Q501. Find the minor and cofactor respectively for the element 3 in the determinant \( \Delta = \begin{vmatrix} 1 & 5 \\ 3 & 2 \end{vmatrix} \)

Q502. \(\mathbf{Passage:}\)

The Turing test, proposed by Alan Turing, is a measure of a machine's ability to exhibit human-like intelligence. In this test, a human judge engages in natural language conversations with both a machine and another human without knowing which is which. If the judge cannot reliably distinguish between them, the machine is considered to have passed the Turing test.

Q.1: What is the Turing test a measure of?
Q.2: How is the Turing test conducted?

Q503. Identify the sentence with the correct use of the gerund.

Q504. If the mean and the mode are given as 45 and 40. Find the Median.

Q505. The team members were ___________ to work on the weekend to meet the project deadline.

Q506. Which part of a letter typically includes the sender's address and date?

Q507. If f is a bijective function, then \( f^{-1} f(x) = \)

Q508. Find the matrix \(M\) and \(N\), if \(M+N= \begin{bmatrix}5 & 6 \\ 4 & 2 \end{bmatrix}\) and \(M-N = \begin{bmatrix}1 & 4 \\ 4 & 2 \end{bmatrix} \)

Q509. \( | \overline{u} | ^2 = _{----------} \)

Q510. What does the phrase "hit the hay" mean?