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 | (i) | 40 years | (ii) | 25 years | (iii) | 30 years | (iv) | none of these |
| | (0) |
| | (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) | (i) | 23 | (ii) | 24 | (iii) | 25 | (iv) | none of these |
| | (0) |
| | (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 | (i) | 100 | (ii) | 75 | (iii) | 50 | (iv) | none of these |
| | (0) |
| 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 = A + iB, then the value of A/B is (where i = √−1) | (i) | | (ii) | 1 | (iii) | | (iv) | none of these. |
| | (0) |
| | (b) | If (a + b) ∝ (a − b) and when a = 6, b = 2, then for b = 3, the value of a is | (i) | 6 | (ii) | 9 | (iii) | 12 | (iv) | none of these. |
| | (0) |
| | (c) | If x = 7 + 4 √3, then the value of √x − is | (i) | √3 | (ii) | 2√3 | (iii) | 3√3 | (iv) | none of these |
| | (0) |
| | (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 | (i) | 120 | (ii) | 480 | (iii) | 2880 | (iv) | None of these |
| | (0) |
| | (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 | (i) | p ∨ q | (ii) | p ∧ q | (iii) | p ∧ ∼ q | (iv) | ∼ p ∧ ∼ q |
| | (0) |
| 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 log2 log3 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 | (i) | 12 sq cm | (ii) | 24 sq cm | (iii) | 48 sq cm | (iv) | none of these |
| | (0) |
| | (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 = ) | (i) | 44 sq cm | (ii) | 144 sq cm | (iii) | 176 sq cm | (iv) | none of these |
| | (0) |
| | (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 | (i) | 144 | (ii) | 216 | (iii) | 432 | (iv) | none of these |
| | (0) |
| | (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 | (i) | 4 cm | (ii) | 4.5 cm | (iii) | 5 cm | (iv) | none of these |
| | (0) |
| | (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 = ) | (i) | 4.4 cm | (ii) | 4.2 cm | (iii) | 4.8 cm | (iv) | none of these |
| | (0) |
| 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 | (i) | 2 | (ii) | 3 | (iii) | 6 | (iv) | none of these |
| | (0) |
| | (b) | If the diameter of a circle x2 + y2 + 4x − 7y − k = 0 be 9, then the value of k is | (i) | 6 | (ii) | − 4 | (iii) | 4 | (iv) | none of these |
| | (0) |
| | (c) | Focus of the parabola y2 − 8y − 8x + 8 = 0 is | (i) | (2, 0) | (ii) | (1,4) | (iii) | (1,2) | (iv) | none of these |
| | (0) |
| | (d) | The eccentricity of the hyperbola 4x2 − 9y2 = 36 is | (i) | | (ii) | | (iii) | | (iv) | none of these |
| | (0) |
| 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 4x2 + 5y2 = 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 | (i) | 0 | (ii) | 2 | (iii) | 4 | (iv) | none of these. |
| | (0) |
| | (b) | If f(x) = x + 1, for x ≤ 1
= 5 – ax2, x > 1
then f(x) is continuous at x = 1,when a is | (i) | 1 | (ii) | 2 | (iii) | 3 | (iv) | none of these |
| | (0) |
| | (c) | If x = ct and y = , then the value of at t = is | (i) | | (ii) | | (iii) | | (iv) | none of these |
| | (0) |
| | (d) | If u = , then x + y is | (i) | 1 | (ii) | 0 | (iii) | −1 | (iv) | None of these. |
| | (0) |
| | (e) | The value of dx is | (i) | 4 loge 2 + 2 | (ii) | 2 loge2 − 2 | (iii) | 4 loge2 | (iv) | None of these. |
| | (0) |
| 10. | Answer any two of the following | 3x2 | |
| | (a) | If y = x3 log , prove that x − 2 + 3x2 = 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 ∫ dx | | (0) |
| 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 | (i) | 11 | (ii) | 10 | (iii) | | (iv) | none of these |
| | (0) |
| | (b) | G.M. of the numbers 3, 6, 24 and 48 is | (i) | 8 | (ii) | 10 | (iii) | 12 | (iv) | none of these |
| | (0) |
| | (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 | (i) | 24 km/h | (ii) | 30 km/h | (iii) | 36 km/h | (iv) | none of these |
| | (0) |
| | (d) | If the median and mode for a moderately skewed distribution are 8 and 5 respectively, the mean of the distribution is | (i) | 6.5 | (ii) | 10 | (iii) | 9.5 | (iv) | none of these |
| | (0) |
| | (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 | (i) | | (ii) | 7 | (iii) | 5 | (iv) | none of these |
| | (0) |
| | (f) | The mean deviation of first six positive even integers about their median is | (i) | 6 | (ii) | 4 | (iii) | 3 | (iv) | none of these |
| | (0) |
| | (g) | If the mean and standard deviation of 100 observations are 40 and 5 respectively, then sum of squares of the observations is | (i) | 16250000 | (ii) | 162500 | (iii) | 1625 | (iv) | none of these |
| | (0) |
| | (h) | | For a variable x if | 8
Σ
i=1 | (xi − 3) = 96 and | 8
Σ
i = 1 | (xi − 10)2 = 736, then its variance is |
| (i) | 65 | (ii) | 66 | (iii) | 67 | (iv) | none of these |
| | (0) |
| | (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 | (i) | 3 | (ii) | 4 | (iii) | 6 | (iv) | none of these |
| | (0) |
| | (j) | In a distribution, mean=24, median=23, coefficient of skewness=0.6, then coefficient of variation is | (i) | 20.83% | (ii) | 10.83% | (iii) | 20% | (iv) | none of these |
| | (0) |
| 12. | (a) | Answer any two of the following: | 5x2 | |
| | | (i) | Represent the following data by line chart using a false base line: Year
Production of
spindles (Nos.) | :
:
: | 2005
8500 | 2006
9000 | 2007
11000 | 2008
9050 | 2009
10000 | 2010
12000 |
| | (0) |
| | | (ii) | Find the median and mode of the following frequency distribution of marks: Marks
No. of students | :
: | 10 – 20
5 | 20 – 30
7 | 30 – 40
18 | 50 – 60
24 | 60– 70
12 | 70– 80
3 |
| | (0) |
| | | (iii) | The mean and variance of 6 values of a variable are 8 and 8 respectively. If 4 values of the variable are 4, 9, 11 and 12, find the other two values of the variable. | | (0) |
| | (b) | Write a short note on any one of the following: | 4x1 | |
| | | (i) | Primary data | | (0) |
| | | (ii) | Cumulative frequency polygon | | (0) |
