Question
Statement-I : The number of real solutions of the equation sin x = 2x + 2–x is zero
Statement-II : Since |sin x| ≤ 1
- Statement-I is True, Statement-II is True; Statement-II is a correct explanation for Statement-I.
- Statement-I is True, Statement-II is True; Statement-II is NOT a correct explanation for Statement-I
- Statement-I is True, Statement-II is False
- Statement-I is False, Statement-II is True
Hint:
In this question, given two statements. It is like assertion and reason. Statement1 is assertion and statement 2 is reason, Find the statement 1 is correct or not and the statement 2 correct or not if correct then is its correct explanation.
The correct answer is: Statement-I is False, Statement-II is True
Here , we have to find the which statement is correct and if its correct explanation or not.
Firstly ,
Statement-I : The number of real solutions of the equation sinx = 2x + 2-x is zero.
2x + 2-xsinx = 2x + 2-x
LHS:
We know that, for all value ,
-1 ≤ sinx ≤ 1
So value of sinx is between 1 to -1.
RHS :
2x + 2-x ,
The minimum value of this term is 2 if we put x = 0.
So here LHS ≠ RHS,
It has no solution,
So, Statement-I is True. Because its solution is zero
Now, we have
Statement-II: Since | sin | ≤ 1.
So, we know that for all value,
-1 ≤ sinx ≤ 1
So, value of sinx is between 1 to -1.
Now,
0 ≤ | sinx | ≤ 1
Hence, | sinx | ≤ 1
Therefore, Statement-II is also true, and it is correct explanation of Statement-I.
The correct answer is Statement-I is true, Statement-II is true; Statement-II is correct explanation for Statement-I.
In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not, is same as assertion and reason. Here, -1 ≤ sinx ≤ 1 for all value, remember that.
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