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Q:

In a Plane there are 37 straight lines, of which 13 pass through the point A and 11 pass through the point B. Besides, no three lines pass through one point, no lines passes through both points A and B , and no two are parallel. Find the number of points of intersection of the straight lines.

A) 525	B) 535
C) 545	D) 555

Answer & Explanation Answer: B) 535

Explanation:

The number of points of intersection of 37 lines is $C_{2}^{37}$ . But 13 straight lines out of the given 37 straight lines pass through the same point A.

Therefore instead of getting $C_{2}^{13}$ points, we get only one point A. Similarly 11 straight lines out of the given 37 straight lines intersect at point B. Therefore instead of getting $C_{2}^{11}$ points, we get only one point B.

Hence the number of intersection points of the lines is $C_{2}^{37} - C_{2}^{13} - C_{2}^{11} + 2$ = 535

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Filed Under: Permutations and Combinations
Exam Prep: CAT , Bank Exams , AIEEE
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Q:

In a G - 20 meeting there were total 20 people representing their own country. All the representative sat around a circular table. Find the number of ways in which we can arrange them around a circular table so that there is exactly one person between two representatives namely Manmohan and Musharraf.

A) 2 x (17!)	B) 2 x (18!)
C) (3!) x (18!)	D) (17!)

Answer & Explanation Answer: B) 2 x (18!)

Explanation:

A person can be chosen out of 18 people in 18 ways to be seated between Musharraf and Manmohan. Now consider Musharraf, Manmohan, and the third person, sitting between them, as a single personality, we can arrange them in 17! ways but Musharraf and Manmohan can also be arranged in 2 ways.

Required number of permutations = 18 x (17!) x 2 = 2 x 18!

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Filed Under: Permutations and Combinations
Exam Prep: GATE , Bank Exams , AIEEE
Job Role: Bank PO , Analyst

Q:

How many 7 digit numbers can be formed using the digits 1, 2, 0, 2, 4, 2, 4?

A) 120	B) 360
C) 240	D) 424

Answer & Explanation Answer: B) 360

Explanation:

There are 7 digits 1, 2, 0, 2, 4, 2, 4 in which 2 occurs 3 times, 4 occurs 2 times.

Number of 7 digit numbers = $\frac{7!}{3! \times 2!}$ = 420

But out of these 420 numbers, there are some numbers which begin with '0' and they are not 7-digit numbers. The number of such numbers beginning with '0'.

= $\frac{6!}{3! \times 2!}$ = 60

Hence the required number of 7 digits numbers = 420 - 60 = 360

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Filed Under: Permutations and Combinations
Exam Prep: AIEEE , Bank Exams , CAT
Job Role: Bank Clerk , Bank PO

Q:

Q 2 3 B 9 V 5 L S R F P

If one is subtracted from each of the numbers, which of the following will be the fourth to the right of the tenth from the right ?

A) 4	B) 8
C) 2	D) 1

Answer & Explanation Answer: A) 4

Explanation:

Fourth to the right of the tenth from the right means (10 - 4 = )6th from the right, ie 5. But according to the queswtion, one is subtracted from each of the numbers, ie 4.

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Filed Under: Alphabet Test

Q:

Among the following, which one has the largest number of neighboring countries sharing the land border?

A) Sudan	B) Brazil
C) China	D) Zaire

Answer & Explanation Answer: C) China

Explanation:

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Filed Under: World Geography

Q:

India accounts for half of the world's total number of :

A) Cattle	B) Sheep
C) Buffaloes	D) Camels

Answer & Explanation Answer: C) Buffaloes

Explanation:

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Filed Under: World Geography

Q:

The 84th Amendment Act has frozen the total number of existing seats in the Lok Sabha on the basis of 1971 Census. They shall remain unaltered till the first Census to be taken after the year:

A) 2010	B) 2015
C) 2021	D) 2026

Answer & Explanation Answer: D) 2026

Explanation:

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Filed Under: Indian Politics

Q:

Which one of the following Constitutional Amendments state that the total number of Ministers, including the Prime Minister in the Council of Ministers shall not exceed 15% of the total numbers of the the house of the people?

A) 90th	B) 91st
C) 92nd	D) 93rd

Answer & Explanation Answer: B) 91st

Explanation:

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Filed Under: Indian Politics

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