Quiz Discussion

The students in a class are seated, according to their marks in the previous examination. Once, it so happens that four of the students got equal marks and therefore the same rank. To decide their seating arrangement, the teacher wants to write down all possible arrangements one in each of separate bits of paper in order to choose one of these by lots. How many bits of paper are required?

• 1]

  24

• 2]

  12

• 3]

  36

• 4]

  48

If (n + 2)! = 2550 (n!); find ’n’

• 1]

  49

• 2]

  35

• 3]

  38

• 4]

  43

Two variants of the CAT paper are to be given to 12 students. In how many ways can the students be placed in two rows of six each so that there should be no identical variants side by side and that the students sitting one behind the other should have the same variant. Find the number of ways this can be done

• 1]

  2 x ¹²C₆ x (6!)²

• 2]

  2 x 6! x 6!

• 3]

  2 x ¹²C₆ x 6!

• 4]

  None of these

The number of triangles that can be formed by choosing the vertices from a set of 12 points, seven of which lie on the same straight line, is

• 1]

  185

• 2]

  175

• 3]

  115

• 4]

  105

From among the 36 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?

• 1]

  1360

• 2]

  1060

• 3]

  1160

• 4]

  1260

There are seven pairs of black shoes and five pairs of white shoes. They are all put into a box and shoes are drawn one at a time. To ensure that at least one pair of black shoes are taken out, what is the number of shoes required to be drawn out?

• 1]

  12

• 2]

  13

• 3]

  17

• 4]

  18

There are 6 letters for 3 envelopes. In how many different ways can the envelopes be filled?

• 1]

  120

• 2]

  130

• 3]

  100

• 4]

  110

Ten participants are participating in a competition. In how many ways can the first three prizes be won?

• 1]

  920

• 2]

  680

• 3]

  720

• 4]

  820

A, B, C, D and E sit on five chairs all of which are facing north. C will sit only on the leftmost chair and B will not sit anywhere to the left of A. In how many ways they can be seated?

• 1]

  10

• 2]

  18

• 3]

  36

• 4]

  12

A five-letter word is to be formed from a group of 5 vowels and 4 consonants, using at least one vowel and at least one consonant. In how many ways the word having a greater number of consonants than vowels can be formed?

• 1]

  40

• 2]

  42

• 3]

  45

• 4]

  52