ISRO Scientist or Engineer Mechanical 2011

The equation of the tangent to the curve y (x - 2)(x - 3) - x + 7 = 0, at the point where it cuts the x-axis is

If the imaginary part of $$\frac {2z + 1}{iz + 1}$$ is —2, then the locus of the point z in the complex plane is

General solution of the differential equation $$(D^2 - 2D + 1)y = e^x$$ is

In a simple micrometer with screw pitch 0.5 mm and divisions on thimble 50, the reading corresponding to 5 divisions on barrel and 12 divisions on thimble is

The value of $$\begin{bmatrix}a & b & c \\b + c & c + a & a + b \\a^2 &b^2 & c^2 \\ \end{bmatrix}$$ is

If $$v = (x^2 + y^2 + z^2)^{\frac {-1}{2}}$$, then $$\frac{\partial^2 v}{\partial x^2} + \frac{\partial^2 v}{\partial y^2} + \frac{\partial^2 v}{\partial z^2}$$ is

The image of the point(1,2,3) in the plane 2x + y + z = 13 is

The value of curl of the vector $$v = (xyz)\widehat{i} + (3x^2y)\widehat{j} + (xz^2 - y^2z)\widehat{k}$$ at the point (2, -1, 1) is

An open tank contains water to a depth of 2 m and oil over it toa depth of 1m. If the specific gravity of oil is 0.8, then the pressure intensity at the interface of the two fluid layers will be

A box contains 6 black and 5 red balls. Twe balls are drawn one after another from the box without replacement. The probability for both balls to be red is