This Paper has 34 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. |
| Section A |
ARITHMETIC (15 marks)
Answer Question No. 1 (compulsory – 5 marks) and any one (10 marks) from the rest. |
| Marks |
| 1. | (a) | The work done by n – 1 persons in n + 1 days is to the work done by n + 1 persons in n + 2 days be in the ratio of 5 : 6; find ‘n’. | 2 | (0) |
| | (b) | The mean of 3 numbers is 15. With inclusion of a fourth number, the mean becomes 17. Find the included number. | 1 | (0) |
| | (c) | Given T.D. = Rs. 10 and P.V. = Rs. 200; find B.G. | 2 | (0) |
| 2. | (a) | A bill of exchange drawn on 5.1.1983 for Rs. 2,000 payable at 3 months was accepted on the same date and discounted on 14.1.83 at 4% p.a. Find out amount of discount. | 5 | (0) |
| | (b) | A dealer offers an item for Rs. 270 cash down or Rs. 30 cash down and 18 equal monthly installments of Rs. 15 each. Find the rate of simple interest charged. | 5 | (0) |
| 3. | (a) | Two vessels contain mixtures of milk and water in the proportion 2 : 3 and 4 : 3 respectively. In what proportions should the two mixtures be mixed so as to form a new mixture containing equal quantities of milk an water? | 5 | (0) |
| | (b) | Monthly rainfall from June to September of a certain year was 12.5 cm, 27.04 cm, 20.05 cm and 6.29 cm respectively. Find the average daily rainfall during these four months. | 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) | Evaluate i–13. | 1 | (0) |
| | (b) | Draw a Venn diagram for three non–empty sets A, B, C which satisfy following:
A ⊂ (B ∩ C); B ⊂ C; C ≠ B and C ≠ A. | 2 | (0) |
| | (c) | In how many ways can the letters of the word SANCHIT be arranged? | 2 | (0) |
| 5. | (a) | As the number of units manufactured increases from 6,000 to 8,000, the total cost of production increases from Rs. 33,000 to Rs. 40,000. Find the relationship between y, the cost and x, the number of units made, considering the relationship as linear. Hence obtain the total cost of production, if the number of units manufactured is 10,000. | 5 | (0) |
| | (b) | | If x = log | | , y =log | | and z = 2log | | , prove that 5x + y - z = 1 |
| 5 | (0) |
| 6. | (a) | If the roots of the equation x2 + ax – b = 0 differ by unity, prove that a2 + 4b – 1 = 0. | 5 | (0) |
| | (b) | In how many ways can a committee of 4 women and 3 men be formed from 10 women and 6 men? what is the number of ways if Ms. X and Mr. Y refuse to join the committee? | 5 | (0) |
| 7. | (a) | | 5 | (0) |
| | (b) | construct the truth table for –[(p ∨ q) ∧ (− p ∨ − q)] (by usual notations). | 5 | (0) |
| Section C |
| (Mensuration — 30 marks) |
| Answer Question No. 8 (compulsory — 6 marks) and any two (12x2=24 marks) from the rest. |
| 8. | (a) | | Find the perimeter of a semi-circle of diameter 7 cm | |
| 2 | (0) |
| | (b) | The perimeter of a rhombus ABCD is 48 cm and one of the diagonals AC is 8 cm. Show that the other diagonal is 16√2 cm. | 2 | (0) |
| | (c) | Find the equation of a straight line passing through (–2, 5) and parallel to x–axis. | 2 | (0) |
| 9. | (a) | A circle of radius 7 cm is inscribed within a square touching the sides. Find the area of one fillet thus formed. Also determine the area of 1 cm wide path that surrounds the square. | 6 | (0) |
| | (b) | In what ratio is the join of the points (4, –1) and (5, 3) divided by the line x + 3y – 8 = 0? | 6 | (0) |
| 10. | (a) | The radius of a sphere is 3 cm. It is melted and formed into a wire of diameter 0.2 cm. Find the length of the wire. | 6 | (0) |
| | (b) | A (2, 0) and B (4, 0) are two given points. A point p moves such that PA2 + PB2 = 10. Find the locus of P. | 6 | (0) |
| 11. | (a) | Find the equation to the circle which passes through the points (4, 1) and (6, 5) and has its centre on the line 4x + y = 16. | 6 | (0) |
| | (b) | The ordinate of a point on the parabola y2 = 4ax is twice the latus rectum of the parabola. Find the relation between abscissa and ordinate of the point. | 6 | (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 the numbers | | , | | , | | , | | , 1. |
| 2 | (0) |
| | (b) | The mean, median and coefficient of variation of 100 items are found to be 90, 84 and 60. Find coefficient of skewness. | 2 | (0) |
| | (c) | | If x is A.M of the observations x1, x2,......,xn then show that | n
Σ
i = 1 | |
| 2 | (0) |
| 13. | (a) | Draw the ‘greater–than’ ogive curve on the basis of the data given below and then find graphically the value of Q3: | Class limits | 10–19 | 20–29 | 30–39 | 40–49 | 50–59 | 60–69 | 70–79 | | f | 3 | 8 | 21 | 38 | 15 | 9 | 6 |
| 6 | (0) |
| | (b) | Draw a pie chart to represent the following data relating to export of cotton (in ’000 bales) by major countries in a certain year: | USA | India | Egypt | Brazil | Argentina | | 6,367 | 2,999 | 1,688 | 650 | 202 |
| 6 | (0) |
| 14. | (a) | A.M. of following distribution is 56.47. Find the missing frequencies: | Daily wages Rs. | 45 | 50 | 55 | 60 | 65 | 70 | 75 | Total | | f | 5 | 48 | — | 30 | — | 8 | 6 | 150 |
| 6 | (0) |
| | (b) | Calculate median of the following distribution: | Class Interval | 0–10 | 10–20 | 20–30 | 30–40 | 40–50 | | No. of observations | 5 | 4 | 6 | 3 | 2 |
| 6 | (0) |
| 15. | (a) | Five students obtained the marks 63, 64, 69, 60 and 66 in mathematics class test. Find the mean deviation of their marks about the median mark. | 4 | (0) |
| | (b) | The scores of two batsmen A and B during a certain cricket season are following: | A | 5 | 7 | 16 | 27 | 39 | 53 | 56 | 61 | 80 | 101 | 105 | | B | 0 | 4 | 16 | 21 | 41 | 43 | 57 | 78 | 83 | 90 | 95 |
Indicate which of the above batsman is more consistent in scoring. | 8 | (0) |
