This Paper has

**49**answerable questions with**0**answered.C—4(BMSF)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 there 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 3, x and 27 are in continued proportion, find x. | 1 | (0) | ||

(b) | What number is to be added to each term of the ratio 2:5 to make it 3:4 | 1 | (0) | |||

(c) | If p exceeds q by 20%, find the percentage by which q is less than p? | 1 | (0) | |||

(d) | An employer pays wages Rs. 60 per male worker and Rs. 45 per female worker each per day. If he engages 8 male and 4 female workers on some day then find the average wage per worker on that day. | 2 | (0) | |||

2. | (a) | At the same rate of simple interest a principal amounts to Rs. 2056 in 4 years and amounts to Rs. 2248 in 7 years. Find the rate of interest and the principal. | 5 | (0) | ||

(b) | Two men will have equal income if the income of one be increased by 7% and that of the other be reduced by 7½%. If their total income is Rs. 8379, find their incomes. | 5 | (0) | |||

3. | (a) | If the difference between true discount and Banker’s discount is Rs. 20, find the amount of the bill for a sum due in 6 months at 4% per annum. | 5 | (0) | ||

(b) | A person drove his car for first 20 km and then 30 km at an average speed of 20km and 30km per hour respectively. At what speed must he drive next 50km if the average speed of the whole distance of his driving is 40km per hour? | 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=5 | ||||

(a) | Simplify: 3√–8 + 2 √–18 | (0) | ||||

(b) | Express √3 as a surd of twelfth order. | (0) | ||||

(c) | Evaluate log_{0.01} (0.001). | (0) | ||||

(d) | Form a quadratic equation whose roots are 2 and 3. | (0) | ||||

(e) | If (a + b) varies as (a – b), prove that a^{2}+b^{2} varies as b^{2}. | (0) | ||||

(f) | Simplify 4P_{2} – 4C_{2} | (0) | ||||

(g) | If A = {1, 2, 3, 4}, B = {2, 4, 5, 8}, C = {3, 4, 5, 6, 7}, find A ∪ (B ∪ C). | (0) | ||||

5. | (a) | The equations x^{2} + 2(p + 2)x + 9p = 0 has equal roots. Find the values of p. | 5 | (0) | ||

(b) | Prove that ^{2n}P_{n} = 2^{n} {1. 3. 5 ..... (2n – 1)} | 5 | (0) | |||

6. | (a) | The expenses of a boarding house are partly fixed and partly varies with the number of boarders. The charge is Rs. 70 per head when there are 20 boarders and Rs. 60 per head when there are 40 boarders. Find the charge per head when there are 50 boarders. | 5 | (0) | ||

(b) | Show by the truth table, p ∧ q = ∼ (∼ p ∨ ∼ q). | 5 | (0) | |||

7. | (a) | A machine is depreciated at the rate of 10% on reducing balance. The original cost of which was Rs. 1,00,000 and the ultimate scrap value was Rs. 37,500. Estimate the effective life of the machine. [Given log 2 = 0.3010 and log 3 = 0.4771]. | 5 | (0) | ||

(b) | Solve by Cramer’s rule: x + y + z =3, x + 2y + 3z = 4, x + 4y + 9z = 6. | 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) | What is the area of the equilateral triangle whose sides are 8cm long? | (0) | ||||

(b) | The circumference of a wheel is 66m. Find its diameter? | (0) | ||||

(c) | How much fencing will be required to fence a square field of 441 square meter? | (0) | ||||

(d) | A right pyramid stands on a square base of side 16cm and has height 15 cm. Find the volume of the pyramid. | (0) | ||||

(e) | Find the point which divides the joining of the points (3,5) and (6,8) by a straight line in the ratio 2:1 internally. | (0) | ||||

(f) | Find the equation of the circle whose center is (3,7) and radius is 5 units. | (0) | ||||

(g) | Find the equation of the straight line which passes through the points (3,4) and making equal intercepts on the two axes. | (0) | ||||

(h) | Find the vertex and the length of latus rectum of the parabola (y + 3)2 = 2 (x +2). | (0) | ||||

9. | (a) | A number of circular pieces of 0.25 cm radius is to be cut from a metal sheet of dimension 11cm by 2cm. Find the possible number of such pieces. | 5 | (0) | ||

(b) | Find vertex, axis, focus and length of the latus rectum of the curve x^{2} – 6x – 3y = 3. | 5 | (0) | |||

10. | (a) | A (–5,3) and B (2,4) are two fixed points. If a point P moves in the (x – y) plane such that PA : PB = 3:2. Find the equation to the locus of p. | 5 | (0) | ||

(b) | A hollow cylinder of iron with height 32cm, internal and external radii 4cm and 5cm respectively, is melted to form a solid sphere. Find the radius of the sphere. | 5 | (0) | |||

11. | (a) | Find the equation of the straight line passing through (2, 3) and is perpendicular to 3x – 5y + 7 = 0. | 5 | (0) | ||

(b) | The major and minor axes of an ellipse are the x and y axes respectively. Its eccentricity is 1/√2 and the length of the latus rectum is 3 units. Find the equation of the ellipse. | 5 | (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. | Answer any five of the following: | 2x5 | |||||||||||||||||||||

(a) | Find the median of the 10 observations : 9, 4, 6, 2, 3, 4, 4, 6, 8, 7. | (0) | |||||||||||||||||||||

(b) | If the relation between two variables x and y be 2x + 5y = 24 and mode of y be 4, find the mode of x. | (0) | |||||||||||||||||||||

(c) |
n respectively. | (0) | |||||||||||||||||||||

(d) |
| (0) | |||||||||||||||||||||

(e) | If the relation between two variables x and y be 2x – y + 3 =0 and range of x be 10, then find the range of y. | (0) | |||||||||||||||||||||

(f) | The mean of 10 observations was found to be 20. Later one observation 24 was wrongly noted as 34. Find the correct mean. | (0) | |||||||||||||||||||||

(g) | Runs made by two groups G1 and G2 of cricketers have means 50 and 40 and variances 49 and 36 respectively. Find which group is more consistent in scoring runs. | (0) | |||||||||||||||||||||

(h) | Calculate which of the following two distributions is more skewed? (i) mean = 22, mode = 20, s.d. = 2, (ii) mean = 24, mode = 18, s.d. = 3. | (0) | |||||||||||||||||||||

13. | (a) | The expenditure during a year in a state is shown as below:
| 5 | (0) | |||||||||||||||||||

(b) | The variance of a series of numbers 2, 3, 11 and x is 12¼. Find the values of x. | 5 | (0) | ||||||||||||||||||||

14. | (a) | Draw a histogram to represent the following distributions:
| 5 | (0) | |||||||||||||||||||

(b) | Find the mean deviation about the mean of the following series:
| 5 | (0) | ||||||||||||||||||||

15. | (a) | Calculate the median of the following frequency distribution:
| 5 | (0) | |||||||||||||||||||

(b) | The mean and standard deviation of the marks obtained by the groups of the students consisting of 50 each are given below:
Calculate the mean and standard deviation of the marks obtained by all 100 students. | 5 | (0) |