Let r and c be real numbers. If r and −r are roots of 5x³ + cx² − 10x + 9 = 0, then c equals

Let f(x) be a quadratic polynomial in x such that f(x) ≥ 0 for all real numbers x. If f(2) = 0 and f(4) = 6, then f(−2) is equal to

Manu earns ₹4000 per month and wants to save an average of ₹550 per month in a year. In the first nine months, his monthly expense was ₹3500, and he foresees that, tenth month onward, his monthly expense will increase to ₹3700. In order to meet his yearly savings target, his mont…

The average of a non-decreasing sequence of N numbers a₁, a₂, . . . , a_N is 300. If a₁ is replaced by 6a₁, the new average becomes 400. Then, the number of possible values of a₁ is

Five students, including Amit, appear for an examination in which possible marks are integers between 0 and 50, both inclusive. The average marks for all the students is 38 and exactly three students got more than 32. If no two students got the same marks and Amit got the least m…

For some natural number n, assume that (15,000)! is divisible by (n!)!. The largest possible value of n is:

The number of integral solutions of the equation (x² − 10)^(x² − 3x − 10) = 1 is:

Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio 5 : 8 : 10. They accept a job which they can finish in 4 days if they all work together for 8 hours per day. However, Anu and Tanu work together for the first 6 days, working 6 hours 40 minu…

In an election, there were four candidates and 80% of the registered voters casted their votes. One of the candidates received 30% of the casted votes while the other three candidates received the remaining casted votes in the proportion 1 : 2 : 3. If the winner of the election r…