Engineering Mathematics GATE-2001

Q 1: The value of the following determinant

$\begin{bmatrix}1&0&0&0&0\\-2&2&0&0&0\\3&5&3&0&0\\-1&4&7&4&0\\-50&-6&2&1&1\end{bmatrix}$

A) 24
B) 32
C) -112
D) 0

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Q 2: The value of $(1+i)^8$, where $i=\sqrt{-1}$, is

A) 8 + 4 i
B) 8 – 4 i
C) 16
D) 8

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Q 3: The function $f(x,y)=x^2+y^2-xy-x-y+5$ has the

A) Maximum at (1, 1)
B) Saddle point at (1, 1)
C) minimum at (1, 1)
D) None of the above at (1, 1)

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Q 4: A fair die is rolled four times. Find the probability that six shows up twice.

A) 1/2
B) 16/325
C) 1/36
D) 25/216

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