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Q:

If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of $\frac{a^{2} + b^{2} + c^{2}}{3}$ is :

A) M	B) 3 M^2
C) 2 (M/3)	D) M^2

Answer & Explanation Answer: B) 3 M^2

Explanation:

We have : ( a + b + c) / 3 = M or (a + b + c) = 3M.

Now. ${(a + b + c)}^{2} = {(3 M)}^{2} = 9 M^{2}$ .

$< = > a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a) = 9 M^{2}$

$a^{2} + b^{2} + c^{2} = 9 M^{2}, (a b + b c + c a = 0)$

Required mean = $(\frac{a^{2} + b^{2} + c^{2}}{3}) = \frac{9 M^{2}}{3} = 3 M^{2}$ .

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Filed Under: Average
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Q:

A student was asked to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What should be the number in place of x ?

A) 6	B) 7
C) 8	D) 9

Answer & Explanation Answer: B) 7

Explanation:

Clearly, we have (3 + 11 + 7 + 9 + 15 + 13 + 8 + 19 + 17 + 21 + 14 + x) / 12 = 12.

or 137 + x = 144 or x = 144 - 137 = 7.

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Q:

Which of the following establised as the Bretton woods Conference in 1944

A) IMF	B) ILO
C) WHO	D) UNDP

Answer & Explanation Answer: A) IMF

Explanation:

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Filed Under: World Organisations

Q:

The International Human Rights Convention adopted by the United Nations in 1990 relates to

A) Children	B) Dasabled
C) Stateless Persons	D) Migrant workers

Answer & Explanation Answer: A) Children

Explanation:

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Filed Under: World Organisations

Q:

What is Manohar's birthday ?

I. Manohar's father was born on 27th May, 1948.

II. Manohar is 25 years younger than his mother.

A) If the data in statement I alone are sufficient to answer the question	B) If the data in statement II alone are sufficient answer the question
C) If the data either in I or II alone are sufficient to answer the question;	D) If the data even in both the statements together are not sufficient to answer the question

Answer & Explanation Answer: D) If the data even in both the statements together are not sufficient to answer the question

Explanation:

Clearly, even both the statements together do not reveal Manohar's birthday.

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Filed Under: Data Sufficiency

Q:

In which year was Rahul born ?

I. Rahul at present is 25 years younger to his mother.

II. Rahul's brother, who was born in 1964, is 35 years younger to his mother.

A) If the data in statement I alone are sufficient to answer the question	B) If the data in statement II alone are sufficient answer the question
C) If the data either in I or II alone are sufficient to answer the question;	D) If the data in both the statements together are needed.

Answer & Explanation Answer: D) If the data in both the statements together are needed.

Explanation:

From both the given statements, we find that Rahul is (35 - 25) = 10 years older than his brother,

who was born in 1964, So. Rahul was horn in 1954

Thus, both the given statements are needed to answer the query.

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Filed Under: Data Sufficiency

Q:

In which year was Sanjay born ?

I. Sanjay is six years older than Gopal.

II. Gopal's brother was born in 1982.

III. Sanjay's brother as two years younger than Gopal's brother who was eight years younger than Gopal.

A) I and II together	B) II and III together
C) I and III together	D) I, II and III together

Answer & Explanation Answer: D) I, II and III together

Explanation:

From II, we know that Copal's brother was born in 1982. From III, we find that Gopal's brother was 8 years younger to him i.e. Copal was born in 1974. From I, we find that Sanjay is 6 years older than Gopal Thus. Sanjay was born in 1968. So. all the three statements are required.

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Filed Under: Data Sufficiency

Q:

Who among the following was the first President of the Indian Trade Union Congress in 1920?

A) Chittaranjan Das	B) Lala Lajpath Roy
C) Dr. Rajendra Prasad	D) None

Answer & Explanation Answer: B) Lala Lajpath Roy

Explanation:

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Filed Under: Famous Personalities

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