Q 1: Given i=\sqrt{-1} , the ratio \left(\frac{i+3}{i+1}\right) is given by
Q 2: The value of ‘a’ for which the following set of equations
y+2z=0
2x+y+z=0
ax+2y=0
have a non-trivial solution, is
Q 3: The initial condition for which the following equation
(x^2+2x)\frac{dy}{dx}=2(x+1)y;\;\;y(x_0)=y_0has infinitely many solutions, is
Q4: Given that the Laplace transform of the function below over a single period 0 < t < 2 is \frac1{s^2}\left(1-e^{-s}\right)^2 , the Laplace transform of the periodic function over 0 < t < ∞ is
Q 5: If z=x+iy is a complex number, where i=\sqrt{-1} then the derivative of z\overline z at 2 + i is
Q 6: \overset=A and \overset=B are two 3×3 matrix such that \overset=A=\begin{bmatrix}-2&4&6\\1&2&1\\0&4&4\end{bmatrix} , \overset=B=\overset=0 and \overset=A\overset=B=\overset=0 . Then the rank of matrix \overset=B is
Q 7: The solution of the following differential equation x\frac{dy}{dx}+y(y^2-1)=2x^3 is
Q 8: The directional derivative of f=\frac12\sqrt{x^2+y^2} at (1, 1) in the direction of \overrightarrow b=\overrightarrow i-\overrightarrow j is
Q 9: Evaluate the following integral (n ≠ 0) \int_c\left(-xy^ndx+x^nydy\right) within the area of a triangle with vertices (0, 0), (1, 0) and (1, 1) (counter-clockwise).
Q 10: The family of curves that is orthogonal to xy = c is
Q 11: The Laplace transform of f(t)=1/\sqrt t is
Q 12: The thickness of a conductive coating in micrometers has a probability density function of 600x^{-2} for 100 μm < x < 120 μm. The mean and the variance of the coating thickness is