0
Q:

There are five cards lying on the table in one row. Five numbers from among 1 to 100 have to be written on them, one number per card, such that the difference between the numbers on any two adjacent cards is not divisible by 4. The remainder when each of the 5 numbers is divided by 4 is written down on another card (the 6th card) in order. How many sequences can be written down on the 6th card ?

A) 4 x 3^4 B) 3^4
C) 4^3 D) 3 x 4^3

Answer:   A) 4 x 3^4



Explanation:

The remainder on the first card can be 0,1,2 or 3 i.e 4 possibilities.
The remainder of the number on the next card when divided by 4 can have 3 possible values (except the one occurred earlier).

For each value on the card the remainder can have 3 possible values.

The total number of possible sequences is: 4*3^4

Q:

From a group of 7 boys and 6 girls, five persons are to be selected to form a team, so that at least 3 girls are there in the team. In how many ways can it be done?

A) 427 B) 531
C) 651 D) 714
 
Answer & Explanation Answer: B) 531

Explanation:

Given in the question that, there are 7 boys and 6 girls. 

Team members = 5

Now, required number of ways in which a team of 5 having atleast 3 girls in the team = 

6C3  x 7C2  + 6C4 x 7C1 + 6C5= 6x5x43x2x1 x 7x62x1 + 6x5x4x34x3x2x1 x 7 + 6x5x4x3x25x4x3x2x1= 420 + 105 + 6= 531.

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2 193
Q:

The number of ways in which 8 distinct toys can be distributed among 5 children?

A) 5P8 B) 5^8
C) 8P5 D) 8^5
 
Answer & Explanation Answer: B) 5^8

Explanation:

As the toys are distinct and not identical,

For each of the 8 toys, we have three choices as to which child will receive the toy. Therefore, there are 58 ways to distribute the toys.

 

Hence, it is 58 and not 85.

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1 696
Q:

In how many different ways can the letters of the word 'THERAPY' be arranged so that the vowels never come together?

A) 1440 B) 720
C) 2250 D) 3600
 
Answer & Explanation Answer: D) 3600

Explanation:

Given word is THERAPY.

Number of letters in the given word = 7

These 7 letters can be arranged in 7! ways.

Number of vowels in the given word = 2 (E, A)

The number of ways of arrangement in which vowels come together is 6! x 2! ways

 

Hence, the required number of ways can the letters of the word 'THERAPY' be arranged so that the vowels never come together = 7! - (6! x 2!) ways = 5040 - 1440 = 3600 ways.

 

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1 436
Q:

In how many different ways can the letters of the word 'HAPPYHOLI' be arranged?

A) 89,972 B) 90,720
C) 72,000 D) 81,000
 
Answer & Explanation Answer: B) 90,720

Explanation:

The given word HAPPYHOLI has 9 letters

These 9 letters can e arranged in 9! ways.

But here in the given word letters H & P are repeated twice each

Therefore, Number of ways these 9 letters can be arranged is 

9!2! x 2! = 9 x 8 x 7 x 6 x 5 x 4 x 32 = 90,720 ways.

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5 557
Q:

How many words can be formed with or without meaning by using three letters out of k, l, m, n, o without repetition of alphabets.

A) 60 B) 120
C) 240 D) 30
 
Answer & Explanation Answer: A) 60

Explanation:

Given letters are k, l, m, n, o = 5

number of letters to be in the words = 3

Total number of words that can be formed from these 5 letters taken 3 at a time without repetation of letters = 5P3 ways.

 5P3 = 5 x 4 x 3 = 60 words.

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7 565
Q:

The letters of the word PROMISE are to be arranged so that three vowels should not come together. Find the number of ways of arrangements?

A) 4320 B) 4694
C) 4957 D) 4871
 
Answer & Explanation Answer: A) 4320

Explanation:

Given Word is PROMISE.

Number of letters in the word PROMISE = 7

Number of ways 7 letters can be arranged = 7! ways

Number of Vowels in word PROMISE = 3 (O, I, E)

Number of ways the vowels can be arranged that 3 Vowels come together = 5! x 3! ways

 

Now, the number of ways of arrangements so that three vowels should not come together

= 7! - (5! x 3!) ways = 5040 - 720 = 4320.

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7 1009
Q:

In how many different ways can the letters of the word 'POVERTY' be arranged ?

A) 2520 B) 5040
C) 1260 D) None
 
Answer & Explanation Answer: B) 5040

Explanation:

The 7 letters word 'POVERTY' be arranged in 7P7 ways = 7! = 5040 ways.

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12 599
Q:

A decision committee of 5 members is to be formed out of 4 Actors, 3 Directors and 2 Producers. In how many ways a committee of 2 Actors, 2 Directors and 1 Producer can be formed ?

A) 18 B) 24
C) 36 D) 32
 
Answer & Explanation Answer: C) 36

Explanation:

Required Number of ways = 4C2 × 3C2 × 2C1 = 36 = 36

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17 672