  # ISRO Scientist or Engineer Mechanical 2011

Instructions

For the following questions answer them individually

Question 71

# 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 Question 72

# If the imaginary part of $$\frac {2z + 1}{iz + 1}$$ is —2, then the locus of the point z in the complex plane is Question 73

# General solution of the differential equation $$(D^2 - 2D + 1)y = e^x$$ is Question 74

# 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 Question 75

# The value of $$\begin{bmatrix}a & b & c \\b + c & c + a & a + b \\a^2 &b^2 & c^2 \\ \end{bmatrix}$$ is Question 76

# 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 Question 77

# The image of the point(1,2,3) in the plane 2x + y + z = 13 is Question 78

# 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 Question 79

# 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 Question 80

# 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 OR