BUSINESS MATHEMATICS AND STATISTICS

AHSEC CLASS 11 - QUESTION PAPER 2025

ALLOTMENT OF MARKS

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

• (a) 1 acre = ________ sq. yards.
• (b) The first number of a simple ratio is called ________.
• (c) The area of regular hexagon is ________.
• (d) When will one root of a quadratic equation be always equal to zero?
• (e) All facts expressed ________ are not statistics.
• (f) The row head in a statistical table is called stub. (State True or False)
• (g) Find the distance of the point \( (a, -a) \) from the origin.
• (h) If \( \log_{0.01} x = -1 \), then find x.

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

(a) Find the value of: \( \frac{0.0018 \times 0.05}{0.18} \)

(b) Find the diagonal of a square whose sides are 5 cm.

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

(d) Find the value of: \( \log_{2\sqrt{2}} \frac{1}{64} \)

(e) Show that the point (-2, -11) is equidistant from the points (-3, 7) and (4, 6).

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

(a) Show that the points (4, 0), (10, 6) and (1, 3) form a right-angled triangle.

(b) If \( a^x = b^y = c^z \) and \( b^2 = ac \), then prove that \( \frac{1}{x} + \frac{1}{z} = \frac{2}{y} \).

(c) A mixture contains paint and spirit in the ratio 7:5. If the volume of paint is 56 litres, then find the total volume of the mixture.

(d) If \( \frac{5}{8} \) mile = 1 km, express 49200 metres in miles.

(e) If \( a + b + c = 0 \), then prove that:

Section C: Descriptive Questions (5 Marks Each)

4. (a) A trader mixed tea costing Rs. 100 per kg with tea costing Rs. 75 per kg. By selling the mixture at Rs. 108 per kg, he made a profit of 20%. In what proportion did he mix the two kinds?

(b) If the parallel sides of a trapezium are 24 cm and 52 cm and the remaining two sides are 30 cm and 26 cm, then find its area.

5. (a) Kabir buys an article at 25% discount on the list price and makes a profit of 10% by selling it at Rs. 660. Find the list price.

(b) How many metres of cloth 1.1 metres wide will be required to make a conical tent whose vertical height is 12 metres and radius of the base is 16 metres? Find also the cost of cloth used at the rate of Rs. 3.50 per metre.

6. Discuss briefly the uses of Statistics in business and commerce.
OR Write a note about the reasons for distrust of men towards Statistics.

7. Show that the points (-1, -1), (1, 0), (0, 2) and (-2, 1) are the vertices of a square.

8. Solve the equation:
\[ 6\sqrt{\frac{2x+1}{x+2}} + \sqrt{\frac{x+2}{2x+1}} = 5 \]

9. If \( x = \log_{2a} a, y = \log_{3a} 2a \) and \( z = \log_{4a} 3a \), then show that \( 2yz - xyz = 1 \).
OR 2 men and 7 boys can complete a work in 14 days, 3 men and 8 boys can complete that work in 11 days. In how many days will 8 men and 6 boys complete three times of this work?

10. What is tabulation? What are its objects?

Section D: Long Answer Questions (8 Marks Each)

11. (a) Distinguish between graph and diagrams. (4)
(b) Write any four essential qualities of a good questionnaire. (4)

12. (a) What are the advantages of sampling over census method? (4)
(b) Prepare a blank table, showing the distribution of employees in two industries according to the following characteristics: (4)
(i) Sex (M/F), (ii) Marital status (married/unmarried), (iii) Literate/Illiterate.

13. (a) Write a note on histogram. (4)
(b) What precautions would you take in using secondary data? (4)

14. Prepare a frequency distribution table from the following data taking class interval as 20-30, 30-40, etc. (4):

Also find:
(a) The frequency density of each class (2)
(b) The percentage of students getting marks less than 70 (2)