This Paper has 30 answerable questions with 0 answered.
C—4(BMSF)
Revised Syllabus |
| Time Allowed : 3 Hours | Full Marks : 100 |
| Section A |
ARTHMETIC (15 marks)
Answer Question No. 1 (compulsory – 5 marks) and any one from the rest (10 marks). |
| Marks |
| 1. | (a) | A man invested his savings as follows: | Rs. 10,000 in Post Office Savings Bank at 8% p.a. | | Rs. 6,000 in a National Bank at 7% p.a. | | Rs. 4,000 in a Private Firm at 10% p.a. |
Find the average rate of interest per cent p.a. | 3 | (0) |
| | (b) | The ratio of present age of father to that of his son is 5:3. Ten years before the ratio was 2:1. Find the present ages. | 2 | (0) |
| 2. | (a) | | If x1, x2, ......., xn be in continued proportion, show that | | = | { | | } | n – 1 |
| 5 | (0) |
| | (b) | There are four containers of milk and water in the ratio of 2:1, 3:2, 5:3 and 7:5. A mixture is prepared with equal quantities drawn from the four containers. Find the ratio of milk to water in the final mixture. | 5 | (0) |
| 3. | (a) | Compute the Banker’s Gain (B.G.) on a bill of Rs. 2,500 due in 6 months at 5% p.a. | 5 | (0) |
| | (b) | A bill for Rs. 12,750 was payable on two months (30 days a month) after sight. It was accepted on September 4 and discounted on September 25. Find the discounted value of the bill, the rate being 3½% p.a. | 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. | (a) | If U = {1, 2, 3, 4, 5, 6, 7}, A= {2, 4, 6}, B = {1, 3, 5, 7} where U is the universal set,
show that (A∪B)c = Ac ∪ Bc. | 3 | (0) |
| | (b) | | If | | = x + iy, where x and y are real and i = √−1, find the value of x and y. |
| 2 | (0) |
| 5. | (a) | | If | | = | | prove that | | a2 + ab + b2 | | a2 – ab + b2 |
| = | |
| 4 | (0) |
| | (b) | Solve the following system of linear equations: | x + y − z = 1 | | 8x + 3y − 6z = 1 | | − 4x − y + 3z = 1 | | using Cramer’s rule. |
| 6 | (0) |
| 6. | (a) | The expenses of a hotel are partly fixed and the rest varies as the number of boarders. When the number of boarders are 450, the expense is Rs. 1,800 and when the number of boarders is 920, the expense Rs. 3,210. Find the expenses per head when there are 100 boarders. | 5 | (0) |
| | (b) | | If p ≠ q and p2 = 5p − 3, q2 = 5q − 3, from a quadratic equation whose roots are | | and | |
| 5 | (0) |
| 7. | (a) | | Evaluate: | | 2 log 6 + 6 log 2 | | 4 log 2 + log 27 − log 9 |
|
| 5 | (0) |
| | (b) | A cricket club consists of 16 members of which only 6 can bowl. Find the number of ways in which eleven players be chosen to include at least 4 bowlers. | 5 | (0) |
| Section C |
| MENSURATION (25 marks) |
| Answer Question No.8 (compulsory – 5 marks) and any two (10 x 2 = 20 marks) from the rest. |
| 8. | (a) | The perimeter of a rectangle is 25.5 m. Its length is 9.5 m. Find its area. | 2 | (0) |
| | (b) | The mid points of the sides of a triangle are (1, 4), (4, 8) and (5, 6). Find the co–ordinates of the vertices of the triangle. | 3 | (0) |
| 9. | (a) | A cubical metal box is open at the top and the cost of painting its inside at Rs. 1.60 per square cm is Rs. 392. The box is wholly filled with a liquid. Find the volume of the liquid. | 5 | (0) |
| | (b) | In the parabola 4(y − 1)2 = − 7(x − 3) find (i) latus rectum, (ii) co–ordinates of focus and vertex. | 5 | (0) |
| 10. | (a) | A bicycle wheel makes 5000 revolutions in moving 11 km. Find the diameter of the wheel. | 5 | (0) |
| | (b) | In a parallelogram ABCD slope of AB = −2, slope of BC = 3/5. Find the (i) gradient of AD; (ii) gradient of altitude to AD and (iii) gradient of height of the triangle ABC. | 5 | (0) |
| 11. | (a) | Two hexagonal coins of the same metal have weights in the ratio 3:2. If the sides are in the ratio 5:2, find the ratio of their thickness. | 5 | (0) |
| | (b) | (i) | The radius of the circle x2 + y2 − 2x + 3y + λ = 0 is 2½. Find the value of λ. | 2 | (0) |
| | | (ii) | Find the eccentricity of the ellipse whose major axis is double the minor axis. | 3 | (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. | (a) | | Find the harmonic mean of | | , | | , | | , | | and 1. |
| 2 | (0) |
| | (b) | Examine the validity of the statement: If each observation in a series is increased by 10, then their A.M. changes but not their standard deviation. | 2 | (0) |
| | (c) | The mean, median and the coefficient of variation of 100 items are found to be 90, 84 and 60. Find the coefficient of skewness of the distribution. | 2 | (0) |
| 13. | The distribution of weight of the students of a school is given below: | Weight (in lbs.) | 100–105 | 105–110 | 110–115 | 115–120 | 120–125 | | No. of students | 105 | 210 | 220 | 300 | 315 |
| (a) | Draw a histogram. | | (b) | Draw both “less than type” and “more than type” “OGIVES” and hence estimate the median. | | (c) | Compute the mean. |
| 12 | (0) |
| 14. | Arithmetic mean of the frequency distribution is Rs. 56.47: | Daily wages in Rs. | 45 | 50 | 55 | 60 | 65 | 70 | 75 | Total | | Frequency | 5 | 48 | – | 30 | – | 8 | 6 | 150 |
| (a) | Find the missing frequencies. | | (b) | Find the mode. | | (c) | Find the standard deviation. | | (d) | Find the coefficient of skewness. |
| 12 | (0) |
| 15. | (a) | Following is the statement of marks obtained by two students A and B in 10 examination papers: | Paper | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | | Marks scored by A | 44 | 80 | 76 | 48 | 52 | 72 | 68 | 56 | 60 | 54 | | Marks scored by B | 48 | 75 | 54 | 60 | 63 | 69 | 72 | 51 | 57 | 66 |
If the consistency of performance is the criterion for awarding a prize, find the prize winner among A and B. | 8 | (0) |
| | (b) | For a distribution Bowley’s coefficient of skewness is − 0.36, Q1 = 8.6 and median = 12.3. Find the coefficient of quartile deviation. | 4 | (0) |
