AIOU 247 Mathematics-I Solved Assignment 2 Spring 2025
AIOU 247 Assignment 2
Q1.(a). Find 3 A.Ms between √3 and 9√3(10 Marks)
Arithmetic Means between √3 and 9√3
We want three arithmetic means inserted between the two terms so the full sequence has five terms.
a₁ = √3, a₅ = 9√3
For an arithmetic sequence with five terms the common difference d satisfies
a₅ = a₁ + 4d
Substitute the values and solve for d
9√3 = √3 + 4d → d = 2√3
Now compute the three arithmetic means
• a₂ = a₁ + d = 3√3
• a₃ = a₁ + 2d = 5√3
• a₄ = a₁ + 3d = 7√3
Answer: 3√3, 5√3, 7√3
Q1.(b). The positive G.M between two numbers is 9 and the A.M between them is 15. Find the numbers.(10 Marks)
Finding the Numbers from A.M and G.M
The positive geometric mean (G.M) between two numbers a and b is 9. This gives:
√(ab) = 9 → ab = 81
The arithmetic mean (A.M) between them is 15. This gives:
(a + b) / 2 = 15 → a + b = 30
Step 1: The equations are:
a + b = 30, ab = 81
Step 2: Form quadratic equation:
x² - 30x + 81 = 0
Step 3: Solve:
x = (30 ± √(900 - 324)) / 2 = (30 ± 24) / 2
x = 27 or x = 3
Answer: The two numbers are 27 and 3
Q2.(a). Using a logarithmic table evaluate(10 Marks)
Q2.(b). Prove that(10 Marks)
Q3.(a). If A = {1,2,3,4,5}, B = {6,7,8} and C = {3,4,6} - Verify that (A∩B)∩C=A∩(B∩C)(10 Marks)
Q3.(b). If X = {0,3,5} and Y = {2,4,8} then establish four binary relations in X × Y(10 Marks)
Q4.(a). Draw the graph(10 Marks)
Q4.(b). Draw the graph(10 Marks)
Q5.(a). (10 Marks)
Q5.(b). (10 Marks)
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