Match List-I with List-II | List-I | List-II | |---|---| | (A) Maximum value of $f(x) = \sin^2 x - \cos^2 x$, $\forall x \in (\pi, 2\pi)$ is | (I) 0 | | (B) Minimum value of $f(x) = \sin x \cos x$ | (II) 1 | | (C) Point of Minima of $f(x) = x^x$ $(x > 0)$ | (III) $-\frac{1}{2}$ | | (D) Maximum value of $f(x) = -x^{2026}$ | (IV) $\frac{1}{e}$ | Choose the correct answer from the options given below:

The greatest possible value of '$a$' such that the function $f(x) = x^2 + a x + 1$ is always decreasing in the interval [1, 2] is:

The real valued function $f(x) = x^{15} + 5x^9 + 10$ is increasing for___________.

Let $f(x) = \log_e(\sin x), x \in (0, \pi)$, then which of the following statements is/are TRUE?

(A) $f(x)$ is increasing on $(0, \pi/2)$

(B) $f(x)$ is decreasing on $(\pi/2, \pi)$

(C) $f(x)$ is increasing on $(0, \pi)$

(D) $f(x)$ is decreasing on $(0, \pi)$

Choose the correct answer from the options given below:

The function $f(x)=x^2-x\sqrt{2}$ is strictly decreasing in the interval :

The interval on which the function $f(x) = x^3 + 2x^2 - 1$ is decreasing, is

The function $f(x) = 6(2x^4 - x^2)$ is strictly increasing in