Maths-
General
Easy

Question

Statement-I : The number of real solutions of the equation sin x = 2x + 2–x is zero

Statement-II : Since |sin x| ≤ 1

  1. Statement-I is True, Statement-II is True; Statement-II is a correct explanation for Statement-I.
  2. Statement-I is True, Statement-II is True; Statement-II is NOT a correct explanation for Statement-I
  3. Statement-I is True, Statement-II is False
  4. Statement-I is False, Statement-II is True

hintHint:

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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