Q 1: The direction of largest increase of the function xy3 – x2 at the point (1, 1) is
Q 2: The modulus of the complex number \frac{1+i}{\sqrt2} is
Q 3: The system of linear equations Ax = 0, where A is an n×n matrix, has a non-trivial solution only if
Q 4: The value of the limit \lim\limits_{x\rightarrow\mathrm\pi/2}\frac{\cos x}{\left(\mathrm x-\mathrm\pi/2\right)^3} is
Q 5: The general solution of the differential equation \frac{d^2y}{dx^2}-\frac{dy}{dx}-6y=0 , where C1 and C2 are constants of integration, is
Q 6: Using the residue theorem, the value of the integral (counter-clockwise)
\oint\frac{8-7z}{z-4}dzaround a circle with center at z = 0 and radius = 8 (where z is a complex number and i=\sqrt{-1} , is
Q 7: Consider the integral
\iint(2x\widehat i-2y\widehat j+5z\widehat k\;).\widehat ndSover the surface of a sphere of radius = 3 with center at the origin and surface unit normal \widehat n pointing away from the origin. Using the Gauss divergence theorem, the value of this integral is
Q 8: Using the trapezoidal rule and 4 equal intervals (n = 4), the calculated value of the integral (rounded to the first place of the decimal) \int_0^\pi\sin\theta d\theta is
Q 9: The eigen values of matrix A=\begin{bmatrix}1&2\\4&3\end{bmatrix} are 5 and -1 then the eigen values of -2A + 3I (I is a 2×2 identity matrix) are
Q 10: A fair die is rolled. Let R denotes the event of obtaining a number less than or equal to 5 and S denotes the event of obtaining an odd number. Then which one of the following about the probability (P) is true?
Q 11: The inverse Laplace transform of \frac1{2s^2+3s+1} is