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Q1
Nine friends are to be seated around a round table. Among them, Amit and Rohit insist on sitting next to each other. In how many ways can the friends be seated around a circular table?
Integer answer
Q2
Amit wants to create a -digit numerical PIN for his ATM card. In how many ways can he create a -digit number between and using the digits , if repetition of digits is allowed?
Integer answer
Q3
How many 's are there between and ?
Single correct
Q4
How many numbers greater than can be formed using the digits without repetition?
Single correct
Q5
A group of teachers and students is to be seated around a circular table for a discussion. They decide that all students must sit together. Find the number of ways they can be seated around the table such that all students are sitting together.
Integer answer
Q6
How many -digit numbers can be formed using the digits where digits may be repeated such that the number is divisible by ?
Integer answer
Q7
In how many different ways can the letters of the word 'ARTICLE' be arranged such that all the vowels always come together?
Integer answer
Q8
In how many ways can people be arranged in a line such that two specific people, and , must never be next to each other?
Single correct
Q9
In how many different ways can the letters of the word “AMERICA” be arranged such that the consonants always come together?
Single correct
Q10
The number of ways to arrange objects in a line is equal to times the number of ways to arrange objects in a line. Find the value of .
Integer answer
Q11
In how many ways can people be arranged around a circular table if one specific person must always occupy a fixed seat, which cannot be changed?
Integer answer
Q12
Administration section of a university has started to create roll numbers for the students, following the format '232174' using the digits and a capital letter at the third position. Assume no digits are repeated. Find the number of ways in which the administration section can create a unique roll number.
Single correct
Q13
How many four letter words, with or without meaning, can be formed using the letters of the word 'ENGLISH' without repetition such that 'E' is one of the alphabet in each of the word formed?
Single correct
Q14
Praveen attempts a question paper of questions. Each question has choices. If he answers the questions randomly, then find the number of ways in which he can attempt the entire paper.
Single correct
Q15
In a dinner party, there are males and females who need to be seated around a round table. In how many ways can they be seated so that no two males are seated next to each other?
Single correct
Q16
If , then what is the value of ?
Single correct
Q17
In how many different ways can the letters of the word be arranged such that the vowels always come together?
Integer answer
Q18
Choose the correct options from the following:
Comprehension
Q19
Choose the correct options from the following:
Comprehension
Q20
Find the number of ways in which performers can be arranged in a circular order such that no two violinists will sit together.
Comprehension
Q21
Choose the correct options from the following:
Comprehension
Q22
Choose the correct options from the following:
Comprehension
Q23
Find the number of ways in which employees can sit around a circular table such that all leaders will sit together.
Comprehension
Q24
Administration section of a university has started to create roll numbers for the students, following the format using the digits , and a capital letter at the third position. Assume no digits are repeated. Find the number of ways in which the administration section can create a unique roll number.
Single correct
Q25
In how many ways can letters in the word “ADAMANT” be arranged such that no two A's are adjacent to each other?
Integer answer
Q26
In a gaming room, brothers and other boys are playing together. In a particular game, how many ways can all the boys be seated in a circular order so that two brothers are not seated together?
Integer answer
Q27
A logo is to be designed with five horizontal stripes using some or all of the colours Black, Blue, Red, and Green. In how many ways can that be done such that no two adjacent stripes have same colour?
Single correct
Q28
How many 3-digit numbers can be made using only 2 different digits taken from 1 to 9? Repetition of digits is allowed.
Single correct
Q29
The number of whole numbers, starting from zero, smaller than , of which all the digits are distinct, is:
Single correct
Q30
How many 9's are there between 1 and 1000?
Single correct
Q31
How many four-digit numbers, each divisible by 4, can be formed using the digits 5, 6, 7, 8, 9, if repetition of digits is allowed in any number?
Single correct
Q32
If there are ways to arrange persons at a round table such that two particular persons, say and , will sit together, then find the value of .
Comprehension
Q33
Consider the events: : the number of outcomes in which the sum of the digits that appear on the face is even when a fair die is rolled thrice. : the number of ways in which beads can be arranged to form a necklace. : the number of ways of posting different letters in different post boxes such that at least one letter is posted in each of the boxes. In which of these events do the total number of outcomes exceed ?
Multiple correct
Q34
A basketball coach wants to draft a team. For drafting the team, players are available for the position of point guard, players are available for shooting guard, players are available for small forward, players are available for power forward and players are available for center. If he needs to select one player for each of these positions, then in how many ways can he draft the team?
Comprehension
Q35
In how many ways can the letters of the word be arranged such that the vowels either occupy only odd or even positions?
Comprehension
Showing 35 questions.