This Paper has

**32**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) | Number of candidates in a certain examination is increased by 25%. In the last term the strength was 880. Find the present strength of the examinees. | 1 | (0) | ||||||||||||||

(b) | Speed of a car to go up a hill is 10 km per hour and to go down is 20 km per hour. Compute its average speed. | 2 | (0) | |||||||||||||||

(c) | A person has deposited Rs. 78,000 in Post Office Monthly Interest Scheme (MIS) after retirement at 7% p.a. Calculate his monthly income. | 2 | (0) | |||||||||||||||

2. | (a) | Monthly income of two persons Ram and Rahim are in the ratio 5 : 7 and their monthly expenditures are in the ration 7 : 11. If each of them saves Rs. 60 per month, determine their monthly incomes. | 5 | (0) | ||||||||||||||

(b) | In a firm out of 1200 employees 650 are males and rest are females. Average monthly wages of males is Rs. 4,500 and females is Rs. 5,000. Find the average wage paid by the firm. | 5 | (0) | |||||||||||||||

3. | (a) | A property of value of Rs. 45,000 passes to another, due to death of its owner, and the rates of duty charged are as follows:
| 5 | (0) | ||||||||||||||

(b) | Calculate Banker’s Gain on a bill of Rs. 2,500 due in 6 months at 5% 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 2^{m+4} −2^{m+2} = 3. find m^{7}. | 3 | (0) | |||||||||||||||

(b) | Evaluate (2√3)^{2} x (−3√−2)^{2} | 2 | (0) | ||||||||||||||||

5. | (a) | Show that (p∧q) ∧~ (p∨q) is a contradiction. | 5 | (0) | |||||||||||||||

(b) | 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 25 boarders and Rs. 60 per head when there are 50 boarders. Find the charge per head when there are 100 boarders. | 5 | (0) | ||||||||||||||||

6. | (a) | The population of a country increases every year by 2.4% of the population at the beginning of that year. In what time will the population double itself? Answer to the nearest year. | 5 | (0) | |||||||||||||||

(b) | If ∝ and β be the roots of 2x^{2} + 3x + 7 = 0. Find out the values of ∝^{2} + β^{2} and ∝β^{−1} + β∝^{−1}. | 5 | (0) | ||||||||||||||||

7. | (a) | In how many ways 6 books out of 10 different books can be arranged in a bookshelf so that 3 particular books are always together? | 5 | (0) | |||||||||||||||

(b) | Show that:
| 5 | (0) |

Section C |

MENSURATION (30 marks) |

Answer Question No.8 (compulsory – 6 marks) and any two (12 x 2 = 24 marks) from the rest. |

8. | (a) | The three sides of a triangle are 3, 4 and 5 cm respectively; find its area. | 2 | (0) | |||||||||||

(b) | The circumference of a circle is 44 cm. Find the perimeter of its semicircle. | 2 | (0) | ||||||||||||

(c) | Find the equation to the straight line which passes through the point (5, –5) and is perpendicular to the line: 7x – 9y + 11 = 0. | 2 | (0) | ||||||||||||

9. | (a) | A solid metal cylinder with height 45 cm and diameter 4 cm is melted to get a number of spheres with diameter 6 cm. Find the number of such spheres. | 6 | (0) | |||||||||||

(b) | A point P (x, y) moves in such a way that sum of its distances from the points (0, 2) and (2, 0) is 6 units. Find the equation to the locus of P. | 6 | (0) | ||||||||||||

10. | (a) | The radil of a frustum of a right circular cone are 6 cm and 4 cm respectively. If the height of the frustum is 5 cm, find the volume of the frustum. | 6 | (0) | |||||||||||

(b) | Find the equation of the ellipse whose foci are (–3, 0) and (3, 0) and whose eccentricity is ¼. | 6 | (0) | ||||||||||||

11. | (a) |
| 6 | (0) | |||||||||||

(b) | How many litres of water flows out of a pipe of cross–sectional area 5 cm^{2} in 1 minute if the speed of the water in the pipe is 30 cm/sec. | 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 A.M. of first 10 natural numbers. | 2 | (0) | ||||||||||||||||||||||||||||

(b) |
What will be G.M. if ‘0’ is added to above set of values? | 2 | (0) | |||||||||||||||||||||||||||||

(c) | Find the mode of the following frequency distribution:
| 2 | (0) | |||||||||||||||||||||||||||||

13. | (a) | Following data represent the proposed outlay during a plan period:
Using this table draw a pie–chart to represent the above data. | 4 | (0) | ||||||||||||||||||||||||||||

(b) | Following is the statement of marks obtained by 150 students in a supplementary examination:
| 8 | (0) | |||||||||||||||||||||||||||||

14. | The A.M. of the following frequency is 1.46. Find f_{1} and f_{2}
Also find coefficient of variation. | 12 | (0) | |||||||||||||||||||||||||||||

15. | (a) | For the numbers 5, 6, 7,6 8, 10, 12, if S_{1} and S_{2} be the respective Root–Mean–Square Deviation about the mean and about an arbitrary number 9, show that 17 S_{2}^{2} = 20 S_{1}^{2}. | 6 | (0) | ||||||||||||||||||||||||||||

(b) | A sample of 35 values has mean 80 and variance 16. A second sample of 65 values from the same population has mean 70 and s.d. 3. Find s.d. of the combined sample of 100 values. | 6 | (0) |