Q1: In a decreasing arithmetic progression, the sum of all its terms except the first is -75. The sum of all its terms except the last is 0, and the difference between the 9th and 13th terms is -20. What is the first term of this series?
- A) -40
- B) 35
- C) -35
- D) None of these
Correct Answer: Option B
After applying the arithmetic progression formulas, the first term of the series is calculated to be 35.
Q2: The cost price of each item is Rs. 20, and their selling prices follow the sequence Rs. 2, 4, 6, and so on. If the minimum profit percentage is 40%, what is the minimum number of items?
- A) 25
- B) 26
- C) 27
- D) None of these
Correct Answer: Option C
Using the arithmetic series formula, the minimum number of items required is 27.
Q3: From each vertex of an equilateral triangle, corners are cut to form a regular hexagon. If the area of the equilateral triangle is 240, find the area of the hexagon.
- A) 160
- B) 430/3
- C) 500/3
- D) None of these
Correct Answer: Option A
After calculating the side lengths and areas, the hexagon’s area is found to be 160.
Q4: If \( \log(1 + xz) = 2A \) and \(x, y,\) and \(z\) are consecutive integers, find \(A\).
- A) 1
- B) \( \log y \)
- C) \( 2 \times \log y \)
- D) None of these
Correct Answer: Option C
The calculation simplifies to \(A = \log y\), and the correct answer is \(2 \times \log y\).
Q5: An article is sold for Rs. 17,600 after a 12% discount with a 10% profit. Find the profit percentage if no discount is given.
- A) 20%
- B) 22%
- C) 27.5%
- D) 25%
Correct Answer: Option D
Without the discount, the profit percentage is calculated to be 25%.
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