Arts (English Medium) Class 11 - CBSE Question Bank Solutions

The number of permutations of n different things taking r at a time when 3 particular things are to be included is

The number of five-digit telephone numbers having at least one of their digits repeated is

The number of words that can be formed out of the letters of the word "ARTICLE" so that vowels occupy even places is

How many numbers greater than 10 lacs be formed from 2, 3, 0, 3, 4, 2, 3 ?

The number of different signals which can be given from 6 flags of different colours taking one or more at a time, is

If A, B, C are three sets such that \[A \subset B\]then prove that \[C - B \subset C - A\] 

The number of words from the letters of the word 'BHARAT' in which B and H will never come together, is

For any two sets A and B, prove that \[\left( A \cup B \right) - B = A - B\]

The number of six letter words that can be formed using the letters of the word "ASSIST" in which S's alternate with other letters is

For any two sets A and B, prove that \[A - \left( A \cap B \right) = A - B\] 

For any two sets A and B, prove that \[A - \left( A - B \right) = A \cap B\]

The number of arrangements of the word "DELHI" in which E precedes I is

For any two sets A and B, prove that

\[A \cup \left( B - A \right) = A \cup B\]

For any two sets A and B, prove that \[\left( A - B \right) \cup \left( A \cap B \right) = A\]

The number of ways in which the letters of the word 'CONSTANT' can be arranged without changing the relative positions of the vowels and consonants is

If A and B are two sets such that \[n \left( A \cup B \right) = 50, n \left( A \right) = 28 \text{ and } n \left( B \right) = 32\]\[n \left( A \cap B \right)\]

If P and Q are two sets such that P has 40 elements, \[P \cup Q\]has 60 elements and\[P \cap Q\]has 10 elements, how many elements does Q have?