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Q:

How many different words can be made using the letters of the word ' HALLUCINATION ' if all constants are together?

A) 129780 B) 1587600
C) 35600 D) None of these

Answer:   B) 1587600

Explanation:

 H   L   C   N    T    A   U   I   O

      L        N          A        I

There are total 131 letters out of which 7 are consonants and 6 are vowels. Also ther are 2L's , 2N's, 2A's and 2I's.

If all the consonants  are together then the numberof arrangements = \inline \frac{7!}{2!2!} . But the 7 consonants  can be arranged themselves in \inline \frac{7!}{2!2!} ways. 

Hence the required number of ways = \inline \frac{7!}{2!\times 2!}\times \frac{7!}{2!\times 2!} = \inline (1260)^{2} = 1587600

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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2 14
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 29
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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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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4 92
Q:

How many parallelograms will be formed if 7 parallel horizontal lines intersect 6 parallel vertical lines?

A) 215 B) 315
C) 415 D) 115
 
Answer & Explanation Answer: B) 315

Explanation:
Parallelograms are formed when any two pairs of parallel lines (where each pair is not parallel to the other pair) intersect.
Hence, the given problem can be considered as selecting pairs of lines from the given 2 sets of parallel lines.
Therefore, the total number of parallelograms formed = 7C2 x 6C2 = 315
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