Engineering Mathematics GATE-1995

Q 1: The rank of matrix $\begin{vmatrix}1&0&0\\0&2&0\\3&0&0\end{vmatrix}$ is

A) 0
B) 1
C) 2
D) 3

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Q 2: The angle between two vectors $2\overline i-\overline j+\overline k$ and $\overline i+\overline j+2\overline k$ is

A) 0˚
B) 30˚
C) 45˚
D) 60˚

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Q 3: A function $f(x)=12x-x^3$ has maximum value at x =

A) -2
B) 0
C) 2
D) $\sqrt{12}$

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Q 4: $\lim\limits_{x\rightarrow0}\frac{\tan x}x=$

A) ∞
B) 1
C) 0
D) -1

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Q 5: The second order Taylor series expansion for a function $f(x)=x^2$ at x = 1 is

A) x²
B) 1 + x²
C) 1 + x + x²
D) 1 – x + x²

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Q 6: The average value of function $f(x)=x^3$ in the interval 0 ≤ x ≤ 2

A) 1
B) 2
C) 4
D) 8

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Q 7: Match the items in the left column with the appropriate items in the right column.

(I) y = x2	(A) linear ODE
(II) dy/dx = 2x	(B) nonlinear ODE
	(C) linear algebraic equation
	(D) nonlinear algebraic equation

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Q 8: Match the items in the left column with the appropriate items in the right column.

(I) dy/dx + 5y = 0, y(0) = yo	(A) y = yo + 5x
(II) dy/dx + 5 = 0, y(0) = yo	(B) y = yo – 5x
	(C) y = yoe-5x
	(D) y = yoe5x

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Q 9: Find eigen values and eigenvectors of $\begin{bmatrix}4&-5\\1&-2\end{bmatrix}$

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