This Paper has

**50**answerable questions with**0**answered.P—4(BMS)Syllabus 2008 | |

Time Allowed : 3 Hours | Full Marks : 100 |

Answer all questions. |

The figures in the margin on the right side indicate full marks. |

Notations and symbol have usual meanings |

SECTION I (Arithmetic — 10 marks) |

Marks |

1. | Answer any two of the following: Choose the correct option showing the proper reasons/calculations. | 3x2 | ||||||||||||

(a) | If 2 – x, 3 – x, 5 – x and 7 – x are in proporation,then the value of X is
| (0) | ||||||||||||

(b) | The average of 10 numbers is 21. If an additional number is included the average becomes 20. The additional number is
| (0) | ||||||||||||

(c) | True discount of a bill value due in 2 years at 4% per annum. Simple interest is Rs.40. Then bill value is
| (0) | ||||||||||||

2. | Answer any one of the following. | 4x1 | ||||||||||||

(a) | Due to fall in rate of interest from 12% to 10% per annum in 4 years, home loan amount of a person decreases by Rs. 4800. Find the home loan he took first. | (0) | ||||||||||||

(b) | At what ratio sugar at Rs. 30 per kg be mixed with sugar at Rs. 35 per kg to produce a mixture making profit 25% when sold at Rs. 40 per kg? | (0) |

SECTION II (Algebra — 15 marks) |

Marks |

3. | Answer any three of the following: Choose the correct option showing necessary reasons/calculations. | 3x3 | |||||||||||||||||||||||||

(a) | The number of ways in which 9 different things can be divided into 3 groups containing 2, 3 and 4 things respectively is
| (0) | |||||||||||||||||||||||||

(b) |
| (0) | |||||||||||||||||||||||||

(c) | If c varies directly as x + b, c = 8 when b = 2 and c = 10 when b = 3 then value of x is
| (0) | |||||||||||||||||||||||||

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

(e) | Let p be " the student is a girl " and q be " the student is studious". Then the symbolic form of the statement " the student is a boy but he is not studious " is
| (0) | |||||||||||||||||||||||||

4. | Answer any two of the following: | 3x2 | |||||||||||||||||||||||||

(a) | In a class of students 20 passed in Statistics, 25 passed in Mathematics and 10 passed in Statistics but not in Mathematics. Find the number of students who passed in Mathematics but not in Statistics. | (0) | |||||||||||||||||||||||||

(b) | Solve : 2^{x + 1} + 2^{x – 1} = 160 | (0) | |||||||||||||||||||||||||

(c) |
| (0) |

SECTION III (Mensuration — 15 marks) |

Marks |

5. | Answer any three of the following: Choose the correct option showing necessary reasons/calculations. | 3x3 | |||||||||||||||||

(a) | The perimeter of a rectangale, having area 18 sq cm and its length being twice its breadth, is
| (0) | |||||||||||||||||

(b) |
| (0) | |||||||||||||||||

(c) | If the diameter of the base of a cylinder is equal to its height and its volume is 2156 cc,
| (0) | |||||||||||||||||

(d) | The radius of a sphere is 3 cm. It is melted and drawn into a wire of diameter 0.2 cm. Then length of the wire (in cm) is
| (0) | |||||||||||||||||

(e) | Three sides of a cuboid are 18, 37.5 and 40 cm. Then the edge of that cube whose volume is equal to this cuboid is
| (0) | |||||||||||||||||

6. | Answer any two of the following: | 3x2 | |||||||||||||||||

(a) | If the area of an equilateral triangle is √3 sq cm then find the perimeter of the triangle. | (0) | |||||||||||||||||

(b) |
| (0) | |||||||||||||||||

(c) | A right pyramid stands on a base 12 cm square and its height is 8 cm. Find the slant surface area of it. | (0) |

SECTION IV (Co–ordinate Geometry — 10 marks) |

Marks |

7. | Answer any two of the following: Choose the correct option showing proper reasons/calculations. | 3x2 | ||||||||||||

(a) | If x (2,a), y (3,–1) and z(4,–5) are collinear then a is
| (0) | ||||||||||||

(b) | A line passing through (1,3) and perpendicular to the line 2x – 3y = 7 is
| (0) | ||||||||||||

(c) | The length of intercept of the circle x ^{2} + y^{2} – 2x – 10y + 22 = 0 on the line x = 1 is
| (0) | ||||||||||||

