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Consider the system of equations A<sub>(n × n)</sub> X<sub>(n × 1)</sub> = λ<sub>(n × 1)</sub> where, λ is a scalar. Let (λ<sub>i</sub>, x<sub>i</sub>) be an eigen-pair of an eigen value and its corresponding eigen vector for real matrix A. Let $$I$$ be a(n × n) unit matrix. Which one of the following statement is NOT correct?

Correct Answer: For matrix A<sup>m</sup>, m being a positive integer, (λ<sub>i</sub><sup>m</sup>, x<sub>i</sub><sup>m</sup>) will be the eigen-pair for all i

Let the eigen values of a 2 × 2 matrix A be 1, -2 with eigen vectors x1 and x2 respectively. Then the eigen values and eigen vectors of the matrix A2 - 3A + 4$$I$$ would, respectively, be

Nsub = n + log2(N/Nsub) is used to find the suffix length.

Read the passage carefully and select the best answer to each question out of the given four alternatives.
Public opinion may be passive and false or active and real. It is claimed in theory that all governments are ultimately based on the opinion or sanction of the governed. But we find that in practice the people's rights are often trodden down and tyranny and oppression are allowed to continue. The government does it not because the people want it to do so but because they are too idle, too uneducated and too disunited or timid to oppose the govern ment. Such public opinion is passive and false and not an active verdict. But when we find people alert, intelligent and determined to let the government know their will, when they want to exercise actively their voice in the management of their country, we have an instance of true or active public opinion. True public opinion is formed by and expressed through the press, the platform, political parties and educational institutions. These have sacred duties to perform, duties on which depends the ultimate good of the entire community. The press today wields a tremendous influence, So it should support the causes and move ments and condemn the wrong one's and thus teach people to form correct opinion. A free and fair press ventilates the grievances of the public. Thus a healthy relationship develops between the people and the government through out an unbiased press. Political parties also help to create and regulate opinions. No less important part is played by the educational Institutions which train the minds of the young people who will be the citizens of tomorrow. It has been said that modern Germany and China have been made by their universities. It is necessary that the young and the growing minds should imbibe the spirit of fellow-feeling, the spirit of tolerance, the habit of compromise, and show due regard for the feelings and opinion of others without which a democratic society cannot function, let alone succeed. When there is true awakening of the people, we shall have the real and conscious public opinion. And justice will reign on earth and truly will the voice of the people be the voice of God.
Which of the following is not the reason for the oppression caused to general public by the running government in the country?

Read the passage carefully and select the best answer to each question out of the given four alternatives.
Public opinion may be passive and false or active and real. It is claimed in theory that all governments are ultimately based on the opinion or sanction of the governed. But we find that in practice the people's rights are often trodden down and tyranny and oppression are allowed to continue. The government does it not because the people want it to do so but because they are too idle, too uneducated and too disunited or timid to oppose the govern ment. Such public opinion is passive and false and not an active verdict. But when we find people alert, intelligent and determined to let the government know their will, when they want to exercise actively their voice in the management of their country, we have an instance of true or active public opinion. True public opinion is formed by and expressed through the press, the platform, political parties and educational institutions. These have sacred duties to perform, duties on which depends the ultimate good of the entire community. The press today wields a tremendous influence, So it should support the causes and move ments and condemn the wrong one's and thus teach people to form correct opinion. A free and fair press ventilates the grievances of the public. Thus a healthy relationship develops between the people and the government through out an unbiased press. Political parties also help to create and regulate opinions. No less important part is played by the educational Institutions which train the minds of the young people who will be the citizens of tomorrow. It has been said that modern Germany and China have been made by their universities. It is necessary that the young and the growing minds should imbibe the spirit of fellow-feeling, the spirit of tolerance, the habit of compromise, and show due regard for the feelings and opinion of others without which a democratic society cannot function, let alone succeed. When there is true awakening of the people, we shall have the real and conscious public opinion. And justice will reign on earth and truly will the voice of the people be the voice of God.
According to the passage, which of the following is needed from the people to have true or active public opinion? 1. Alertness
2. Determination
3. Intelligence
4. Raising their voice

