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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:   B) 535

Explanation:

The number of points of intersection of 37 lines is . But 13 straight lines out of the given 37 straight lines pass through the same point A. Therefore instead of getting  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  points, we get only one point B.

Hence the number of intersection points of the lines is  = 535

  

Q:

How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed ?

A) 5040 B) 2525
C) 2052 D) 4521
 
Answer & Explanation Answer: A) 5040

Explanation:

The Word LOGARITHMS  contains 10 letters.
To find how many 4 letter words we can form from that = 10p4 =10x9x8x7 = 5040.

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Q:

There are 3 sections with 5 questions each. If four questions are selected from each section, the chance of getting different questions is ?

A) 1000 B) 625
C) 525 D) 125
 
Answer & Explanation Answer: D) 125

Explanation:

Methods for selecting 4 questions out of 5 in the first section = 5x4x3x2x1/4x3x2x1 = 5
similarly for other 2 sections also i.e 5 and 5
so total methods = 5 x 5 x 5 = 125.

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3 32
Q:

If two cards are taken one after another without replacing from a pack of 52 cards. What is the probability for the two cards be Ace ?

A) 51/1221 B) 42/221
C) 1/221 D) 52/1245
 
Answer & Explanation Answer: C) 1/221

Explanation:

Total Combination of getting a card from 52 cards = 52C1
Because there is no replacement, so number of cards after getting first card= 51
Now, Combination of getting an another card= 51C1
Total combination of getting 2 cards from 52 cards without replacement= (52C1)x(51C1)
There are total 4 Ace in stack. Combination of getting 1 Ace is = 4C1
Because there is no replacement, So number of cards after getting first Ace = 3
Combination of getting an another Ace = 3C1
Total Combination of getting 2 Ace without replacement=(4C1)x(3C1)
Now,Probability of getting 2 cards which are Ace = (4C1)x(3C1)/(52C1)x(51C1) = 1/221.

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3 42
Q:

A Cricket team of 23 people all shake hands with each other exactly once. How many hand shakes occur ?

A) 142 B) 175
C) 212 D) 253
 
Answer & Explanation Answer: D) 253

Explanation:

The first person shakes hands with 22 different people, the second person also shakes hands with 22 different people, but one of those handshakes was counted in the 22 for the first person, so the second person actually shakes hands with 21 new people. The third person, 20 people, and so on...
So,
22 + 21 + 20 + 19 + 18 + 17 + 16 + 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1
= n(n+1)/2 = 22 x 23 /2 = 11 x 23 = 253.

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3 44
Q:

There are three rooms in a Hotel: one single, one double and one for four persons. How many ways are there to house seven persons in these rooms ?

A) 105 B) 7! x 6!
C) 7!/5! D) 420
 
Answer & Explanation Answer: A) 105

Explanation:

Choose 1 person for the single room & from the remaining choose 2 for the double room & from the remaining choose 4 people for the four person room,

Then, 7C1 x 6C2 x 4C4
     = 7 x  x 1
     = 7 x 15 = 105.
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