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Bernoulli's equation for fluid flow is derived following certain assumptions. Out of the assumptions listed below, which set of assumptions is used in derivation of Bernoulli's equation?<br>1. Fluid flow is frictionless &amp; irrotational<br>2. Fluid flow is steady<br>3. Fluid flow is uniform &amp; turbulent<br>4. Fluid is compressible<br>5. Fluid is incompressible

Correct Answer: 1, 2, 5

Consider the 5 × 5 matrix \[{\text{A}} = \left[ {\begin{array}{*{20}{c}} 1&2&3&4&5 \\ 5&1&2&3&4 \\ 4&5&1&2&3 \\ 3&4&5&1&2 \\ 2&3&4&5&1 \end{array}} \right

Let A be an m × n matrix and Ban n × m matrix. It is given that determinant ($$I$$m + AB) = determinant ($$I$$n + BA), where $$I$$k is the k × k identity matrix. Using the above property, the determinant of the matrix given below is
\[\left[ {\begin{array}{*{20}{c}} 2&1&1&1 \\ 1&2&1&1 \\ 1&1&2&1 \\ 1&1&1&2 \end{array}} \right

Eigen values of the matrix \[\left[ {\begin{array}{*{20}{c}} 0&1&0&0 \\ 1&0&0&0 \\ 0&0&0&{ - 2i} \\ 0&0&{2i}&0 \end{array}} \right

The parse tree below represents a rightmost derivation according to the grammar S → AB, A → aS|a, B → bA. Which of the following are right-sentential forms corresponding to this derivation?

In the following question, two statements are given each followed by two conclusions I and II. You have to consider the statements to be true even ifthey seem to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements. Statements:
(I) Empty set is a subset of any set.
(II) A set is a subset of power set. Conclusion:
(I) Empty set is a power set.
(II) A set is a subset of power set.

The value of x for which all the eigen-values of the matrix given below are real is \[\left[ {\begin{array}{*{20}{c}} {10}&{5 + {\text{j}}}&4 \\ {\text{x}}&{20}&2 \\ 4&2&{ - 10} \end{array}} \right

For which value of x will the matrix given below become singular?
\[\left[ {\begin{array}{*{20}{c}} 8&{\text{x}}&0 \\ 4&0&2 \\ {12}&6&0 \end{array}} \right

Consider the matrix as given below:
\[\left[ {\begin{array}{*{20}{c}} 1&2&3 \\ 0&4&7 \\ 0&0&3 \end{array}} \right

The eigen values of the matrix given below are
\[\left[ {\begin{array}{*{20}{c}} 0&1&0 \\ 0&0&1 \\ 0&{ - 3}&{ - 4} \end{array}} \right

The sum of the eigen values of the matrix given below is \[\left[ {\begin{array}{*{20}{c}} 1&2&3 \\ 1&5&1 \\ 3&1&1 \end{array}} \right