MCQ
If $\text{g}(\text{x}) = 1 +\sqrt{\text{x}}$ and $ \text{fg} (\text{x}) = 3 + 2\sqrt{\text{x} +\text{ x}},$ then $\text{f}(\text{x})=$
- A$1 + 2x^2$
- ✓$2 + x^2$
- C$1 + x$
- D$2 + x$
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$(A)$ $a_x=1 ms ^{-2}$ implies that when the particle is at the origin, $a_y=1 ms ^{-2}$
$(B)$ $a_x=0$ implies $a_y=1 ms ^{-2}$ at all times
$(C)$ at $t=0$, the particle's velocity points in the $x$-direction
$(D)$ $a_x=0$ implies that at $t=1 s$, the angle between the particle's velocity and the $x$ axis is $45^{\circ}$
$2 \cos x\left(4 \sin \left(\frac{\pi}{4}+x\right) \sin \left(\frac{\pi}{4}-x\right)-1\right)=1, x \in[0, \pi]$
and $S$ is the sum of all these solutions, then the ordered pair $(\mathrm{n}, \mathrm{S})$ is :