36
Q:

# In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys ?

 A) 36 B) 25 C) 24 D) 72

Explanation:

The toys are different; The boxes are identical

If none of the boxes is to remain empty, then we can pack the toys in one of the following ways

a. 2, 2, 1

b. 3, 1, 1

Case a. Number of ways of achieving the first option 2 - 2 - 1

Two toys out of the 5 can be selected in $5C2$ ways. Another 2 out of the remaining 3 can be selected in $3C2$ ways and the last toy can be selected in $1C1$ way.

However, as the boxes are identical, the two different ways of selecting which box holds the first two toys and which one holds the second set of two toys will look the same. Hence, we need to divide the result by 2

Therefore, total number of ways of achieving the 2 - 2 - 1 option is ways $5C2*3C2$= 15 ways

Case b. Number of ways of achieving the second option 3 - 1 - 1

Three toys out of the 5 can be selected in $5C3$ ways. As the boxes are identical, the remaining two toys can go into the two identical looking boxes in only one way.

Therefore, total number of ways of getting the 3 - 1 - 1 option is $5C3$ = 10 = 10 ways.

Total ways in which the 5 toys can be packed in 3 identical boxes

= number of ways of achieving Case a + number of ways of achieving Case b= 15 + 10 = 25 ways.

Q:

If each of the vowels in the word 'MEAT' is kept unchanged and each of the consonants is replaced by the previous letter in the English alphabet, how many four-lettered meaningful words can be formed with the new letters, using each letter only once in each word?

 A) 3 B) 4 C) 1 D) 2

Explanation:

20 1449
Q:

In a bag containing red, green and pink tokens, the ratio of red to green tokens was 5 : 12 while the ratio of pink to red tokens was 7 : 15. What was the ratio of green to pink tokens?

 A) 25 : 28 B) 36 : 7 C) 8 :25 D) 12 : 7

Explanation:

6 1156
Q:

The ratio of the members of blue to red balls in abag is constant. When there were 44 red balls, the number of blue balls was 36. If the number of blue balls is 54, how many red balls will be in the bag?

 A) 68 B) 32 C) 64 D) 66

Explanation:

26 2342
Q:

If each vowel of the word NICELY is changed to the next letter in the English alphabetical series and each consonant is changed to the previous letter in the English alphabetical series and then the alphabets are arranged in alphabetical order, which of the following will be fourth from the left?

 A) M B) J C) B D) O

Explanation:

Thus after arranging the letters as per English alphabetical series; we get; Thus 4th letter from the left end will be K.

16 2378
Q:

How many such pair of letters are there in the word ‘TROUBLED’ which have as many letters between them in the word as they have between them in the English alphabet?

 A) 2 B) 3 C) 4 D) 5

Explanation:

Hence there are two pairs.

13 1876
Q:

If it is possible to make a meaningful word with the first, the seventh, the ninth and the tenth letters of the word RECREATIONAL, using each letter only once, which of the following will be the third letter of the word? If more than one such word can be formed, give ‘X’ as the answer. If no such word can be formed, give ‘Z’ as the answer.

 A) T B) X C) N D) R

Explanation:

The first, the seventh, the ninth and the tenth letters of the word RECREATIONAL are R, T, O and N respectively. Meaningful word from these letters is only TORN. The third letter of the word is ‘R’.

6 1662
Q:

16 persons are participated in a party. In how many differentways can they host the seat in a circular table, if the 2particular persons are to be seated on either side of the host?

 A) 16! × 2 B) 14! × 2 C) 18! × 2 D) 14!

Explanation:

(16 – 2)! × 2 = 14! × 2

3 2487
Q:

From a pack of 52 cards, 3 cards are drawn together atrandom, What is the probability of both the cards are king?

 A) 1/5225 B) 1/5525 C) 5525 D) 1/525