This Paper has

**34**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. |

Section A |

ARITHMETIC (15 marks)Answer Question No. 1 (compulsory – 5 marks) and any one(10 marks) from the rest. |

Marks |

1. | (a) | The ratio of the present age of a father to that of his son is 5 : 3. Ten years hence the ratio would be 3 : 2. Find their present ages. | 2 | (0) | ||

(b) | After spending 69% of his money a person has Rs.93 left. How much had he at first? | 2 | (0) | |||

(c) | Calculate the interest on Rs.10,000 for 10 years at 10% p.a. | 1 | (0) | |||

2. | (a) | X, Y, Z are three children. Y was born when X was 4 years 7 months old and Z was born when Y was 3 years 4 months old. Find the average age when Z was 5 years 2 months old. | 5 | (0) | ||

(b) | A radio–dealer offers a radio for Rs.270 cash down or Rs.30 cash down and 18 equal monthly installments of Rs. 15 each. Find the rate of simple interest charged. | 5 | (0) | |||

3. | (a) | The true discount (TD) on a bill for Rs.2,160 due sometime hence is Rs.180; find the Banker’s gain (BG) on the same bill at the same rate. | 5 | (0) | ||

(b) | A dealer mixes tea costing Rs.8 per kg with tea costing Rs.7 per kg and thereafter, sells the mixture at Rs.8 per kg and earns a profit of 7.5% on his sale price. In what proportion does he mix them? | 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) | Write 1.35 as a rational number. | 1 | (0) | ||

(b) | Find the logarithm of 0.0001 to the base 0.1 | 2 | (0) | |||

(c) | Exhibit the following set in tabular form A = {x : x ∈N, x < 8 is odd}, where N is the set of natural numbers. | 2 | (0) | |||

5. | (a) | Find the square root of 7 + 24i. | 5 | (0) | ||

(b) | If one root of ax^{2} + bx + c = 0 is four times the other, then show that 4b^{2} = 25 ca. | 5 | (0) | |||

6. | (a) | If p = log_{10} 20 and q = log_{10} 25, find x such that 2 log_{10}(x + 1) = 2p − q. | 5 | (0) | ||

(b) | In how many ways can the letters of the word MONDAY be arranged? How many of them do not begin with ‘M’? How many of them do not begin with ‘M’ and end with ‘Y’? | 5 | (0) | |||

7. | (a) | The total expenses of a hostel are partly constant and partly vary as the number of boarders. If the expenses for 120 boarders be Rs.20,000 and for 100 boarders be Rs.17,000, find for how many boarders will cost come to Rs.18,800? | 5 | (0) | ||

(b) | Prove with the help of a Truth table that (~p ∨ q) ∧ (~q ∨ p) = p ⇔ q. | 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) | Find the area of the triangle made by the straight line 3x + y = 5 with the coordinate axes. | 2 | (0) | ||||||||||

(b) | The surface area of a sphere is 154sq.cm. Find the surface area of its hemisphere. | 2 | (0) | |||||||||||

(c) | Show that the point (1, − 2) lies outside the circle x^{2} + y^{2} − 8x + 6y + 16 = 0. | 2 | (0) | |||||||||||

9. | (a) | The volumes of two spheres are in the ratio 27 : 8. Find their diameters if the sum of their diameters is 20cms. | 6 | (0) | ||||||||||

(b) | Find the locus of a point such that the difference of its distances from (4, 0) and (− 4, 0) is always equal to 2. Assign a geometric name to the locus. | 6 | (0) | |||||||||||

10. | (a) | The circumference of the base of a right circular cone is 44cms and the slant height is 25cms. Find the volume and curved surface (area) of the cone. | 6 | (0) | ||||||||||

(b) | Find the equation of the line joining the points of intersection of 2x + y = 4 with x − y + 1 = 0 and 2x − y − 1 = 0 with x + y − 8 = 0. | 6 | (0) | |||||||||||

11. | (a) | Find the equation of the circle whose center lies on X – axis and which passes through (0, 4) and (3, − 1). | 6 | (0) | ||||||||||

(b) | Find the co–ordinates of the center, foci and the equations of directries, latus rectum, eccentricity of the hyperbola
| 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 H.M of 3, 6, 12 and 15. | 1 | (0) | ||||||||||||||||

(b) | Find median of the following distribution:
| 2 | (0) | |||||||||||||||||

(c) |
| 3 | (0) | |||||||||||||||||

13. | (a) | Draw histogram and frequency polygon of the following data:
| 6 | (0) | ||||||||||||||||

(b) | Draw the ‘less–than’ ogive curve on the basis of the data given below and then find graphically the value of Q_{3}.
| 6 | (0) | |||||||||||||||||

14. | (a) | The cost of manufacturing of an article was Rs.150. A pie diagram was drawn to show the cost. If the labour charges are represented by a sector of 114^{0}, find the sum spent for other purposes. | 4 | (0) | ||||||||||||||||

(b) | In an examination, a candidate scores the following percentage of marks:
Find the candidate’s weighted mean percentage if weights of 3, 4, 4, 5 and 2 respectively are allotted to the subjects. Find also the coefficient of variation. | 8 | (0) | |||||||||||||||||

15. | (a) | Two samples of sizes 40 and 50 respectively have the same mean 53 but different standard deviation 19 and 8 respectively. Find the standard deviation of the combined sample of size 90. | 6 | (0) | ||||||||||||||||

(b) | Pearson’s coefficient of skewness of a distribution is 0.32. Its s.d id 6.5 and A. M is 29. 6. Find the mode and median of the distribution. In case mode is 24.8, then find the changed s.d. | 6 | (0) |