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Let a, b, c be in AP and k ≠ 0 be a real number. Which of the following are correct? 1. ka, kb, kc are in AP 2. k - a, k - b, k - c are in AP 3. \(\frac{a}{k},\frac{b}{k},\frac{c}{k}\) are in AP Select the correct answer using the code given below:

Let a, b, c be in AP and k ≠ 0 be a real number. Which of the following are correct? 1. ka, kb, kc are in AP 2. k - a, k - b, k - c are in AP 3. \(\frac{a}{k},\frac{b}{k},\frac{c}{k}\) are in AP Select the correct answer using the code given below: Correct Answer 1, 2, and 3

Concept:

If each term of a given AP is multiplied or divided by a non-zero constant k, then the resultant sequence is also an AP with common difference k × d or k / d, where d is the common difference of the given AP.

If a, b and c are in AP then k - a, k - b, k - c are in AP where k ≠ 0.

Related Questions

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?
Consider the following numbers: 1. Every irrational number is a real number. 2. Every real number is a rational number. 3. Every rational number is a real number. 4. Every integer is a real number. Which of the above statements are correct?
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Consider a circle with centre at O and radius 7 cm. Let QR be the chord of length 2 cm and let P be the midpoint of QR. Let CD be another chord of this circle passing through P such that ∠CPQ is acute. If M is the midpoint of CD and MP = √24 cm, then which of the following statements are correct? (1) ∠QPD = 135° (2) If CP = m cm and PD = n cm, then m and n are the roots of the quadratic equation x2 – 10x + 1 = 0 (3) The ratio of triangle OPR to the area of triangle OMP is 1 ∶ 2√2 Select the correct answer using the code given below.
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