1
IIT-JEE 2008 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-1

Match the Statements/Expressions in Column I with the Statements/Expressions in Column II.

Column I Column II
(A) The minimum value of $${{{x^2} + 2x + 4} \over {x + 2}}$$ is (P) 0
(B) Let A and B be 3 $$\times$$ 3 matrices of real numbers, where A is symmetric, B is skew-symmetric and (A + B) (A $$-$$ B) = (A $$-$$ B) (A + B). If (AB)$$^t$$ = ($$-1$$)$$^k$$ AB, where (AB)$$^t$$ is the transpose of the matrix AB, then the possible values of k are (Q) 1
(C) Let $$a=\log_3\log_3 2$$. An integer k satisfying $$1 < {2^{( - k + 3 - a)}} < 2$$, must be less than (R) 2
(D) If $$\sin \theta = \cos \varphi $$, then the possible values of $${1 \over \pi }\left( {\theta + \varphi - {\pi \over 2}} \right)$$ are (S) 3

A
A - iii; B - ii, iv; C - iii, iv; D - i, iii
B
A - iii; B - ii; C - iii, iv; D - i, iii
C
A - ii; B - ii, iv; C - iii, iv; D - i
D
A - ii; B - ii, iv; C - iii, iv; D - i, iii
2
IIT-JEE 2007
MCQ (Single Correct Answer)
+3
-0.75
The number of solutions of the pair of equations $$$\,2{\sin ^2}\theta - \cos 2\theta = 0$$$ $$$2co{s^2}\theta - 3\sin \theta = 0$$$

in the interval $$\left[ {0,2\pi } \right]$$

A
zero
B
one
C
two
D
four
3
IIT-JEE 2006
MCQ (Single Correct Answer)
+3
-0.75
Let $$\theta \in \left( {0,{\pi \over 4}} \right)$$ and $${t_1} = {\left( {\tan \theta } \right)^{\tan \theta }},\,\,\,\,{t_2} = \,\,{\left( {\tan \theta } \right)^{\cot \theta }}$$, $${t_3}\, = \,\,{\left( {\cot \theta } \right)^{\tan \theta }}$$ and $${t_4}\, = \,\,{\left( {\cot \theta } \right)^{\cot \theta }},$$then
A
$${t_1} > {t_2} > {t_3} > {t_4}$$
B
$${t_4} > {t_3} > {t_1} > {t_2}$$
C
$${t_3} > {t_1} > {t_2} > {t_4}$$
D
$${t_2} > {t_3} > {t_1} > {t_4}$$
4
IIT-JEE 2006 Screening
MCQ (Single Correct Answer)
+3
-0.75
The values of $$\theta \in \left( {0,2\pi } \right)$$ for which $$2\,{\sin ^2}\theta - 5\,\sin \theta + 2 > 0,$$ are
A
$$\left( {0,{\pi \over 6}} \right)\, \cup \,\left( {{{5\pi } \over 6},2\pi } \right)$$
B
$$\,\left( {{\pi \over 8},{{5\pi } \over 6}} \right)$$
C
$$\left( {0,{\pi \over 8}} \right)\, \cup \,\left( {{\pi \over 6},{{5\pi } \over 6}} \right)$$ v
D
$$\,\left( {{{41\pi } \over {48}},\,\pi } \right)$$
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