(d) | For the parabola y^{2} = 4x intersecting the line y + 4 = 2x, the length of the chord thus formed is
| (0) | ||||||||||||

8. | Answer any one of the following: | 4x1 | ||||||||||||

(a) | In the hyperbola 25 y^{2} – 16 x^{2} = 400, find the equation of latus rectum and length of the axes. | (0) | ||||||||||||

(b) | Find the equation of the ellipse whose focii are (2,0), (–2,0) and eccentricity is ⅓ | (0) |

SECTION V (Calculus — 15 marks) |

Marks |

9. | Answer any three of the following: Choose the correct option showing proper reasons/calculations. | 3x3 | ||||||||||||||||||||||||

(a) |
| (0) | ||||||||||||||||||||||||

(b) |
| (0) | ||||||||||||||||||||||||

(c) |
| (0) | ||||||||||||||||||||||||

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

(e) | If u = x^{2}y + y^{2}z + z^{2} x then u _{x} + u_{y} + u_{z} is
| (0) | ||||||||||||||||||||||||

10. | Answer any two of the following: | 3x2 | ||||||||||||||||||||||||

(a) |
| (0) | ||||||||||||||||||||||||

(b) |
| (0) | ||||||||||||||||||||||||

(c) |
| (0) |

SECTION VI (Statistical Methods — 35 marks) |

Marks |

11. | Answer any seven of the following: Choose the correct option showing proper reasons/calculations. | 3x7 | |||||||||||||||||||||||||||||||

(a) | If 1 , 2 , 3 , 4 occur with respective frequencies 1 , 2 , 3 , 4 then their arithmetic mean is
| (0) | |||||||||||||||||||||||||||||||

(b) | In a group of 150 observations the arithmetic mean is 60 and arithmetic mean of first 100 observations of the group is 50. Then arithmetic mean of the remaining observations of the group is
| (0) | |||||||||||||||||||||||||||||||

(c) | If the observations 2,4,8 and 16 occur 8 , 6 , 4 and 2 times respectively then the geometric mean of the observations is
| (0) | |||||||||||||||||||||||||||||||

(d) | If the arithmetic mean of 10 observations x_{1}, x_{2} , .....x_{10} is 20 then harmonic mean of 10
| (0) | |||||||||||||||||||||||||||||||

(e) | If the Variables x and y are related by 3x – 2y + 6 = 0 and the range of x is 10 then range of y is
| (0) | |||||||||||||||||||||||||||||||

(f) | If sum of deviations of 4 values about 2 is 4and standard deviation of those 4 values is 2 then sum of squares of the 4 observations is
| (0) | |||||||||||||||||||||||||||||||

(g) | Mean deviation about mean of first 6 positive integers is
| (0) | |||||||||||||||||||||||||||||||

(h) | The median of the following distribution
| (0) | |||||||||||||||||||||||||||||||

(i) | If the mean and coefficient of variation of x are 10 and 50% respectively, then the standard deviation of 3 – 2x is
| (0) | |||||||||||||||||||||||||||||||

(j) | If the coefficient of skewness,mean and variance of a set of values are –3 , 40 and 4 respectively then median of the values is
| (0) | |||||||||||||||||||||||||||||||

12. | (a) | Answer any two of the following: | 5x2 | ||||||||||||||||||||||||||||||

(i) | Tabulate the following data in a suitable tabular form "2000 men and 1600 women participated in a poll on the opinion about a certain measure. 1200 persons of whom 800 were male, voted against the measure. In all 1800 persons voted for the measure and 300 women were in different. " Find percentage of women voted against the measure. | (0) | |||||||||||||||||||||||||||||||

(ii) | Find mean and median of the following frequency distribution. Then calculate the mode using the empirical relation between them.
| (0) | |||||||||||||||||||||||||||||||

(iii) | For a group containing 90 observations the mean and standard deviation are 59 and 9 respectively. For 40 observations of them mean and standard deviation are 54 and 6 respectively. Find the mean and standard deviation of the remaining 50 observations. | (0) | |||||||||||||||||||||||||||||||

(b) | Write short note on any one of the following: | 4x1 | |||||||||||||||||||||||||||||||

(i) | Pie Chart, | (0) | |||||||||||||||||||||||||||||||

(ii) | Dispersion of data. | (0) |