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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 $\inline&space;0\leq&space;x,&space;y,z\leq&space;9.$

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

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

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

Hence, the number of times 8 occur is

$\inline&space;1\times&space;(3\times&space;9^{2})+2\times&space;(3\times&space;9)+3\times&space;1=300$

Q:

Some children goto ice-cream shop. 9 flavours are available there. Each child takes a cone with two different flavours. No two children take same combination and they have taken all such possible combinations. How many children went to ice cream shop ?

 A) 28 B) 56 C) 44 D) 36

Answer & Explanation Answer: D) 36

Explanation:

Given there are 9 flavours of ice creams.
Each child takes the combination of two flavours and no two children will have the same combination
This can be done by 9C2 ways i.e children.
Number of children = 9C2 = 9 x 8 / 2 = 36.

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Q:

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

 A) 360 B) 420 C) 576 D) 220

Answer & Explanation Answer: A) 360

Explanation:

No. of letters in the word = 6
No. of 'E' repeated = 2
Total No. of arrangement = 6!/2! = 360

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Q:

In how many different ways could couples be picked from 6 men and 9 women ?

 A) 26 B) 54 C) 52 D) 28

Answer & Explanation Answer: B) 54

Explanation:

Number of mens = 8
Number of womens = 5

Different ways could couples be picked = 6c1 x 9c1 = 9 x 6 = 54 ways.

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Q:

How many 6-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 and 7 so that the digits should not repeat and the second last digit is even ?

 A) 521 B) 720 C) 420 D) 225

Answer & Explanation Answer: B) 720

Explanation:

Let last digit is 2
when second last digit is 4 remaining 4 digits can be filled in 120 ways, similarly second last digit is 6 remained 4 digits can be filled in 120 ways.
so for last digit = 2, total numbers=240

Similarly for 4 and 6
When last digit = 4, total no. of ways =240
and last digit = 6, total no. of ways =240
so total of 720 even numbers are possible.

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Q:

How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed ?

 A) 5040 B) 2525 C) 2052 D) 4521

Answer & Explanation Answer: A) 5040

Explanation:

The Word LOGARITHMS  contains 10 letters.
To find how many 4 letter words we can form from that = 10p4 =10x9x8x7 = 5040.

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