 And welcome to the session. I am Deepika here. Let's discuss the question. On which of the following interval is the function given by, fx is equal to x is to power 100 plus sin x minus 1, strictly decreasing, a, an open interval 0, 1, b, an open interval pi by 2 to pi, c, 0 to pi by 2, d, none of these. So let's start the solution. Given fx is equal to 400 plus sin x minus 1, therefore f dash x is equal to 100 x raise to power 99 plus cos x. Now let's take the a interval a. Now for 0 less than x, x less than 1 is to power 99 is positive, greater than 0. And also cos x is positive because cos x lies between 0 is less than cos x is less than equal to 1. This implies f dash x which is equal to 100 x raise to power 99 plus cos x is greater than 0. Hence function increases an open interval 0 to 1. Let's see the interval b for pi by 2 less than x, less than pi for f dash x which is equal to 100 x raise to power 99 plus cos x is greater than 0 in this interval. Because x raise to power 99 is greater than 1 because x lies in the interval pi by 2 to pi. Therefore 100 x raise to power 99 is greater than 100 and also in this interval decreases from minus 1 to 0. That is cos x lies between minus 1 is less than cos x, cos x is less than 0. So their sum is greater than 0. This implies increasing in the interval pi by 2 to pi. Now let's discuss the interval c, 0 less than x, x less than pi by 2. This also 100 x raise to power 99 plus cos x is greater than 0 because to power 99 is greater than 1 because x is in the interval 0 to pi by 2. This implies 100 x raise to power 99 is greater than 100 and cos x is positive because cos x lies in the first quadrant because it lies in the first quadrant. This implies is greater than 0 and this implies increasing in the interval 0 to pi by 2. This is strictly decreasing in any of the above intervals and the answer for the above question is D. That is in none of these intervals the function is strictly decreasing. I hope the question is clear to you. Bye and take care.