CAT 2025 Slot 2 Answer Key QA: Download Question Paper with Answer Key PDF

A and B can complete a work in 12 days and 18 days respectively. They start together, but A leaves after 4 days. How many more days will B take to finish the remaining work?

If the quadratic equation \(ax^2 + bx + c = 0\) has roots that differ by 4, and \(a + b + c = 12\), what is the value of \(b^2 - 4ac\)?

A number when divided by 7 leaves a remainder 4 and when divided by 9 leaves a remainder 5. What is the smallest such number greater than 100?

In a triangle ABC, the sides are in the ratio 3 : 4 : 5. If the area of the triangle is 96 sq units, what is its perimeter?

Using digits 1 to 6 (each at most once), how many 4-digit numbers can be formed that are divisible by 4?

N is a 3-digit number with non-zero digits. No digit is a perfect square and only 1 of the digits is a prime number. What is the number of factors of the smallest such number possible?

Adam's savings are equal to Ben's expenditure, which in turn is equal to Mary's savings. If Mary's savings are Rupees 50,000 and the incomes of Adam, Ben, and Mary are in the ratio 3:1:4, Mary's expenditure is less than thrice of Adam's expenditure and twice of Adam's expenditure is less than two times Ben's income, then which of the following could be true about Ben's income (\(I_B\))?

• (A) \(18000 < I_B < 22000\)
• (B) \(20000 < I_B < 25000\)
• (C) \(23000 < I_B < 28000\)
• (D) Data Inconsistent

If \(N = 2^3 \times 3^7 \times 5^7 \times 7^9 \times 10!\), then how many factors of N are there which are perfect squares as well as multiples of 420?

• (A) 500
• (B) 1080
• (C) 9000
• (D) 15840