Q 1: The rank of matrix \begin{vmatrix}1&0&0\\0&2&0\\3&0&0\end{vmatrix} is
Q 2: The angle between two vectors 2\overline i-\overline j+\overline k and \overline i+\overline j+2\overline k is
Q 3: A function f(x)=12x-x^3 has maximum value at x =
Q 4: \lim\limits_{x\rightarrow0}\frac{\tan x}x=
Q 5: The second order Taylor series expansion for a function f(x)=x^2 at x = 1 is
Q 6: The average value of function f(x)=x^3 in the interval 0 ≤ x ≤ 2
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 |
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 |
Q 9: Find eigen values and eigenvectors of \begin{bmatrix}4&-5\\1&-2\end{bmatrix}