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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
Job Role: Bank PO , Bank Clerk

Q:

A Committee of 5 persons is to be formed from a group of 6 gentlemen and 4 ladies. In how many ways can this be done if the committee is to be included atleast one lady?

A) 123	B) 113
C) 246	D) 945

Answer & Explanation Answer: C) 246

Explanation:

A Committee of 5 persons is to be formed from 6 gentlemen and 4 ladies by taking.

(i) 1 lady out of 4 and 4 gentlemen out of 6

(ii) 2 ladies out of 4 and 3 gentlemen out of 6

(iii) 3 ladies out of 4 and 2 gentlemen out of 6

(iv) 4 ladies out of 4 and 1 gentlemen out of 6

In case I the number of ways = $C_{1}^{4} \times C_{4}^{6}$ = 4 x 15 = 60

In case II the number of ways = $C_{2}^{4} \times C_{3}^{6}$ = 6 x 20 = 120

In case III the number of ways = $C_{3}^{4} \times C_{2}^{6}$ = 4 x 15 = 60

In case IV the number of ways = $C_{4}^{4} \times C_{1}^{6}$ = 1 x 6 = 6

Hence, the required number of ways = 60 + 120 + 60 + 6 = 246

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

Q:

In how many ways can 5 letters be posted in 4 letter boxes?

A) 512	B) 1024
C) 625	D) 20

Answer & Explanation Answer: B) 1024

Explanation:

First letter can be posted in 4 letter boxes in 4 ways. Similarly second letter can be posted in 4 letter boxes in 4 ways and so on.

Hence all the 5 letters can be posted in = 4 x 4 x 4 x 4 x 4 = 1024

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Filed Under: Permutations and Combinations

Q:

The following question consist of two words each that have a certain relationship to each other, followed by lettered pairs of words . Select the lettered pair that has the same relationship as the original pair of words.

Proscenium : Stage

A) Lamp : Table	B) Lines : Bed
C) Portico : House	D) Compass : Needle

Answer & Explanation Answer: C) Portico : House

Explanation:

First is a part of the second.

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Filed Under: Analogy

Q:

S L U A Y J V E I O N Q G Z B D R H

What will come in place of question (?) mark in the following series :

LA UJ YI EG ?

A) ZH	B) IB
C) NR	D) QH

Answer & Explanation Answer: D) QH

Explanation:

The first letter follows +1, +2, +3, +4, ....

The second letter follows +2, +3, +4, +5,....

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Filed Under: Alphabet Test

Q:

LAP BUT CAR SON HID

If the positions of the first and the third alphabets of each of the words are interchanged, which of the following would form a meaningful word in the new arrangement?

A) HID	B) SON
C) Both LAP and BUT	D) Both CAR and LAP

Answer & Explanation Answer: C) Both LAP and BUT

Explanation:

When positions of first and the third alphabets of each of the words are interchanged, we have PAL TUB RAC NOS DIH

Clearly, PAL and TUB are the only meaningful words. These words are obtained from LAP and BUT respectively.

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Filed Under: Alphabet Test

Q:

B M N G O P C Q R H S T F L U V W X Y A K Z D I E J

Counting from left if it is possible to make a meaningful word from the third and fifth letters from left, using each at least twice and third letter from right in sequence, only once , write the first letter of the word as your answer. If more than one such word can be formed write "M" as your answer, and if no word can be formed write 'X' as your answer.

A) M	B) X
C) O	D) I

Answer & Explanation Answer: C) O

Explanation:

Specified letters from the left are N and O , and the letter from the right is I.

With these letters , according to the conditions given in the question , one Word ONION can be formed. Clearly , first letter of this word is O.

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Filed Under: Alphabet Test

Q:

Which of the following will be the changed form of the word OBLIQUE when the word is written again by substituting each vowel by the second letter following it in the English alphabet and each consonant is substituted by the third letter following it in the English alphabet?

A) MEDGTSD	B) RDNLSXH
C) QEOKTXG	D) QEOKTWG

Answer & Explanation Answer: D) QEOKTWG

Explanation:

The Given word is OBLIQUE. After making necessary changes that is all vowels are substituted by the next second letter and all consonants are substituted by the next third letter in the English alphabet, we get the following form of the given word: QEOKTWG.

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Filed Under: Alphabet Test

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