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 mile = ________ yards.
• (b) Which is greater? 6:11 or 7:17
• (c) Area of a rhombus is ________.
• (d) Write True or False: \( \log_{a} m = \log_{b} m \times \log_{a} b \).
• (e) What are the coordinates of the origin in coordinate geometry?
• (f) A sample survey is less expensive than a census survey. (Write True or False)
• (g) What do you mean by primary data?
• (h) Define classification.

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

(a) If \( x:5:8 = 2:y:4 \), then find the value of x and y.

(b) Find the distance between the points (3, -5) and (-2, 6).

(c) Express \( 0.\overline{27} \) in the form \( \frac{p}{q} \).

(d) If the length and breadth of a rectangle are 4 cm and 6 cm respectively, then find its perimeter.

(e) Simplify: \( \frac{x^{m+2n} \cdot x^{3m-8n}}{x^{5m-6n}} \)

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

(a) If \( x:y = 3:2 \), then find the value of \( (4x-2y):(x+y) \).

Divide 1,260 between A, B and C in the ratio \( \frac{1}{5} : \frac{1}{6} : \frac{1}{3} \).

(b) A table with marked price 1,600 is sold for 1,280, after allowing a certain discount. Find the rate of discount.

(c) The base of an isosceles triangle is 12 m and its perimeter is 32 m. Find its area.

(d) Solve: \( \sqrt{5x-1} - 5 = -x \)

(e) Prove that \( \sqrt{2} \) is an irrational number.

Solve: \( |5x| > 3 \)

Descriptive Questions (5 Marks Each)

4. (a) A bicycle seller allows 25% discount on marked price and makes a profit of 20%. What was the marked price of the bicycle on which he gains 30?

(b) Water flows from a pipe of 7 cm in diameter at the rate of 1 litre per second. How many litres of water would flow out per hour?

5. (a) A man sells his TV at a loss of 10%. If he sells it for 1,500 more, he would have gained 5%. Find the cost price of the TV.

(b) The area of a circular garden is \( 22176\text{ m}^2 \). How long a man will take to go round it 10 times at a speed of 2.2 km per hour?

6. Discuss the scope of statistics in business and commerce.

What are the limitations of statistics?

7. If the point \( C(-4, 1) \) divides the line segment joining the points \( A(2, -2) \) and B in the ratio 3:5, then find the point B.

8. If \( \sqrt[3]{a} + \sqrt[3]{b} + \sqrt[3]{c} = 0 \), then show that \( (a+b+c)^3 = 27abc \).

9. The diameter of a garden roller which is 80 cm long is 1.40 m. If it takes 600 complete revolutions to level a playground, find the cost of levelling the ground at 60 paise per square metre.

Prove that \( \log_{10} 2 \) lies between \( \frac{1}{4} \) and \( \frac{1}{3} \).

10. Discuss the merits of sampling over census method.

Discuss the different sources of collecting secondary data.

Long Answer Questions (8 Marks Each)

11. (a) Evaluate: \( \sqrt{6+\sqrt{6+\sqrt{6+\dots \text{to } \infty}}} \)

(b) Distinguish between questionnaire and schedule.

Define the following: 

(i) Hemisphere, 

(ii) Marked price.

12. (a) Define the following:

(i) Sample and population,

(ii) Tabulation of data.

(b) Explain the different parts of a table.

13. (a) Draw a percentage bar diagram to represent the following data:

Items of expenditure	Expenditure (in ₹)
Food	150
Clothing	125
Rent	25
Light and fuel	10
Others	190

(b) What are the uses of diagrams and graphs?

14. Prepare a frequency distribution table from the following data taking the class intervals as 21-30, 31-40, ..., etc.:

Also find: 

(a) The frequency density of each class, 

(b) Percentage frequency between 31-40.

Write a note on the main points involved in the construction of frequency distribution tables. Also define class interval and class limits.