question_answer

The number of solutions of \[\sin 3x=\cos 2x\], in the interval \[\left( \frac{\pi }{2},\pi  \right)\]is [JEE Online 15-04-2018 (II)]

A)         3                             

B)          4             

C) 2                             

D)          1

Correct Answer: D

Solution :

Let us see the solution graphically as depicted above. Clearly there is only 1 solution in the given interval. Note we are asked about the number of solutions and not the solutions themselves, so drawing a graph is enough or one could just check the signs of the function \[\sin 3x-\cos 2x\]in this interval and discover that there is only one sign change so there is only one solution. There is no need to solve the equation. So option D is the correct answer.