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Q:

From a deck of 52 cards, a 5 card hand is dealt.How may distinct five card hands are there if the queen of spades and the four of diamonds must be in the hand?

 A) 52C5 B) 50C3 C) 52C4 D) 50C4

Explanation:

If the queen of spades and the four of diamonds must be in hand,we have 50 cards remaining out of which we are choosing 3.

So, 50${C}_{3}$

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

Explanation:

Required Number of ways = = 36

6 115
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

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.

3 44
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

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.

3 47
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

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.

7 89
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

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

6 161
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!

7 232
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

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

9 523
Q:

A,B,C,D,E,F,G and H are sitting around a circular table facing the centre but not necessarily in the same order. G sits third to the right of C. E is second to the right of G and 4th to the right of H. B is fourth to the right of C. D is not an immediate neighbour of E. A and C are immediate neighbours.

Which of the following is/are correct ?

 A) F is third to the left of B B) F is second to the right of B C) B is an immediate neighbour of D D) All of the above

Answer & Explanation Answer: B) F is second to the right of B

Explanation:

From the given information, the circular arrangement is

Here F is second to the right of B and the remaning all are wrong.