[Download PDF] ISRO Scientist or Engineer Mechanical 2012 Paper with Solutions

Instructions

For the following questions answer them individually

Question 41

Rank of the matrix
$$ A = \begin{bmatrix}1 & 1 & 2 \\1 & 2 & 3 \\ 0 & -1 & 1 \end{bmatrix} $$ is

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Question 42

The value of $$t$$ for which $$A + tB$$ is perpendicular to $$C$$ where $$A = i + 2j + 3k, B = -i + 2j + k$$ and $$C = 3i + j$$

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Question 43

$$ \overline{A} \times \overline{B} $$ is a vector

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Question 44

The equation of the plane through the line $$ \frac {x - 1}{3} = \frac {y - 4}{2} = \frac {z - 4}{-2} $$ and parallel to the line $$ \frac {x + 1}{2} = \frac {y - 1}{-4} = \frac {z + 2}{1} $$ is

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Question 45

Let $$E$$ and $$F$$ be any two events with $$4 P(E \cup F) = 0.8, P(E) = 0.4$$ and $$P (E/F) = 0.3$$.Then $$(F)$$ is .

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Question 46

The approximate value of y(0.1) from $$\frac {dy} {dx} = x^2 y-1, y(0) = 1$$ is

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Question 47

1+ i is equivalent to

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Question 48

In a class of 45 students, the mean mark of 25 girls is 32 and the mean mark of 20 boys is 27.5. What is the class mean?

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Question 49

If $$ L \left\{ f(t) \right\} = F (s),$$ then the value of $$ L \left\{ e^{-at} f(t) \right\} $$ is

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Question 50

The probability that A happens is $$\frac{1}{3}$$. The odds against happening of A are

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CAT Content

ISRO Scientist or Engineer Mechanical 2012

ISRO Scientist or Engineer Mechanical 2012

Rank of the matrix$$ A = \begin{bmatrix}1 & 1 & 2 \\1 & 2 & 3 \\ 0 & -1 & 1 \end{bmatrix} $$ is

The value of $$t$$ for which $$A + tB$$ is perpendicular to $$C$$ where $$A = i + 2j + 3k, B = -i + 2j + k$$ and $$C = 3i + j$$

$$ \overline{A} \times \overline{B} $$ is a vector

The equation of the plane through the line $$ \frac {x - 1}{3} = \frac {y - 4}{2} = \frac {z - 4}{-2} $$ and parallel to the line $$ \frac {x + 1}{2} = \frac {y - 1}{-4} = \frac {z + 2}{1} $$ is

Let $$E$$ and $$F$$ be any two events with $$4 P(E \cup F) = 0.8, P(E) = 0.4$$ and $$P (E/F) = 0.3$$.Then $$(F)$$ is .

The approximate value of y(0.1) from $$\frac {dy} {dx} = x^2 y-1, y(0) = 1$$ is

1+ i is equivalent to

In a class of 45 students, the mean mark of 25 girls is 32 and the mean mark of 20 boys is 27.5. What is the class mean?

If $$ L \left\{ f(t) \right\} = F (s),$$ then the value of $$ L \left\{ e^{-at} f(t) \right\} $$ is

The probability that A happens is $$\frac{1}{3}$$. The odds against happening of A are

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Rank of the matrix
$$ A = \begin{bmatrix}1 & 1 & 2 \\1 & 2 & 3 \\ 0 & -1 & 1 \end{bmatrix} $$ is