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81. S - (I): The acceleration due to gravity decreases with increase in height from the surface of the Earth. S - (II): The acceleration due to gravity is inversely proportional to the square of the distance from the centreEarth.	NDA-I (2014)	2014	Physics
82. S - (I): The acceleration due to gravity decreases with increase in height from the surface of the Earth. S - (II): The acceleration due to gravity is inversely proportional to the square of the distance from the centrerth.	NDA-I (2014)	2014	Physics
83. S - (I): The acceleration due to gravity decreases with increase in height from the surface of the Earth. S - (II): The acceleration due to gravity is inversely proportional to the square of the distance from the .	NDA-I (2015)	2015	Physics
84. S - (I): The acceleration due to gravity decreases with increase in height from the surface of the Earth. S - (II): The acceleration due to gravity is inversely proportional to the square of the distance from the . $$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$ When \(a \ne 0\), there are two solutions to \(ax^2 + bx + c = 0\) and they are \[x = {-b \pm \sqrt{b^2-4ac} \over 2a}.\] ${\displaystyle \begin{array}{lll}f\left(x\right)& =& (x+2)(x-3)\\ & =& x^2-3x+2x-6\\ & =& x^2-x-6\\ f^{\prime }\left(x\right)& =& 2x-1\end{array}}$	NDA-I (2016)	2016	Physics
85. S - (I): The acceleration due to gravity decreases with increase in height from the surface of the Earth. S - (II): The acceleration due to gravity is inversely proportional to the square of the distance from the .	NDA-I (2017)	2017	Physics

${\displaystyle \begin{array}{lll}F\left(x\right)& =& \frac{KQ1}{Q-2}\\ f^{\prime }\left(x\right)& =& \frac{(x-2)-(x+1)}{{(x-2)}^2}\\ & =& -\frac{3}{x^2-4x+4}\end{array}}$ $$\begin{array}{rl}\cos 2\theta & ={\cos }^2\theta +{\sin }^2\theta -{\sin }^2\theta -{\sin }^2\theta \\ \\ & =1-2{\sin }^2\theta \end{array}$$