ISRO Scientist or Engineer Mechanical 2006

Instructions

For the following questions answer them individually

Question 71

A unit vector perpendicular to the vectors $$\overrightarrow{a} = 2i - 3j + k$$ and $$\overrightarrow{b} = i + j - 2k,$$ is

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Question 72

The region of the z plane for which $$|\frac {z - a}{z + a}| = (Re a \neq 0)$$ is

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Question 73

If $$\alpha, \beta, \gamma$$ are the roots of equations $$X^3 + Px^2 + qx + p = 0$$, Then the value of $$\tan^{-1} \alpha + \tan^{-1} \beta + \tan^{-1} \gamma$$ is

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Question 74

The value of the determinant 

is

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Question 75

The value of $$\int_{0}^{1} \int_{0}^{1} \frac{dx dy} {\sqrt{ (1 -x^2)(1 - y^2)}}$$ is

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Question 76

Solution of $$(D^2 + 16)y = \cos 4x,$$ is

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Question 77

Laplace transform of $$t^2 + 2t + 3$$ is

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Question 78

Equation of a straight line passing through the point (-1,2) and making equal intercepts on the axes is

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Question 79

A bag contains eight white and six red marbles. The probability of drawing two marbles of same colour is

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Question 80

The Algebraic multiplicity of the matrix $$A = \begin{bmatrix}0 & 1 & 0 \\0 & 0 & 1 \\ 1 & -3 & 3 \end{bmatrix}$$ is

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