Tag: measures and relations

Questions Related to measures and relations

$n^2-n+1$ is an odd number for all

  1. $n>1$

  2. $n>2$

  3. $n\ge1$

  4. $n\ge5$


Correct Option: C
Explanation:

For $ n = 1 $, we have $ n^2 - n + 1 = 1^2 -1 + 1 = 1 $ which is an odd number


For $ n =2 $, we have $ n^2 - n + 1 = 2^2 -2 + 1 = 3 $ which is an odd number

For $ n = 3 $, we have $ n^2 - n + 1 = 3^2 -3 + 1 = 7 $ which is an odd number

For $ n = 4 $, we have $ n^2 - n + 1 = 4^2 -4 + 1 = 13 $ which is an odd number

For $ n = 5 $, we have $ n^2 - n + 1 = 5^2 -5 + 1 = 19 $ which is an odd number

Hence, $ n^2 - n + 1 = 1^2 -1 + 1 = 1 $ is an odd number for all $ n \ge 1 $

Find the number of variables in the expression: $3x^2+25xy+7x2+5y^2+z^2$

  1. $4$

  2. $2$

  3. $3$

  4. $5$


Correct Option: C
Explanation:

The variables are $ x$,$ y$ and $z $