ISRO Scientist or Engineer Civil 2018

Instructions

For the following questions answer them individually

Question 71

The value of

is

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Question 72

A rectangular sheet of metal of length 6m and width 2 m is given. Four equal squares are removed from the corners. The sides of this sheet are now turned up to form an open rectangular box. The height of box such that the volume of the box is maximum will be

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Question 73

The complete solution of the linear differential equation
$$\frac{\text{d}^2z}{\text{d}t^2} + (p + q) \frac{\text{d}z}{\text{d}t} + pqz = 0$$

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Question 74

The sequence $$\lim_{a \rightarrow \infty} \left[ 3 + (-1)^n\right]$$ is

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Question 75

Then the product of determinant P and Q ( PQ ) has the value

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Question 76

The differential equation $$y = x \frac{\text{d}y}{\text{d}x} + \frac{x}{\frac{dy}{dx}}$$ is

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Question 77

In a square matrix $$A = [ a_ij ],$$ if $$a_ij = − a_ji$$ for all i and j so that all the leading diagonal elements are zero, then the matrix is called

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Question 78

The difference of two complex numbers $$(x_1 + iy_1)$$ and $$(x_2 + iy_2)$$ is

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Question 79

The value of $$\lim_{x \rightarrow 0} \frac {\log x}{\cot x}$$ is

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Question 80

A box contains 5 red and 10 green balls. Eight (8) of them are placed in another box. The chances that the latter box contains 2 red and 6 green balls are

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