Read the passage carefully and select the best answer to each question out of the given four alternatives.
Public opinion may be passive and false or active and real. It is claimed in theory that all governments are ultimately based on the opinion or sanction of the governed. But we find that in practice the people's rights are often trodden down and tyranny and oppression are allowed to continue. The government does it not because the people want it to do so but because they are too idle, too uneducated and too disunited or timid to oppose the govern ment. Such public opinion is passive and false and not an active verdict. But when we find people alert, intelligent and determined to let the government know their will, when they want to exercise actively their voice in the management of their country, we have an instance of true or active public opinion. True public opinion is formed by and expressed through the press, the platform, political parties and educational institutions. These have sacred duties to perform, duties on which depends the ultimate good of the entire community. The press today wields a tremendous influence, So it should support the causes and move ments and condemn the wrong one's and thus teach people to form correct opinion. A free and fair press ventilates the grievances of the public. Thus a healthy relationship develops between the people and the government through out an unbiased press. Political parties also help to create and regulate opinions. No less important part is played by the educational Institutions which train the minds of the young people who will be the citizens of tomorrow. It has been said that modern Germany and China have been made by their universities. It is necessary that the young and the growing minds should imbibe the spirit of fellow-feeling, the spirit of tolerance, the habit of compromise, and show due regard for the feelings and opinion of others without which a democratic society cannot function, let alone succeed. When there is true awakening of the people, we shall have the real and conscious public opinion. And justice will reign on earth and truly will the voice of the people be the voice of God.
Who among the following has tremendous influence in forming the true public opinion?

Read the passage carefully and select the best answer to each question out of the given four alternatives.
Public opinion may be passive and false or active and real. It is claimed in theory that all governments are ultimately based on the opinion or sanction of the governed. But we find that in practice the people's rights are often trodden down and tyranny and oppression are allowed to continue. The government does it not because the people want it to do so but because they are too idle, too uneducated and too disunited or timid to oppose the govern ment. Such public opinion is passive and false and not an active verdict. But when we find people alert, intelligent and determined to let the government know their will, when they want to exercise actively their voice in the management of their country, we have an instance of true or active public opinion. True public opinion is formed by and expressed through the press, the platform, political parties and educational institutions. These have sacred duties to perform, duties on which depends the ultimate good of the entire community. The press today wields a tremendous influence, So it should support the causes and move ments and condemn the wrong one's and thus teach people to form correct opinion. A free and fair press ventilates the grievances of the public. Thus a healthy relationship develops between the people and the government through out an unbiased press. Political parties also help to create and regulate opinions. No less important part is played by the educational Institutions which train the minds of the young people who will be the citizens of tomorrow. It has been said that modern Germany and China have been made by their universities. It is necessary that the young and the growing minds should imbibe the spirit of fellow-feeling, the spirit of tolerance, the habit of compromise, and show due regard for the feelings and opinion of others without which a democratic society cannot function, let alone succeed. When there is true awakening of the people, we shall have the real and conscious public opinion. And justice will reign on earth and truly will the voice of the people be the voice of God.
What is important for the democratic society to function properly?

A 3 × 3 matrix has elements such that its trace is 11 and its determinant is 36. The eigen values of the matrix are all known to be positive integers. The largest eigen value of the matrix is

Let us consider a square matrix A of order n with Eigen values of a, b, c then the Eigen values of the matrix AT could be.

Consider the following statements and select which of the following statement are true. Statement 1: The maximum sum rectangle can be 1X1 matrix containing the largest element If the matrix size is 1X1 Statement 2: The maximum sum rectangle can be 1X1 matrix containing the largest element If all the elements are zero Statement 3: The maximum sum rectangle can be 1X1 matrix containing the largest element If all the elements are negative

Consider a 3 × 3 real symmetric matrix S such that two of its eigen values are a ≠ 0, b≠ 0 with respective eigen vectors \[\left[ {\begin{array}{*{20}{c}} {{{\text{x}}_1}} \\ {{{\text{x}}_2}} \\ {{{\text{x}}_3}} \end{array}} \right