectum is | | √6. |
| 5 | (0) |
| 11. | (a) | A right prism has a triangular base whose sides are 13 cm, 20 cm and 21 cm. If the altitude of the prism is 9 cm, find the volume and total surface area of the prism. | 5 | (0) |
| | (b) | Find the equation of the straight line passing through the point of intersection of the lines 2x + y = 4 and x – y + 1 = 0 and is perpendicular to the line 3x – 5y + 7 = 0. | 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) | Find the geometric mean of 8 observations: 2 occurring 4 times, 4 occurring twice, 8 and 32 occurring once each. | | (0) |
| | (b) | | Find the harmonic mean of the observations | | , | | | , | | , | | and | |
| | (0) |
| | (c) | If the means of two groups of m and n observations are 40 and 50 respectively and the combined group mean is 42, find the ratio m : n. | | (0) |
| | (d) | | For a group of 5 items | 5
Σ
i=1 | (xi – 4) = 40 and | 5
Σ
i=1 | xi2 = 1600. Find the variance of the group. |
| | (0) |
| | (e) | Compute the standard deviation of 6 numbers 5, 5, 5, 7, 7, 7. | | (0) |
| | (f) | Determine the mean deviation about the mean of six observations: 4, 4, 4, 6, 6, 6. | | (0) |
| | (g) | Means and standard deviations of runs of 10 innings of two players are as follows: First player
Second player | :
: | mean = 50, s.d. = 4.
mean = 40, s.d. = 5. |
Player who is more consistent in scoring runs? | | (0) |
| | (h) | Which group is more skewed? Group I
Group II | :
: | a.m. = 20, mode = 25, s.d. = 8;
a.m. = 18, mode = 27, s.d. = 9. |
| | (0) |
| 13. | (a) | Prepare a frequency distribution table with the help of tallymarks for the words in the expression given below taking number of letters in the words as a variable: “Business Mathematics and Statistics Fundamentals in the Institute of Cost and Works Accounts of India”. Also calculate the mean, median and mode of the distribution. | 5 | (0) |
| | (b) | Find the mean and variance of first 10 natural numbers. | 5 | (0) |
| 14. | (a) | Calculate the median of the table given below: Class interval
Frequency | :
: | 0–10
5 | 10–20
4 | 20–30
6 | 30–40
3 | 40–50
2 |
| 5 | (0) |
| | (b) | The means of two samples of sizes 50 and 100 are 54.4 and 50.3 and their standard diveations are 8 and 7 respectively. Obtain the mean and standard deviation of the combined sample of size 150. | 5 | (0) |
| 15. | (a) | In a distribution mean = 65, median = 70, coefficient of skewness = –0.6. Find the mode and coefficient of variation. | 5 | (0) |
| | (b) | Draw the histogram of the following data and comment on the shape of the distribution. Wages (in Rs.)
No. of employees | :
: | 50–59
8 | 60–69
10 | 70–79
16 | 80–89
12 | 90–99
7 |
| 5 | (0) |
