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Write which of the following statement are true? Justify your answer.
The sets P = {a} and B = {{a}} are equal.
Concept: undefined >> undefined
Write which of the following statement are true? Justify your answer.
The sets A = {x : x is a letter of the word "LITTLE"} and,B = {x : x is a letter of the word "TITLE"} are equal.
Concept: undefined >> undefined
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Given 7 flags of different colours, how many different signals can be generated if a signal requires the use of two flags, one below the other?
Concept: undefined >> undefined
A team consists of 6 boys and 4 girls and other has 5 boys and 3 girls. How many single matches can be arranged between the two teams when a boy plays against a boy and a girl plays against a girl?
Concept: undefined >> undefined
Twelve students complete in a race. In how many ways first three prizes be given?
Concept: undefined >> undefined
How many A.P.'s with 10 terms are there whose first term is in the set {1, 2, 3} and whose common difference is in the set {1, 2, 3, 4, 5}?
Concept: undefined >> undefined
From among the 36 teachers in a college, one principal, one vice-principal and the teacher-incharge are to be appointed. In how many ways can this be done?
Concept: undefined >> undefined
How many three-digit numbers are there with no digit repeated?
Concept: undefined >> undefined
How many three-digit numbers are there?
Concept: undefined >> undefined
How many three-digit odd numbers are there?
Concept: undefined >> undefined
How many different five-digit number licence plates can be made if
first digit cannot be zero and the repetition of digits is not allowed,
Concept: undefined >> undefined
How many different five-digit number licence plates can be made if
the first-digit cannot be zero, but the repetition of digits is allowed?
Concept: undefined >> undefined
How many four-digit numbers can be formed with the digits 3, 5, 7, 8, 9 which are greater than 7000, if repetition of digits is not allowed?
Concept: undefined >> undefined
Since the number has to be greater than 8000, the thousand's place can be filled by only two digits, i.e. 8 and 9.
Now, the hundred's place can be filled with the remaining 4 digits as the repetition of the digits is not allowed.
The ten's place can be filled with the remaining 3 digits.
The unit's place can be filled with the remaining 2 digits.
Total numbers that can be formed = `2xx4xx3xx2=48`
Concept: undefined >> undefined
In how many ways can six persons be seated in a row?
Concept: undefined >> undefined
How many 9-digit numbers of different digits can be formed?
Concept: undefined >> undefined
How many odd numbers less than 1000 can be formed by using the digits 0, 3, 5, 7 when repetition of digits is not allowed?
Concept: undefined >> undefined
How many 3-digit numbers are there, with distinct digits, with each digit odd?
Concept: undefined >> undefined
Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[a \subset A\]
Concept: undefined >> undefined
Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[\left\{ a, b, e \right\} \subset A\]
Concept: undefined >> undefined
