1
Q:

The Number of times the digit 8 will be written when listing the integers from 1 to 1000 is :

A) 100 B) 200
C) 300 D) 400

Answer:   C) 300



Explanation:

 Since 8 does not occur in 1000, we have to count the number of times 8 occurs when we list the integers from 1 to 999. Any number between 1 and 999 is of the form xyz, where \inline 0\leq x, y,z\leq 9.

Let us first count the numbers in which 8 occurs exactly once.

Since 8 can occur atone place in \inline ^{3}\textrm{C}_{1} ways. There are \inline ^{3}\textrm{C}_{1}(9\times 9)=3\times 9^{2} such numbers.

Next, 8 can occur in exactly two places in \inline ^{3}\textrm{C}_{2}(9)=3\times 9 such numbers. Lastly, 8 can occur in all three digits in one number only.

Hence, the number of times 8 occur is 

\inline 1\times (3\times 9^{2})+2\times (3\times 9)+3\times 1=300

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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2 10
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 5C3 ways = 10

Remaining vacancies are 5 that are to be filled by 12

=> 12C5 = (12x11x10x9x8)/(5x4x3x2x1) = 792

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

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9 321
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

EXP.

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

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5 193
Q:

Nine different letters of alphabet are given, words with 5 letters are formed from these given letters. Then, how many such words can be formed which have at least one letter repeated ?

A) 43929 B) 59049
C) 15120 D) 0
 
Answer & Explanation Answer: A) 43929

Explanation:

Number of words with 5 letters from given 9 alphabets formed =

Number of words with 5 letters from given 9 alphabets formed such that no letter is repeated is = 

Number of words can be formed which have at least one letter repeated =  -  

= 59049 - 15120

= 43929

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8 323
Q:

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

A) 5040 B) 3650
C) 4150 D) 2520
 
Answer & Explanation Answer: D) 2520

Explanation:

Total number of letters in the word ABYSMAL are 7

Number of ways these 7 letters can be arranged are 7! ways

But the letter is repeated and this can be arranged in 2! ways

=> Total number of ways arranging ABYSMAL = 7!/2! = 5040/2 = 2520 ways.

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11 525