Consider the following in respect of sets A and B:
1. \( (A - B) \cup B = A \)
2. \( (A - B) \cup A = A \)
3. \( (A - B) \cap B = \phi \)
4. \( A \subseteq B \Rightarrow A \cup B = B \)
Which of the above are correct?
In the binary equation \( (1p101)_{2} + (10q1)_{2} = (100r00)_{2} \), where p, q and r are binary digits, what are the possible values of p, q and r respectively?
The expansion of \( (x - y)^{n} \), \( n \geq 5 \) is done in the descending powers of x. If the sum of the fifth and sixth terms is zero, then \( \frac{x}{y} \) is equal to
If \( a \neq b \neq c \), then one value of x which satisfies the equation \( \begin{vmatrix} 0 & x-a & x-b \\ x+a & 0 & x-c \\ x+b & x+c & 0 \end{vmatrix} = 0 \) is given by
If \( A = \begin{bmatrix} \cos\alpha & \sin\alpha \\ -\sin\alpha & \cos\alpha \end{bmatrix} \), then what is \( AA^{T} \) equal to (where \( A^{T} \) is the transpose of A)?
