Science (English Medium) कक्षा ११ - CBSE Question Bank Solutions

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? 

In a school there are 20 teachers who teach athematics or physics. Of these, 12 teach mathematics and 4 teach physics and mathematics. How many teach physics? 

In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. How many like both coffee and tea? 

The number of ways to arrange the letters of the word CHEESE are

Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is

If the letters of the word KRISNA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word KRISNA is

Let A and B be two sets such that :\[n \left( A \right) = 20, n \left( A \cup B \right) = 42 \text{ and } n \left( A \cap B \right) = 4\] Find\[n\left( B \right)\]

In a group of 950 persons, 750 can speak Hindi and 460 can speak English. Find: 

how many can speak both Hindi and English: 

If in a group of n distinct objects, the number of arrangements of 4 objects is 12 times the number of arrangements of 2 objects, then the number of objects is

In a group of 50 persons, 14 drink tea but not coffee and 30 drink tea. Find:
(i) how may drink tea and coffee both;
(ii) how many drink coffee but not tea. 

In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspapers. Find:
(i) the numbers of people who read at least one of the newspapers.
(ii) the number of people who read exactly one newspaper. 

The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is

Of the members of three athletic teams in a certain school, 21 are in the basketball team, 26 in hockey team and 29 in the football team, 14 play hockey and basket ball 15 play hockey and football, 12 play football and basketball and 8 play all the three games. How many members are there in all? 

A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is

The product of r consecutive positive integers is divisible by