Engineering Mathematics GATE-1995

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





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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





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





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





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





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





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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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