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In how many arrangements can three white marbles, two black marbles, and five pink marbles be placed in a single row?
a) 3!7!
b) 2!8!
c) 10!
d) 2!3!5!
e) Cannot say
Option d – 2!3!5!
How many ways can the letters of the word MAHIMA be arranged if all the vowels must be placed together?
a) 14
b) 18
c) 22
d) 35
e) 70
Option d – 35
Four teachers and four students are to be seated in a row so that no two teachers and no two students sit next to each other. How many possible arrangements are there?
a) 1082
b) 1152
c) 1257
d) 1832
e) 1654
Option b – 1152
If the letters of the word ADVANCE are rearranged, in how many arrangements will all the vowels appear together?
a) 7!/2!
b) 4!3!
c) 5!/2!
d) 5!3!/2!2!
Option d – 5!3!/2!2!
In the rearrangements of the letters of the word GORGENGEN, in how many cases will all G’s be placed together?
a) 8!/3!2!
b) 8!/2!2!
c) 8!3!/2!
d) 5!/3!2!
e) None of these
Option b – 8!/2!2!
A coin is tossed five times. What is the probability that the fourth toss results in a head?
a) ½
b) ¾
c) 1/4
d) 1/2!
e) None of these
Option c – 1/4
In a banquet hall with three doors, the bride may enter from any of two specific doors. In how many ways can she enter and exit using different doors?
a) 2
b) 3
c) 9
d) 12
e) 6
Option b – 3
In a banquet hall with three doors, the bride may enter from any of two specific doors, while the bridegroom can enter and exit from any of the three doors. How many total arrangements are possible?
a) 2
b) 3
c) 12
d) 9
e) 6
Option c – 12
A lecture hall has five doors—two red and three green. In how many ways can a person enter through one color and leave through a door of the other color?
a) 8
b) 3
c) 9
d) 12
Option d – 12
How many distinct arrangements (meaning not necessarily valid dictionary words) can be formed from the letters of the word SUCCEED?
a) 90
b) 80
c) 40
d) 420
Option d – 420
Using all digits 2, 7, 7, 7, 6, and 6, how many different numbers greater than one lakh can be formed?
a) 50
b) 40
c) 30
d) 60
Option d – 60
In a banquet hall with three doors, the bride may enter from any of two specific doors. How many total ways is this possible?
a) 2
b) 3
c) 9
d) 12
e) 6
Option b – 3
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