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1

IIT-JEE 1995 Screening

MCQ (Single Correct Answer)
$$\,3{\left( {\sin x - \cos x} \right)^4} + 6{\left( {\sin x + \cos x} \right)^2} + 4\left( {{{\sin }^6}x + {{\cos }^6}x} \right) = $$
A
11
B
12
C
13
D
14
2

IIT-JEE 1994

MCQ (Single Correct Answer)
Let $$2{\sin ^2}x + 3\sin x - 2 > 0$$ and $${x^2} - x - 2 < 0$$ ($$x$$ is measured in radians). Then $$x$$ lies in the interval
A
$$\left( {{\pi \over 6},\,{{5\pi } \over 6}} \right)\,\,$$
B
$$\left( { - 1,\,{{5\pi } \over 6}} \right)$$
C
$$\left( { - 1,\,2} \right)\,\,\,$$
D
$$\left( {{\pi \over 6},\,2} \right)$$
3

IIT-JEE 1994

MCQ (Single Correct Answer)
If $$\omega \,$$ is an imaginary cube root of unity then the value of $$\sin \left\{ {\left( {{\omega ^{10}} + {\omega ^{23}}} \right)\pi - {\pi \over 4}} \right\}$$ is
A
$$ - {{\sqrt 3 } \over 2}\,$$
B
$$ - {1 \over {\sqrt 2 }}$$
C
$${1 \over {\sqrt 2 }}$$
D
$${{\sqrt 3 } \over 2}$$
4

IIT-JEE 1994

MCQ (Single Correct Answer)
Let $$n$$ be a positive integer such that $$\sin {\pi \over {2n}} + \cos {\pi \over {2n}} = {{\sqrt n } \over 2}.$$ Then
A
$$6 \le n \le 8$$
B
$$4 < n \le 8$$
C
$$4 \le n \le 8$$
D
$$4 < n < 8$$

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