7
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:   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 = $\frac{7!}{3!×2!}$ = 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'.

=$\frac{6!}{3!×2!}$ = 60

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

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 $\mathbf{7}{\mathbit{P}}_{\mathbf{7}}$ ways = 7! = 5040 ways.

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5 49
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 = = 36

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8 178
Q:

How many six digit odd numbers can be formed from the digits 0, 2, 3, 5, 6, 7, 8, and 9 (repetition not allowed)?

 A) 8640 B) 720 C) 3620 D) 4512

Answer & Explanation Answer: A) 8640

Explanation:

Let the 6 digits of the required 6 digit number be abcdef

Then, the number to be odd number the last digit must be odd digit i.e 3, 5, 7 or 9

The first digit cannot be ‘0’ => possible digits = 3, 5, 7, 2, 6, 8

Remaining 4 places can be of 6 x 5 x 4 x 3 ways

This can be easily understood by

Therefore, required number of ways = 6 x 6 x 5 x 4 x 3 x 4 = 36 x 20 x 12 = 720 x 12

8640 ways.

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3 63
Q:

In how many ways can letter of the word RAILINGS arrange so that R and S always come together?

 A) 1260 B) 2520 C) 5040 D) 1080

Answer & Explanation Answer: C) 5040

Explanation:

The number of ways in which the letters of the word RAILINGS can be arranged such that R & S always come together is

Count R & S as only 1 space or letter so that RS or SR can be arranged => 7! x 2!

But in the word RAILINGS, I repeated for 2 times => 7! x 2!/2! = 7! ways = 5040 ways.

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3 65
Q:

On the occasion of New Year, each student of a class sends greeting cards to the others. If there are 21 students in the class, what is the total number of greeting cards exchanged by the students?

 A) 380 B) 420 C) 441 D) 400

Answer & Explanation Answer: B) 420

Explanation:

Given total number of students in the class = 21

So each student will have 20 greeting cards to be send or receive (21 - 1(himself))

Therefore, the total number of greeting cards exchanged by the students = 20 x 21 = 420.

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7 97
Q:

How many more words can be formed by using the letters of the given word 'CREATIVITY'?

 A) 851250 B) 751210 C) 362880 D) 907200

Answer & Explanation Answer: D) 907200

Explanation:

The number of letters in the given word CREATIVITY = 10

Here T & I letters are repeated

=> Number of Words that can be formed from CREATIVITY = 10!/2!x2! = 3628800/4 = 907200

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6 171
Q:

If (1 × 2 × 3 × 4 ........ × n) = n!, then 15! - 14! - 13! is equal to ___?

 A) 14 × 13 × 13! B) 15 × 14 × 14! C) 14 × 12 × 12! D) 15 × 13 × 13!

Answer & Explanation Answer: D) 15 × 13 × 13!

Explanation:

15! - 14! - 13!

= (15 × 14 × 13!) - (14 × 13!) - (13!)

= 13! (15 × 14 - 14 - 1)

= 13! (15 × 14 - 15)

= 13! x 15 (14 - 1)

= 15 × 13 × 13!

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7 256
Q:

To fill 8 vacancies there are 15 candidates of which 5 are from ST. If 3 of the vacancies are reserved for ST candidates while the rest are open to all, Find the number of ways in which the selection can be done ?

 A) 7920 B) 74841 C) 14874 D) 10213

Answer & Explanation Answer: A) 7920

Explanation:

ST candidates vacancies can be filled by ${}^{5}C_{3}$ ways = 10

Remaining vacancies are 5 that are to be filled by 12

=> ${}^{12}C_{5}$= (12x11x10x9x8)/(5x4x3x2x1) = 792

Total number of filling the vacancies = 10 x 792 = 7920

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9 541