Home
Class 10
MATHS
Write whether every positive integer can...

Write whether every positive integer can be of the form `4q+2` where q is an integer, Justify your answer

Text Solution

AI Generated Solution

To determine whether every positive integer can be expressed in the form \(4q + 2\) where \(q\) is an integer, we will analyze the possible forms of integers based on the division by 4. ### Step-by-Step Solution: 1. **Understanding the Division Algorithm**: According to Euclid's division algorithm, any integer \(a\) can be expressed as: \[ a = 4m + r ...
Promotional Banner

Topper's Solved these Questions

  • REAL NUMBERS

    NCERT EXEMPLAR ENGLISH|Exercise SHORT ANSWER TYPE QUESTIONS|14 Videos

  • REAL NUMBERS

    NCERT EXEMPLAR ENGLISH|Exercise LONG ANSWER TYPE QUESTIONS|5 Videos

  • REAL NUMBERS

    NCERT EXEMPLAR ENGLISH|Exercise LONG ANSWER TYPE QUESTIONS|5 Videos

  • QUADRIATIC EQUATIONS

    NCERT EXEMPLAR ENGLISH|Exercise LONG ANSWER TYPE|12 Videos

  • STATISTICS AND PROBABILITY

    NCERT EXEMPLAR ENGLISH|Exercise LONG ASWERS QUESTIONS|14 Videos

Similar Questions

Explore conceptually related problems

Write whether the square of any positive integer can be of the form 3m+2, where m is a natural number. Justify answer.

Every even integer is of the form 2m , where m is an integer (True/false).

Every odd integer is of the form 2m-1 , where m is an integer (True/false).

Show that any positive odd integer is of the form 4q+1 or 4q+3 , where q is some integer.

Show that any positive odd integer is of the form 4q+1 or 4q+3 , where q is some integer.

Show that any positive odd integer is of the form 4q+1 or 4q+3 , where q is some integer.

Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q+1 , where q is some integer.

Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q+1 , where q is some integer.

Show that every positive even integer is of the form 2q , and that every positive odd integer is of the form 2q+1 , where q is some integer.

Show that every positive even integer is of the form 2q , and that every positive odd integer is of the form 2q+1 , where q is some integer.