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Q1
A person won a special pass to an amusement park that allows him to bring friends with him for free. He has friends, but two of them are twins who will only attend if both are included. How many different groups of friends can the person choose to take along?
Integer answer
Q2
If , find the value of .
Integer answer
Q3
From a group of students, a team of students is to be selected. From this selected team, one student is chosen as the leader. In how many different ways can this be done?
Single correct
Q4
In how many ways can a committee be formed if at least one girl must be included?
Comprehension
Q5
In a quiz competition, eight students are competing, each assigned a roll number from to . What is the probability that only students with prime-numbered roll numbers, i.e. , secure the top four ranks, in any order? Enter the answer correct to three decimal places.
Integer answer
Q6
A company has offices and wants to set up two-way communication between every pair of offices. However, the smallest offices will not have direct communication with one another, though each of them can still connect directly with the remaining offices. How many communication channels are needed in total?
Integer answer
Q7
A basket contains red balls and green balls. If balls are to be selected at random without replacement, in how many ways can the balls be selected such that at least one green ball is included?
Integer answer
Q8
A committee of people is to be formed from a group of people. The number of possible committees in which two particular people and are both included together is . Find the number of ways in which the committee can be formed.
Integer answer
Q9
How many panels include at least one Mathematics student?
Comprehension
Q10
A company needs to select a team of members from a group of employees. Out of these, specific roles need to be assigned: Team Leader, Manager, and Analyst. How many different ways can the team be selected and the roles allocated?
Single correct
Q11
Out of boys and girls, how many queues of boys and girls can be formed?
Single correct
Q12
A box contains three distinct white balls, four distinct black balls, and three distinct red balls. Find the number of ways in which three balls can be drawn from the box so that all three drawn balls have different colors.
Integer answer
Q13
In a school, there are students in section-A, students in section-B and students in section-C. Find the number of ways, in which students can be selected such that it includes at least students from each section and at most students from the total students in section-A and section-B.
Integer answer
Q14
Which of the following option(s) is/are correct for selecting and arranging objects from a total of distinct objects without replacement?
Multiple correct
Q15
If and , find the value of .
Single correct
Q16
What is the probability that a black pair of balls is chosen? Enter the answer correct to two decimal places.
Comprehension
Q17
What is the probability that they are of same colour? Enter the answer correct to two decimal places.
Comprehension
Q18
In how many ways can this be done when the committee consists of exactly Women?
Comprehension
Q19
In how many ways can this be done when the committee consists of at least Women?
Comprehension
Q20
In a hockey team consisting of players, each player shakes hands with every other player exactly once before the match begins. How many handshakes occur among the teammates?
Single correct
Q21
A box contains white balls, black balls and red balls. In how many ways can balls be drawn from the box, if at least one red ball is to be included in the draw?
Single correct
Q22
What is the probability that a black pair of balls is chosen? Enter the answer correct to two decimal places.
Comprehension
Q23
What is the probability that they are of same colour? Enter the answer correct to two decimal places.
Comprehension
Q24
Choose the correct options from the following:
Comprehension
Q25
Choose the correct options from the following:
Comprehension
Q26
Find the number of ways in which the students can be selected such that at least one student likes Statistics.
Comprehension
Q27
Choose the correct options from the following:
Comprehension
Q28
Choose the correct options from the following:
Comprehension
Q29
Find the number of ways in which Manoj and Nitin can invite their friends.
Comprehension
Q30
Out of boys and girls, how many queues of boys and girls can be formed?
Single correct
Q31
The sum of three natural numbers starting from is . How many ordered triplets exist? Note: or , also is allowed. For example, ordered triplets and are different.
Single correct
Q32
Select the steps from the following options that you will use to arrange the persons at a round table. Note: This question is optional.
Comprehension
Q33
Select the steps from the following options that you will use for selection of players to draft a team. Note: This question is optional.
Comprehension
Q34
Select the steps from the following options that you will use to arrange the letters of the given word. Note: This question is optional.
Comprehension
Showing 34 questions.