| Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below. |
| Assertion [A] \[{{n}^{2}}-n\] is divisible by 2 for every positive integer. |
| Reason [R] \[\sqrt{2}\]is not a rational number. |
A) A is true, R is true; R is a correct explanation for A.
B) A is true, R is true; R is not a correct explanation for A.
C) A is true; R is False.
D) A is false; R is true.
Correct Answer: B
Solution :
| Case I If n=2q |
| \[{{n}^{2}}-n=4{{q}^{2}}-2q\] |
| \[=2q\left( 2q-1 \right)\] (divisible by 2) |
| Case II If \[n=2q+1\] |
| \[{{n}^{2}}-n={{\left( 2q+1 \right)}^{2}}-\left( 2q+1 \right)\] |
| \[=4{{a}^{2}}+4q+1-2q-1\] |
| \[=2q\left( 2q+1 \right)\] (divisible by 2) |
| Hence, Assertion and Reason both are true but Reason is not a correct explanation of Assertion. |
You need to login to perform this action.
You will be redirected in
3 sec
