Explore topic-wise InterviewSolutions in .

The area of the region bounded by the parabola $y=x^2+1$ and the straight line $x+y=3$ is

The closed loop line integral

${\oint }_{|z|=5}\frac{z^3+z^2+8}{z+2}dz$

evaluated counterclockwise, is

The probability that two friends share the same birth-month is:

Consider the following second-order differential equation:

$y^{\prime \prime }-4y^{\prime }+3y=2t-3t^2$

The particular solution of the diffrential equation is

If $A=\left[\begin{array}{ccc}5& 0& 2\\ 0& 3& 0\\ 2& 0& 1\end{array}\right],then{A}^{-1}=$

The value of the integral ${\int }_C\frac{2z+5}{(z-\frac{1}{2})(z^2-4z+5)}$

over the contour $|z|=1$, taken inthe anti-clockwise direciton , would be