The figures in the margin indicate full marks for the questions

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

• (a) ________ is the only even prime number. (Fill in the blanks)
• (b) 63 is a prime number. (State True or False)
• (c) ________ is known as 'Father of Statistics'. (Fill in the blanks)
• (d) Sampling method is more expensive than Census method. (True/False)
• (e) The total surface area of a hemisphere is ________. (Fill in the blanks)
• (f) Define frequency density of a class interval.
• (g) 10% profit on CP = ________ profit on SP. (Fill in the blanks)
• (h) Bar diagram is two-dimensional diagram. (True/False)

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

(a) Solve: \( |5x - 2| < 7 \)

(b) If logarithm of a number to the base \( \sqrt{5} \) is K, what is the logarithm to the base \( 5\sqrt{5} \)?

(c) Simplify: \( \frac{3^{n+1} + 3^n}{3^{n+3} - 3^{n+1}} \)

(d) Find the third proportional to \( \frac{8}{7} \) and \( \frac{12}{35} \).

(e) Solve: \( 3x^2 + 8x = 0 \)

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

(a) If \( a=xy^{q-r}, b=xy^{r-p}, c=xy^{p-q} \), prove that \( a^{q-r}b^{r-p}c^{p-q}=1 \).

OR

 If \( x=3^{2/3} + 3^{-2/3} \), show that \( 9x^3 - 27x = 82 \).

(b) Define trade discount and fourth proportional.

(c) If 1 meter = 3.2809 ft, find the distance in miles travelled with a speed of 6 km/h in 46 min 40 sec.

(d) From a copper plate, which is a square of side 12.5 cm, a circular disc of diameter 7 cm is cut off. Find the weight of the remaining part if 1 sq. cm of the plate weighs 0.8 gm.

Or

How many tiles of size 40 cm x 20 cm will be required to have a footpath 1 meter wide round the outside of

a 36 m x 30 m grass plot?

(e) Solve (any one):
(i) \( 5^x + \frac{1}{5^x} = \frac{26}{5} \)
(ii) \( \sqrt{\frac{x}{1-x}} + \sqrt{\frac{1-x}{x}} = \frac{13}{6} \)

Descriptive Questions (5 Marks Each)

4. Answer either (a) or (b):

(a) A toy in the form of a cone mounted on a hemisphere of radius 3.5 cm. If the total height of the toy is 15.5 cm, find its total surface area.

(b) A room is of length 22 m, breadth 16 m and height 5 m. find the cost of papering the four walls with papers 2 m wide at the cost of Rs. 5.20 per meter. The room has 4 doors and 4 windows of dimension 2.5 m x 1.2 m and 3 m x 2 m respectively. Allow 5% extra paper for wastage.

5. A shopkeeper purchases 50 dozen eggs at Rs. 40 per dozen. Of these 40 eggs are found to be broken. At what price should he sell the remaining eggs to make a profit of 5%?

OR

Two mixtures P and Q contain paint and turpentine in the ratio 4:5 and 3:2 respectively. How many litres of Q mustbe mixed with 72 litres of P so that the resulting mixture may contain equal quantities of paint and turpentine?

6. What are the advantages of sampling survey over census method? 

Or

Discuss the importance of statistics in business and commerce.

7. Under what condition the point (x, y) is equidistant from the two points (-3, 2) and (-4, 1) ?

8. 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.

9. Find the coordinates of the points which divided the line segment joining the points (8, - 7) and (-7, 3) internally in the ratio 2:3. 

Or

If P, Q, R re the midpoints of the sides BC, CA and AB respectively ofΔABCwhereA(-3, 7),B(5, 3) and C(7, 9) ,find the area of the ΔPQR .

10. Discuss the reasons for distrust in Statistics.

ORGive your opinion on the statement – “Statistics can prove anything”.

OR Solve for x:

(b) What is the difference between questionnaire and schedule?

(c) Define the following (any two): (1 × 2 = 2)
1) Primary Data
2) Parameter
3) Frequency Density

12. (a) Write a note on the advantages of graphs and diagrams.

(b) Represent the following data by a histogram:

Weight (kg)	40-50	50-60	60-70	70-80	80-90
Frequency	5	14	20	10	1

13. (a) Fill in the blanks:
1) 1 acre = ________ sq. yards.
2) The volume of a cone is ________.
3) ________ may be located from ogive.

(b) Write a brief note on various parts of a statistical table. (5)

14. Following are the ages of 50 workers in a business concern:

Prepare a frequency distribution table showing tally marks taking the class intervals as 20-29, 30-39, 40-49, ..... (5)

Also find:
a) The frequency density of each class; (1)
b) The percentage of workers whose ages lie between 40-69 years; (1)
c) The percentage frequency of each class. (1)