# Engineering Mathematics GATE-2002

**Q 1:** In the complex plane, the angle between lines 1 + i and -1 + i (where i=\sqrt{-1} ) is

**Q 2:** The inverse of the matrix \begin{bmatrix}0.2&0&0\\0&1&0\\0&0&0.5\end{bmatrix} is

**Q 3:** Which of the following holds for any non-zero vector **a**

**Q 4:** The coefficient x^{2} in the Taylor series of cos^{2} x about 0 is

**Q 5:** Three grades of paint (A, B, and C, production rates 12, 24 & 18 batches per day, respectively) are produced in independent batch production lines and stored in separate areas. The number of off-specification batches in a day is 1, 3, and 2 for grades A, B, and C, respectively. The probability of picking an off-specification batch from a randomly chosen storage area is