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

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

(a) Find the mean proportion between 1.21 and 1.69.

(b) Define fourth proportion with an example.

(c) Simplify: \((64x^{-3} \div 27y^{-3})^{-2/3}\)

(d) Solve for x: \(\log_{0.25}(32)^{-2} = x\)

(e) Express in the form of \(\frac{p}{q}\): \(0.\overline{54}\)

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

(a) Evaluate (any one):
(i) \(\log_{2}\log_{2}\log_{3}\log_{3}(27)^3\)
(ii) \(\left[ \frac{9^{n+1/4} \sqrt{3 \cdot 3^n}}{3 \cdot \sqrt{3^{-n}}} \right]^{1/n}\)

(b) If 1 mile = 1600 meters, find the number of acres in 90,000 sq.m.

(c) From a square copper plate of side 25 cm, a circular disc of diameter 14 cm is cut off. Find the weight of the remaining part if 1 sq. cm. of the plate weighs 0.9 gram.

OR A room has an attached Store Room and a balcony as shown in the diagram below. Find (i) the total floor area including the store room and balcony. Also find (ii) how many pieces of tiles measuring \(50\text{cm} \times 20\text{cm}\) will be required to cover the whole floor area.

(d) Solve any one:
(i) \(x^{2/3} + 3x^{1/3} - 2 = 0\)
(ii) \(\sqrt{\frac{x}{y}} + \sqrt{\frac{y}{x}} = \frac{5}{2}\) ; \(x + y = 5\)

(e) Define marked price and inverse ratio.

Descriptive Questions (5 Marks Each)

4. (a) A conical vessel with radius 10cm and height 48cm is filled with water. If the water is poured into a cylindrical vessel, whose radius is 20cm, find the height (level) of water in the cylindrical vessel.

OR (b) How many spherical balls each of radius 2cm can be made out of a solid metallic cube of edge 44cm?

5. (a) A fruit seller buys two kinds of Oranges—one at Rs. 24 per dozen and other at Rs. 16 per dozen. These are then mixed up and he sells these for Rs. 24 per 15 and thereby makes 5% profit on his outlay. Find the mixing ratio of two kinds of oranges.

OR (b) The list price of an article is 20% above S.P. and C.P. is 30% below the list price. Find the rate of discount and percentage of profit.

6. Write a short note on limitations of statistics.

OR Distinguish between census and sample survey. Give reasons why sample survey is preferred.

7. If the points \((7, a), (-5, 2)\) and \((3, 6)\) are collinear, find the value of \(a\).

8. The diameter of a roller 120cm long is 98cm. If it takes 400 complete revolutions to level a plot of land, determine the cost of leveling at the rate of 50 paisa per sq. meter.

9. In what ratio the line segment joining \(A(3, 4)\) and \(B(5, -7)\) will be divided by x-axis?

OR If D, E and F are the middle points of the sides BC, CA and AB respectively of \(\Delta ABC\) where \(A(-1, 5), B(3, 1)\) and \(C(5, 7)\), show that \(\Delta DEF = \frac{1}{4} \Delta ABC\).

10. Discuss the importance of tabulation in a scheme of statistical investigation. What are the different types of tables?

OR What are the various methods of collecting primary data? Write short notes on each of these.

Long Answer Questions

11. (a) Evaluate: \(\sqrt[5]{0.0619}\) given \(\log 619 = 2.7917\) and \(\text{Antilog } 1.7583 = 57.32\). (4)

OR If \(a^{5-x}b^{6x} = a^{x+7}b^{4x}\), prove that \(x \log \frac{b}{a} = \log a\).
(b) What is the difference between Questionnaire and schedule? (2)
(c) Define any two: Parameter, Sample, Statistic. (2)

12. (a) Write a short note on various types of diagram used in statistics. (4)
(b) Represent the following data by multiple bar diagram: (4)

Results of Parley Oak School for two years. No. of students passed

Year	1st Division	2nd Division	3rd Division
2014	240	180	60
2015	300	180	40

13. (a) Fill in the blanks: (3)
(i) 20% of S.P. = __________ % of C.P.
(ii) The area of an equilateral triangle of side 'a' is __________.
(iii) Two ogives (less than and more than) intersect at the point __________.
(b) What are the objectives of classification? Name various types of classification with examples. (5)

OR In a sample study about gender and literacy rate in two villages the following data were observed. Tabulate the following supplying the missing information:
Village A: 70% were males; 80% were literate; 62% were male literate.
Village B: 55% were males; 35% were female literate; 25% were male literate.

14. Following are the weights (in kg) of 40 students in a class. Prepare a frequency distribution table showing tally marks taking class intervals as 15-19, 20-24,  25-49, etc. (6)

Also find: (a) Frequency density of each class. 

(b) Percentage of students whose weights lie between 25-49.