Engineering Mathematics GATE-2002

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

A) π/4
B) π/2
C) 3π/4
D) π

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

A) \begin{bmatrix}2&0&0\\0&1&0\\0&0&5\end{bmatrix}
B) \begin{bmatrix}-0.2&0&0\\0&-1&0\\0&0&-0.5\end{bmatrix}
C) \begin{bmatrix}5&0&0\\0&1&0\\0&0&2\end{bmatrix}
D) \begin{bmatrix}0.5&0&0\\0&1&0\\0&0&0.2\end{bmatrix}

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

A) \nabla.a=0
B) \nabla\times a=0
C) \nabla.(\nabla\times a)=0
D) \nabla(\nabla\times a)=0

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Q 4: The coefficient x² in the Taylor series of cos² x about 0 is

A) 2
B) 0
C) 1
D) -1

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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

A) 23/216
B) 24/216
C) 19/216
D) 18/216

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