1
JEE Main 2014 (Offline)
+4
-1
Let $$f_k\left( x \right) = {1 \over k}\left( {{{\sin }^k}x + {{\cos }^k}x} \right)$$ where $$x \in R$$ and $$k \ge \,1.$$
Then $${f_4}\left( x \right) - {f_6}\left( x \right)\,\,$$ equals :
A
$${1 \over 4}$$
B
$${1 \over 12}$$
C
$${1 \over 6}$$
D
$${1 \over 3}$$
2
JEE Main 2013 (Offline)
+4
-1
The expression $${{\tan {\rm A}} \over {1 - \cot {\rm A}}} + {{\cot {\rm A}} \over {1 - \tan {\rm A}}}$$ can be written as:
A
$$\sin {\rm A}\,\cos {\rm A} + 1$$
B
$$\,\sec {\rm A}\,\cos ec{\rm A} + 1$$
C
$$\tan {\rm A} + \cot {\rm A}$$
D
$$\sec {\rm A} + \cos ec{\rm A}$$
3
AIEEE 2011
+4
-1
If $$A = {\sin ^2}x + {\cos ^4}x,$$ then for all real $$x$$:
A
$${{13} \over {16}} \le A \le 1$$
B
$$1 \le A \le 2$$
C
$${3 \over 4} \le A \le {{13} \over {16}}$$
D
$${{3} \over {4}} \le A \le 1$$
4
AIEEE 2010
+4
-1
Let $$\cos \left( {\alpha + \beta } \right) = {4 \over 5}$$ and $$\sin \,\,\,\left( {\alpha - \beta } \right) = {5 \over {13}},$$ where $$0 \le \alpha ,\,\beta \le {\pi \over 4}.$$
Then $$tan\,2\alpha$$ =
A
$${56 \over 33}$$
B
$${19 \over 12}$$
C
$${20 \over 7}$$
D
$${25 \over 16}$$
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