This Paper has

**50**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) |

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

(a) | 10 years before, the ages of father and son were in the ratio 5:2. If at present their total age is 90 years, the present age of the son is
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(b) | If the speed of a car to go uphill is 20 km/hr and down is 30 km/hr, then average speed of the car is (in km/hr)
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(c) | The difference of Banker's Discount and True Discount for a bill amount of Rs. 2000 due in 5 years at the rate of 5% per annum in Rs. is
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2. | Answer any one of the following. | 4x1 | ||||||||||||

(a) | Two vessels contain mixtures of milk and water in the ratio 5:1 and 9:1. They are mixed together in the ratio 1:5. Find the ratio of milk and water in the final mixture. | (0) | ||||||||||||

(b) | An amount of money at certain rate of simple interest per annum becomes Rs. 2400 in 4 years and Rs. 2500 in 5 years. Find the rate of interest p.a. | (0) |

SECTION II (Algebra — 15 marks) |

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

(a) | If
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(b) | If (a + b) ∝ (a − b) and when a = 6, b = 2, then for b = 3, the value of a is
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(c) | If x = 7 + 4 √3, then the value of √x −
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(d) | The number of ways in which 6 books out of 9 different books can be arranged in a book shelf so that 3 particular books remain together is
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(e) | For the statements p: "it is raining" and q: "it is cloudy", the symbolic form of the statement that "it is neither raining nor cloudy", is
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4. | Answer any two of the following: | 3x2 | ||||||||||||||||||

(a) | In a class of 30 students, 15 students have taken Hindi, 10 students have taken Hindi but not English. All the students in the class have taken at least one of the subjects of English and Hindi. Find the number of students who have taken English but not Hindi. | (0) | ||||||||||||||||||

(b) | Find the value of log
_{2} log_{3} 81 | (0) | ||||||||||||||||||

(c) | The total expenses of a boarding house are partly fixed and the rest varies as the number of boarders. The charges is Rs. 100 per head when there are 25 boarders and Rs. 80 when there are 50 boarders. Find the number of boarders for which the total expense will be Rs. 7000. | (0) |

SECTION III (Mensuration — 15 marks) |

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

(a) | Three sides of a triangle are in the ratio of 3:4:5 and its perimeter is 24 cm. Its area is
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(b) | The sum and difference of the external and inner radii of a circular ring are 14 em and 4 cm respectively. The area of the ring is ( π =
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(c) | Three solid metal cubes with edges 3 ft, 4 ft and 5 ft of same metal are melted without any loss of metal into a single new cube. The surface area of the new cube in sq ft is
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(d) | The volume of two spheres are in the ratio 1 :8. If the sum of their radii is 6 cm then bigger sphere has radius as
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(e) | Slant height and whole surface area of a right circular cone are 7 cm and 147.84 sq cm respectively. The radius of the base of the cone is ( π =
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6. | Answer any two of the following: | 3x2 | ||||||||||||||

(a) | Determine each interior angle of a decagon. | (0) | ||||||||||||||

(b) | Find the area of an equilateral triangle of side 6 cm. | (0) | ||||||||||||||

(c) | If the perimeter and one diagonal of a rectangle are 14 cm and 5 cm respectively, find the area of the rectangle. | (0) |

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

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

(a) | If the x–intercept of a line passing through (1, 3) is 2, then y–intercept of the line is
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(b) | If the diameter of a circle x^{2} + y^{2} + 4x − 7y − k = 0 be 9, then the value of k is
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(c) | Focus of the parabola y^{2} − 8y − 8x + 8 = 0 is
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(d) | The eccentricity of the hyperbola 4x^{2} − 9y^{2} = 36 is
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8. | Answer any one of the following: | 4x1 | ||||||||||||||||||

(a) | Find the equation of a straight line passing through (−4, 3) and being perpendicular to the line passing through points (3, 4) and (6, 8). | (0) | ||||||||||||||||||

(b) | Find the distance between the focii of the ellipse 4x^{2} + 5y^{2} = 20. | (0) |

SECTION V (Calculus — 15 marks) |

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

(a) | If f(x) = x + |x| , the value of f (1) + f (−l) is
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(b) | If f(x) = x + 1, for x ≤ 1 = 5 – ax ^{2}, x > 1 then f(x) is continuous at x = 1,when a is
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(c) | If x = ct and y =
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(d) | If u =
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(e) | The value of
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10. | Answer any two of the following | 3x2 | ||||||||||||||||||||||||

(a) | If y = x^{3} log
^{2} = 0 | (0) | ||||||||||||||||||||||||

(b) | A manufacturer can sell x items per month at a price of Rs. p = 198 − 2x per item. Cost price of those x items is Rs. 2x + 200. How much production will yield maximum profit per month? | (0) | ||||||||||||||||||||||||

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

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

(a) | The arithmetic mean of first n positive odd integers is 10. The value of n is
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(b) | G.M. of the numbers 3, 6, 24 and 48 is
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(c) | If a car moves first 20 km at a speed of 40 km/h and next 40 km at a speed of 20 km/h, then the average speed of the car during whole journey is
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(d) | If the median and mode for a moderately skewed distribution are 8 and 5 respectively, the mean of the distribution is
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(e) | If the relation between two variables u and v is 5v −7u = 1 and range of u is 5, then the range of v is
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(f) | The mean deviation of first six positive even integers about their median is
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(g) | If the mean and standard deviation of 100 observations are 40 and 5 respectively, then sum of squares of the observations is
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(h) |
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(i) | If the coefficient of variation and variance of a group of observations are 50% and 9 respectively then arithmetic mean of deviations of the observations about 2 is
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(j) | In a distribution, mean=24, median=23, coefficient of skewness=0.6, then coefficient of variation is
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12. | (a) | Answer any two of the following: | 5x2 | ||||||||||||||||

(i) | Represent the following data by line chart using a false base line:
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(ii) | Find the median and mode of the following frequency distribution of marks:
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(iii) | The mean and variance of 6 values of a variable are 8 and 8
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(b) | Write a short note on any one of the following: | 4x1 | |||||||||||||||||

(i) | Primary data | (0) | |||||||||||||||||

(ii) | Cumulative frequency polygon | (0) |