ALLOTMENT OF MARKS

Question Number	Marks Per Question	Total Marks
Q. No. 1	1 × 8	8
Q. No. 2	2 × 5	10
Q. No. 3	3 × 5	15
Q. Nos. 4-10	5 × 7	35
Q. Nos. 11-14	8 × 4	32
Total Marks		100

1. Answer the following as directed: (1 × 8 = 8)

• (a) The smallest natural number is ________.
• (b) 2 is the only even prime number. (Write True or False)
• (c) ________ is called the ‘Father of Statistics’.
• (d) Sample is a representative part of the population. (Write True or False)
• (e) Classification is the ________ step in tabulation.
• (f) Write down the formula for finding area of an equilateral triangle.
• (g) Find the distance of the point \( (x, y) \) from the origin.
• (h) What are the coordinates of the origin in coordinate geometry?

2. Answer the following questions: (2 × 5 = 10)

(a) If \( \frac{5}{8} \) mile = 1 km, express 3200 metres in miles.

(b) Divide Rs. 3200 in the ratio 7 : 9.

(c) Simplify: \( \frac{x^{a+b} \cdot x^{a-b}}{x^{2a}} \)

(d) Find the distance between the points (2, 3) and (5, 7).

(e) Find the area of a triangle whose three sides are 26 cm, 28 cm and 30 cm respectively.

3. Answer the following questions: (3 × 5 = 15)

(a) If \( \frac{a}{2} = \frac{b}{3} = \frac{c}{4} \), show that \( \frac{a+b+c}{c} = \frac{9}{4} \).

If \( x = \log_a bc, y = \log_b ca, z = \log_c ab \), show that \( \frac{1}{x+1} + \frac{1}{y+1} + \frac{1}{z+1} = 1 \).

(b) In a 60 litre mixture of water and milk, the ratio of water and milk is 7 : 5. How much milk should be added so that the ratio becomes 5 : 8?

(c) By selling 150 mangoes, a fruit seller gains the selling price of 30 mangoes. Find the gain percentage.

(d) Solve (any one):
1) \( 3^{x+1} = 9^{x-2} \)
2) \( \sqrt{x+5} + \sqrt{x} = 5 \)

(e) Prove that the points (1, 1), (2, 2) and (3, 3) are collinear.

Section C: Descriptive Questions (5 Marks Each)

4. (a) A person buys an article and sells it at a profit of 5%. If he had bought it at 5% less and sold it for 37 paisa less, he would have gained 10%. Find the original cost price.

(b) A rectangular metal plate 1 cm thick, 8 cm broad and 27 cm long is melted into a cube. Find the difference in surface area of the two solids.

5. (a) In mixing two types of tea, 2% is wasted. In what ratio tea costing Rs. 60 per kg be mixed with tea costing Rs. 45 per kg so that by selling the mixture at Rs. 62.50 per kg, there is a gain of 25% on total outlay.

(b) The perimeter of a rhombus is 52 cm and one of its diagonals is 24 cm. Find the other diagonal and the area of the rhombus.

6. Write what do you know about the functions of Statistics.

Write a note on distrust of Statistics.

7. Find the ratio in which the point (2, 3) divides the join of the points (1, 2) and (4, 5).

8. If \( a, b, c \) are in G.P., prove that \( \log a, \log b, \log c \) are in A.P.

9. Prove that: \( \log_2 [\log_2 \{\log_2 16\}] = 1 \).

A 20m deep well with diameter 7m is dug and the earth from digging is evenly spread out to form a platform of 22m x 14m. Find the height of the platform.

10. Mention the points that should be remembered while drafting a good questionnaire.

Section D: Long Answer Questions (8 Marks Each)

11. (a) The area of a square field is 368.64 hectares. Find its perimeter. (4)

Define the following: 1) Hemisphere, 2) Marked price. (4)
(b) Discuss the limitations of Sampling. (4)

12. (a) Define the following: 1) Primary data and Secondary data, 2) Cumulative frequency. (4)
(b) Discuss the advantages of diagrams and graphs. (4)

Write a note on various types of bar diagrams. (4)

13. (a) Draw a Pie chart of the following data: (5)

Heads of Expenditure	Rs.
Agriculture	12,000
Industries	9,000
Irrigation	6,000
Education	8,000
Communication	5,000

(b) Distinguish between (any one): 1) Schedule and Questionnaire, 2) Census and Sample survey. (3)

14. (a) What do you mean by statistical investigation? What are the different stages of statistical investigation? (4)
(b) Prepare a blank table showing the distribution of the population in the four important cities of Assam according to sex, literacy and religion. (4)

Draft a questionnaire for collecting information regarding the socio-economic conditions of the people in a locality. (4)