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Consider the following system of equations in three real variables x<sub>1</sub>, x<sub>2</sub> and x<sub>3</sub><br>2x<sub>1</sub> - x<sub>2</sub> + 3x<sub>3</sub> = 1<br>3x<sub>1</sub> - 2x<sub>2</sub> + 5x<sub>3</sub> = 2<br>-x<sub>1</sub> - 4x<sub>2</sub> + x<sub>3</sub> = 3<br>This system of equations has

Correct Answer: a unique solution

Consider with respect to HusserI's concept of phenomena.
1. Phenomena is a substantial unity that has real properties, real parts and real changes.
2. Phenomena is no substantial unity, that has no real parts and no real changes.
3. Phenomena has no nature, but only essence.
4. Phenomena have no essence, but only nature.

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.
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.
What is important for the democratic society to function properly?

A mining company has three mines (MI, M2 and M3) that supply coal to three power plants (P1, P2 and P3). The three mines produce 900. 1000 and 1200 te of coal per day respectively. The power plant requirements from these three mines are 1200. 1000 and 900 te per day respectively. The unit cost of transporting coal from the three mines to the three power plants in Rs. is given below

Rahim has invited his three buddies over to watch the basketball game on his wide-screen television. They are all hungry, but no one wants to leave to get food. Just as they are arguing about who should make the food run, a commercial comes on for a local pizzeria that delivers. The phone number flashes on the screen briefly and they all try to remember it. By the time Zachary grabs a pen and paper, each of them recollects a different number.i. All of the men agree that the first three numbers are 995.ii. Three of them agree that the fourth number is 9.iii. Three agree that the fifth number is 2.iv. Three agree that the sixth number is 6; three others agree that the seventh number is also 6.Which of the numbers is most likely the telephone number of the pizzeria?

Zachary has invited his three buddies over to watch the basketball game on his wide-screen television. They are all hungry, but no one wants to leave to get food. Just as they are arguing about who should make the food run, a commercial comes on for a local pizze-ria that delivers. The phone number flashes on the screen briefly and they all try to remember it. By the time Zachary grabs a pen and paper, each of them recollects a different number.

#1 : All of the men agree that the first three numbers are 995.
#2 : Three of them agree that the fourth number is 9.
#3 : Three agree that the fifth number is 2.
#4 : Three agree that the sixth number is 6; three others agree that the seventh number is also 6.

Which of the numbers is most likely the telephone number of the pizzeria?

Suppose, you got a situation where you find that your linear regression model is under fitting the data. In such situation which of the following options would you consider?
1. I will add more variables
2. I will start introducing polynomial degree variables
3. I will remove some variables

Consider p(s) = s3 + a2s2 + a1s + a0 with all real coefficients. It is known that it is derivative p'(s) has no real roots. The number of real roots of p(s) is