This Paper has

**47**answerable questions with**0**answered.C—4(BMS)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 their 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) |
| 1 | (0) | |||||||||||||||||||||||||||

(b) | At what rate per annum will a sum of money double itself in 10 years with simple interest? | 2 | (0) | ||||||||||||||||||||||||||||

(c) | What will be the cost price per kg of the mixture of two types of teas, mixed in the ratio 3 : 2 if the first type is purchased in Rs. 200 per kg and the second in Rs. 300 per kg? | 2 | (0) | ||||||||||||||||||||||||||||

2. | (a) |
| 5 | (0) | |||||||||||||||||||||||||||

(b) | A sum of money is to be divided among three sons in such a way that the first son is to get 30% of the whole, the second son is to get 40% of the remainder and the third son the rest. If the third son gets Rs. 21,000, what would be the total sum divided and the amounts in the respective shares of the first and second son? | 5 | (0) | ||||||||||||||||||||||||||||

3. | (a) | Two vessels contain mixture of milk and water in the proportions 2 : 3 and 4 : 3 respectively. In what proportion should the two mixtures be mixed so as to form new mixture containing equal quantities of mild and water? | 5 | (0) | |||||||||||||||||||||||||||

(b) | The difference betw3een interest and true discount on a sum due in 5 years at 5% per annum is Rs. 50. Find the sum. | 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 | |||||||||||||||||

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

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

(c) | Form a quadratic equation whose one root is 2 + √3. | (0) | |||||||||||||||||

(d) | Evaluate (243)^{–1/5} | (0) | |||||||||||||||||

(e) | If ^{n}P_{2} = 56, find n. | (0) | |||||||||||||||||

(f) | Prove that log (1 + 2 + 3) = log 1 + log 2 + log 3. | (0) | |||||||||||||||||

(g) | If A = {1, 2, 3} and B = {2, 3, 4}, find (A – B) ∪ (B – A). | (0) | |||||||||||||||||

5. | (a) | Construct a quadratic equation whose roots are α^{3} and β^{3} when α and β are the roots of x ^{2} + 3x + 2 = 0. | 5 | (0) | |||||||||||||||

(b) |
| 5 | (0) | ||||||||||||||||

6. | (a) |
| 5 | (0) | |||||||||||||||

(b) | As the number of units manufactured in a factory is increased from 200 to 300, the total cost of production increases from Rs. 16,000 to Rs. 20,000. If the total cost of production is partly fixed and other part varies as number of units produced, find the total cost for producing 500 units. | 5 | (0) | ||||||||||||||||

7. | (a) | If a group of 13 workers contains 5 women, in how many ways can a subgroup of 10 workers be selected so as to include atleast 6 men? | 5 | (0) | |||||||||||||||

(b) | In a class test of 70 students, 23 and 30 students passed in Mathematics and in Statistics respectively and 15 passed in Mathematics but not passed in Statistics. Using set theory result, find the number of students who passed in both the subjects and who did not pass in both the subjects. | 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) | A path of 4 ft wide is to be laid outside round the square garden of 60ft by 60ft. Find the area of the path. | (0) | ||||

(b) | Base radius of a conical tent is 5 m and its height is 10 m. Find the area of the canvas of the tent. | (0) | ||||

(c) | If the total surface area of a cube is 54 sq ft, find its volume. | (0) | ||||

(d) | Three solid gold spherical beads of radii 3, 4 and 5 cms respectively are melted to form another solid spherical bead. Find its radius. | (0) | ||||

(e) | Find the equation of the straight line making an intercept 3 on the x–axis and passing through the point (1, 2). | (0) | ||||

(f) | For the equation of the circle x^{2} + y^{2} + 2x – 4y = 11, find the coordinates of its center and also its radius. | (0) | ||||

(g) | Find the vertex of the parabola y^{2} – 2y – 8x = 23. | (0) | ||||

(h) | Find the eccentricity of the ellipse 8x^{2} + 9y^{2} = 288. | (0) | ||||

9. | (a) | The perimeter of a right angled triangle is 30 cm and hypotenuse is 13 cm. Find the other two sides and the area of the triangle. | 5 | (0) | ||

(b) | Volume of a right circular cylinder, whose base has a radius of 7 cm, is same as volume of a cube having an edge of 11 cm. Find the the altitude and the total surface area of the cylinder. | 3+2 | (0) | |||

10. | (a) | A right pyrami9d stands on a square base having a side of 10 cm and its height is 12 cm. Find its total surface area and volume. | 5 | (0) | ||

(b) | If the three points (x, y), (5, –2) and (3, –4) are collinear, prove that 3x + 4y – 7 = 0. | 5 | (0) | |||

11. | (a) | Find the centres and radii of two circles x^{2} + y^{2} + 6x + 14y + 9 = 0 and x^{2} + y^{2} ’ 4x ’ 10y ’ 7 = 0 and hence show that they touch each other externally. | 1½+1½+2 | (0) | ||

(b) | Find the coordinates of center, length of latus rectum, coordinates of foci of the hyperbola 3x^{2} – 4y^{2} – 12x – 8y – 4 = 0. | 2+1+1+1 | (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. | Attempt any five of the following : | 2x5 | ||||||||||||

(a) | Prove that for two numbers 2 and 4, A.M. x H.M. = (G.M)^{2} | (0) | ||||||||||||

(b) | If the relation between two variables x and y is 2x + 3y = 7 and median of y is 2, find the median of x. | (0) | ||||||||||||

(c) | If the observations 2, 4, 8 and 16 occur with frequency 4, 3, 2 and 1 respectively, find the geometric mean of them. | (0) | ||||||||||||

(d) | If the variables x and y are related by 3x – 2y + 5 = 0 and the range of x is 8, find the range of y. | (0) | ||||||||||||

(e) | Determine the mean deviation about mean of 9 observations 4, 4, 4, 6, 6, 6, 8, 8, 8. | (0) | ||||||||||||

(f) | If A.M. and the coefficient of variation of a variable x are 10 and 50% respectively, find the variance of x. | (0) | ||||||||||||

(g) | If two groups of 50 and 100 observations have means 4 and 2 respectively, find the mean of the combined group. | (0) | ||||||||||||

(h) | For a moderately skewed distribution the mean and median are 35 and 37 respectively, find the mode. | (0) | ||||||||||||

13. | (a) | Draw a simple bar chart for the following productions of bicycles of a small factory in 4 consecutive years :
| 5 | (0) | ||||||||||

(b) | Draw an ogive (less than type) from the following distribution:
| 5 | (0) | |||||||||||

14. | (a) | Arithmetic mean of the following frequency distribution is 8.8. Find the missing frequencies:
| 5 | (0) | ||||||||||

(b) | Find the quartile deviation of the following distribution:
| 5 | (0) | |||||||||||

15. | For the following frequency distribution, determine mean, mode, coefficient of skewness:
| 2+3+3+2 | (0) |