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1

### IIT-JEE 1994

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
$$\left( {{\pi \over 6},\,2} \right)$$
2

### IIT-JEE 1994

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
$${{\sqrt 3 } \over 2}$$
3

### IIT-JEE 1994

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
$$4 < n < 8$$
4

### IIT-JEE 1994

Let $$0 < x < {\pi \over 4}$$ then $$\left( {\sec 2x - \tan 2x} \right)$$ equals
A
$$\tan \left[ {x - {\pi \over 4}} \right]$$
B
$$\tan \left[ {{\pi \over 4} - x} \right]$$
C
$$\tan \left[ {x + {\pi \over 4}} \right]$$
D
$${\tan ^2}\left[ {x + {\pi \over 4}} \right]$$

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