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

From Goa to Bombay there are two roots; air, and sea. From Bombay to Delhi there are three routes; air, rail and road. From Goa to Delhi via Bombay, how many kinds of routes are there?

Which of the following statements are true? Give reason to support your answer. 

Every set has a proper subset

A mint prepares metallic calendars specifying months, dates and days in the form of monthly sheets (one plate for each month). How many types of calendars should it prepare to serve for all the possibilities in future years?

Which of the following statements are true? Give reason to support your answer. 

{a, b, a, b, a, b, ...} is an infinite set

There are four parcels and five post-offices. In how many different ways can the parcels be sent by registered post?

Which of the following statements are true? Give reason to support your answer. 

 {a, b, c} and {1, 2, 3} are equivalent sets 

Which of the following statements are true? Give reason to support your answer. 

A set can have infinitely many subsets.

A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?

State whether the following statements are true or false: 

\[1 \in \left\{ 1, 2, 3 \right\}\]

State whether the following statements are true or false: 

\[a \subset {b, c, a}\] 

A letter lock consists of three rings each marked with 10 different letters. In how many ways it is possible to make an unsuccessful attempt to open the lock?

State whether the following statements are true or false: 

\[\left\{ a \right\} \in \left\{ a, b, c \right\}\]

State whether the following statements are true or false: 

\[\left\{ a, b \right\} = \left\{ a, a, b, b, a \right\}\] 

There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 2 each?

State whether the following statements are true or false:

The set {x ; x + 8 = 8} is the null set. 

Decide among the following sets, which are subsets of which:

\[A = {x : x \text{ satisfies } x^2 - 8x + 12 = 0},\]

\[B = \left\{ 2, 4, 6 \right\}, C = \left\{ 2, 4, 6, 8, . . . \right\}, D = \left\{ 6 \right\} .\]

Write which of the following statements are true? Justify your answer. 

The set of all integers is contained in the set of all set of all rational numbers. 

Write which of the following statement are true? Justify your answer. 

The set of all crows is contained in the set of all birds.