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) 1 hectare = ________ sq. metre.
• (b) 20% profit on SP = ________ % profit on CP.
• (c) The curved surface area of a cone is:
  (i) \( 2\pi rl \)   
• (ii) \( 2\pi rh \)   
• (iii) \( \pi r^2h \)   
• (iv) \( \pi rl \)
• (d) y-coordinate of a point on x-axis is ________.
• (e) All facts ________ expressed are not statistics.
• (f) What is a blank table?
• (g) Bar diagram is a ________ dimensional diagram.
• (h) Write True or False: \( \log_{a} a = 1 \).

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

(a) Simplify: \( \{(\sqrt[5]{125})^{-2}\}^{-5/3} \)

(b) For what value of k, will the point (k, 0) be equidistant from the points (a, 0) and (-5a, 0)?

(c) Find the mean proportion of 50 and 128.

(d) The diameter and slant height of a right circular cone are 70 cm and 35 cm respectively. Find its curved surface area.

(e) Find the value of \( \log_{2}\sqrt{6} + \log_{2}\sqrt{\frac{2}{3}} \).

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

(a) A retailer sells an article at a profit of 20% on SP. If CP is 720, find the SP.

(b) Solve: \( 3^x + \frac{1}{3^x} = \frac{10}{3} \) 

OR 

\( 3^{2x} + 9 = 10 \cdot 3^x \)

(c) Find the length of the longest rod that can be placed in a room of 12 ft long, 9 ft broad and 8 ft high.

(d) Show that the points (-2, 5), (0, 1) and (2, -3) are collinear.

(e) The ratio between two numbers is 2:7. If each of them is increased by 14, the ratio between the new numbers obtained becomes 4:7. Find the original numbers.

Descriptive Questions (5 Marks Each)

4. (a) A trader allows his customers 5% discount on list price. What would be the list price of an article costing 712.50 to make a profit of \( 33\frac{1}{3}\% \)?

(b) Find the cost of flooring with square tiles of side 20 cm, each tile costs 25. The dimension of the floor is \( 4\text{ m} \times 3\text{ m} \) and the cost of labour is 75% of the cost of material.

5. (a) Two mixtures A and B contain glycerine and water in the ratio 4:5 and 3:2 respectively. How many litres of B must be mixed with 81 litres of A that the resulting mixture may contain equal quantity of glycerine and water?

(b) A hemispherical bowl of radius 9 cm is full of water. This water is to be filled in cylindrical bottles of diameter 3 cm and height 4 cm. Find the number of bottles required to fill the whole water of the bowl.

6. What are the limitations of statistics? OR What are the characteristics of statistical data?

7. Find the ratio in which the line segment joining the points (-4, 1) and (3, 5) is divided by y-axis.

8. Prove that:

9. If \( \log\frac{x+y}{3} = \frac{1}{2}(\log x + \log y) \), then show that \( \frac{x}{y} + \frac{y}{x} = 7 \).

The diameters of two cylinders are in the ratio 3:2 and the ratio of their heights is 2:3. Find the ratio of their volumes.

10. Write down any five essential characteristics of an ideal questionnaire.

OR 

Discuss the different sources of collecting secondary data.

Long Answer Questions (8 Marks Each)

11. (a) Solve: \( \sqrt{\frac{x}{1-x}} + \sqrt{\frac{1-x}{x}} = \frac{13}{6} \).
(b) What is the difference between primary data and secondary data? 

OR 

Discuss the different stages of statistical investigation.

12. (a) What is classification? Name the four types of classification.
(b) Discuss the importance of diagrams and graphs in business and commerce.

13. (a) Draw a histogram of the following data:

Class Interval	10-15	15-20	20-25	25-30	30-35
Frequency	30	55	80	60	45

(b) Define frequency density and percentage frequency.

14. The following are the weights (in kg) of a group of 55 students. Prepare a frequency distribution table taking the width of each class interval as 10. Find also the frequency density of each class interval:

From the table, calculate: 

(a) Percentage of students with weights less than 80 kg 

(b) Percentage of students with weights between 76-105 kg.

What is tabulation? What is the purpose of tabulation of statistical data? Prepare a blank table showing the distribution in two industries according to: 

(i) Sex (M/F), 

(ii) Marital status (married/unmarried), 

(iii) Literate/Illiterate.