This Paper has

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

Time Allowed : 3 Hours | Full Marks : 100 |

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

Answer all questions. |

Notations and symbols 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) | Let marks obtained by Ram, Rahim and Jadu be A, B and C respectively. Given A : B = 1 : 2, B : C = 3 : 4. The combined ratio A:B:C is
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(b) |
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(c) | The time, in which the discount on amount Rs. 550 due is Rs. 50 at 4% per annum, is
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2. | Answer any one of the following. | 4x1 | |||||||||||||||||||||||||

(a) |
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(b) | A person borrowed Rs. 10,000 at some simple interest rate for 2 years. After expiry of one year he borrowed another Rs. 20,000 at 1% lower interest rate for 1 year. At the end he paid fully Rs. 33,000. Find the rate of interest at which he borrowed first. | (0) |

SECTION II (Algebra — 15 marks) |

Marks |

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

(a) |
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(b) |
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(c) | The value of log_{2} log_{2} log_{3} 81 is
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(d) |
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(e) | If^{m}c_{6} : ^{m–3}c_{3} = 91 : 4, then the value of m is
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4. | Answer any two of the following: | 3x2 | |||||||||||||||||||||||||||||||||||||||||||

(a) | Find the square root of x + √x^{2} – y^{2}. | (0) | |||||||||||||||||||||||||||||||||||||||||||

(b) | The total expenses of a boarding house varies partly with the number of boarders and partly fixed. The total expenses are Rs. 10,000 for 25 boarders and Rs. 11,500 for 30 boarders. Find the fixed expenses. | (0) | |||||||||||||||||||||||||||||||||||||||||||

(c) | Of 50 students appearing in an examination 20 failed in Mathematics, 25 failed in English and 10 failed in both. Find the number of students of those 50 students who passed in both Mathematics and English. Write the formula you use completely. | (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 area of the equilateral triangle with a side of length 2 cm is
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(b) | A circular garden having diameter 60 ft. has a path of width 10 ft. surrounding outside the garden. Area of the path is
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(c) | A rectangular parallelopiped has length 20 cm, breadth 10 cm, and height 5cm. the total surface area of it is
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(d) | For a solid right circular cylinder of height 9 cm and radius of 7 cm the total surface area is
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(e) | The diameter of the base of a conical tent is 14 ft, and height of the tent is 15 ft. The volume of the space covered by the tent is
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6. | Answer any two of the following: | 3x2 | ||||||||||||||||||||

(a) | The area of a rectangle is 96 sq.cm and its perimeter is 40 cm, what are its length and breadth? | (0) | ||||||||||||||||||||

(b) | Find the quantity of water in litre flowing out of a pipe of cross–section area 5 cm^{2} in 1 minute if the speed of the water in the pipe is 30 cm/sec. | (0) | ||||||||||||||||||||

(c) | The volumes of two spheres are in the ratio 8 : 27 and the difference of their radii is 3 cm. Find the radii of both the spheres. | (0) |

SECTION IV (Coordinate Geometry — 10 marks) |

Marks |

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

(a) | The equation of a straight line passing through origin and perpendicular to the line 2x + 3y + 1 = 0 is
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(b) | Eccentricity of the hyperbola 9x^{2} – 16y^{2} = 36 is
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(c) | The equation of a parabola whose vertex and axis are (0, 0) and y = 0 respectively, passing through (5, 4), is
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8. | Answer any one of the following: | 4x1 | ||||||||||||||||||||

(a) |
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(b) | Find the equation of the circle which is concentric to the circle x^{2} + y^{2} + 8x – 10y + 5 = 0 and passes through the point (4, 11). | (0) |

SECTION V (Calculus — 15 marks) |

Marks |

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

(a) |
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(b) |
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(c) |
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(d) |
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(e) |
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10. | Answer any two of the following: | 3x2 | |||||||||||||||||||||

(a) |
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(b) | If y = (x + √1 + x^{2})^{m}, show that (1 + x^{2})y_{2} + xy_{1} = m^{2}y. | (0) | |||||||||||||||||||||

(c) |
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SECTION VI (Statistical Methods — 35 marks) |

Marks |

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

(a) | Arithmetic mean of 5 observations is 8. After calculation it was noted that observations 10 and 20 have been wrongly taken in place of correct values 15 and 25 respectively. The correct mean is
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(b) | Two groups of 10 and 15 observations have means 10 and 20 respectively. Then grouped mean is
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(c) | Geometric mean of first group of 5 observations is 8 and that of second group of 4 observations is 128√2. Then grouped geometric mean is
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(d) |
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(e) | If the two observations have harmonic mean and geometric mean 9 and 15 respectively, then arithmetic mean of the two observations
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(f) | If the two variables x and y are related by 2x + 3y = 12 and standard deviation of x is 6 then standard deviation of y is
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(g) |
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(h) | Mean deviation about mean is 5.8. Coefficient of mean deviation about mean is 0.2. Then mean is
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(i) | For a group of 10 observations, ∑x = 452, ∑x^{2} = 24270 and mode 43.7 the coefficient of skewness is
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(j) | The mean and coefficient of variation of runs made by a batsman in 10 innings are 40 and 125% respectively. Then s.d. of the runs made by the batsman is
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12. | (a) | Answer any two of the following: | 5x2 | |||||||||||||||||||||||||

(i) | Find the median and mode of the following grouped frequency distribution:
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(ii) | Prove that for any two positive real quantities AM ≥ GM ≥ HM. | (0) | ||||||||||||||||||||||||||

(iii) | The following are the sizes of 50 families in a village: 2, 3, 4, 5, 4, 3, 2, 6, 1, 3, 5, 3, 5, 5, 4, 2, 4, 4, 3, 3, 3, 2, 4, 4, 3, 3, 2, 3, 4, 3, 5, 4, 2, 3, 4, 4, 2, 4, 4, 2, 6, 4, 3, 5, 4, 3, 2, 3, 3, 1. Obtain the frequency distribution of the family size and calculate the mean deviation about mean of the family size. | (0) | ||||||||||||||||||||||||||

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

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

(ii) | Primary data. | (0) |