1
IIT-JEE 2009 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
If $${{{{\sin }^4}x} \over 2} + {{{{\cos }^4}x} \over 3} = {1 \over 5},$$ then
A
$${\tan ^2}x = {2 \over 3}$$
B
$${{{{\sin }^8}x} \over 8} + {{{{\cos }^8}x} \over {27}} = {1 \over {125}}$$
C
$${\tan ^2}x = {1 \over 3}$$
D
$${{{{\sin }^8}x} \over 8} + {{{{\cos }^8}x} \over {27}} = {2 \over {125}}$$
2
IIT-JEE 1999
MCQ (More than One Correct Answer)
+3
-0.75
For a positive integer $$\,n$$, let
$${f_n}\left( \theta \right) = \left( {\tan {\theta \over 2}} \right)\,\left( {1 + \sec \theta } \right)\,\left( {1 + \sec 2\theta } \right)\,\left( {1 + \sec 4\theta } \right).....\left( {1 + \sec {2^n}\theta } \right).$$ Then
A
$${f_2}\left( {{\pi \over {16}}} \right) = 1$$
B
$${f_3}\left( {{\pi \over {32}}} \right) = 1$$
C
$${f_4}\left( {{\pi \over {64}}} \right) = 1$$
D
$${f_5}\left( {{\pi \over {128}}} \right) = 1$$
3
IIT-JEE 1988
MCQ (More than One Correct Answer)
+2
-0.5
The values of $$\theta $$ lying between $$\theta = \theta $$ and $$\theta = \pi /2$$ and satisfying the equation

$$\left| {\matrix{ {1 + {{\sin }^2}\theta } & {{{\cos }^2}\theta } & {4\sin 4\theta } \cr {{{\sin }^2}\theta } & {1 + {{\cos }^2}\theta } & {4\sin 4\theta } \cr {{{\sin }^2}\theta } & {{{\cos }^2}\theta } & {1 + 4\sin 4\theta } \cr } } \right| = 0$$ are

A
$$7\pi /24$$
B
$$5\pi /24$$
C
$$11\pi /24$$
D
$$\pi /24$$
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