For real values of $\text{'}\theta \text{'}$

	COLUMN-I		COLUMN-II
a	$A={\sin }^2\theta +{\cos }^4\theta$	p	$A\in [-1,1]$
b	$A=3{\cos }^2\theta +{\sin }^4\theta$	q	$A\in [\frac{3}{4},1]$
c	$A={\sin }^2\theta -{\cos }^4\theta$	r	$A\in [2\sqrt{2},\infty )$
d	$A={\tan }^2\theta +2{\cot }^2\theta$	s	$A\in [1,3]$
		t	$[0,1]$

A) ${\sin }^2\theta +{\cos }^4\theta$  
$={\sin }^2\theta +{\cos }^2\theta -{\cos }^2{\sin }^2\theta$ 
$=1-4{\sin }^{2}2\theta$ 
$\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.\le A\le 1$ 
B) $3{\cos }^2\theta +{\sin }^4\theta$  
$3{\cos }^2\theta +{(1-{\cos }^2\theta )}^2$ 
$3{\cos }^2\theta +1+{\cos }^4\theta -2{\cos }^2\theta$ 
${\cos }^2\theta +{\cos }^4\theta +1$ 
$A_{\max }=1+1+1=3$ 
$A_{\min }=0+0+1=1$ 
C) ${\sin }^2\theta -{\cos }^4\theta =1-{\cos }^2\theta -{\cos }^4\theta$  
$=\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$4$}\right.-{({\cos }^2\theta -\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.)}^2$ 
$0\le {\cos }^2\theta \le 1\Rightarrow 1\le \frac{5}{4}-{({\cos }^2\theta -\frac{1}{2})}^2\le 1$ 
D) ${\tan }^2\theta +2{\cot }^2\theta ={(\tan \theta -\sqrt{2}\cot \theta )}^2+2\sqrt{2}\ge 2\sqrt{2}$