List of top Questions asked in CAT- 2010

In an examination, the average marks obtained by students who passed was \( x\% \), while the average of those who failed was \( y\% \). The average marks of all students taking the exam was \( z\% \). Find in terms of \( x, y, z \), the percentage of students taking the exam who failed.
If three positive real numbers \( a, b, c \) (with \( c>a \)) are in Harmonic Progression, then \( \log(a + c) + \log(a - 2b + c) \) is equal to:

Let \( f \) be an injective map with domain x, y, z and range 1, 2, 3 such that exactly one of the following statements is correct and the remaining are false.} 
[I.] \( f(x) = 1 \Rightarrow f(y) = 1, f(z) = 2 \) 
[II.] \( f(x) = 2 \Rightarrow f(y) = 1, f(z) = 1 \) 
[III.] \( f(x) = 1, f(y) = 1, f(z) = 2 \) Then the value of \( f(1) \) is:

In a factory making radioactive substances, it was considered that three cubes of uranium together are hazardous. So the company authorities decided to have the stack of uranium interspersed with lead cubes. But there is a new worker in the company who does not know the rule. So he arranges the uranium stack the way he wanted. What is the number of hazardous combinations of uranium in a stack of 5?