List of top Engineering Mathematics Questions asked in Telangana State Post Graduate Engineering Common Entrance Test

Three students A, B and C write an entrance exam. The chance that at least one of them passes the exam is \( \frac{3}{4} \). If the probability that A and C pass the exam are respectively \( \frac{1}{2} \) and \( \frac{1}{4} \), then the probability that B does not pass that exam is:

If \( |Z|>2 \) and the coefficients of \( Z^{12} \) and \( \frac{1}{Z^{12}} \) in the Laurent series expansion of \[ \frac{1}{(1 - Z)(2 - Z)} \] are \( A \) and \( B \) respectively, then compute \( 2024 - A \).

A fair coin is tossed three times. Let \( X \) be the number of tails appearing and its distribution is: \[ \begin{array}{|c|c|c|c|c|} \hline X = x & 0 & 1 & 2 & 3 \\ \hline P(X = x) & \frac{1}{8} & \frac{3}{8} & \frac{3}{8} & \frac{1}{8} \\ \hline \end{array} \] Then the variance of \( X \) is: