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1

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
$$4 < n < 8$$
2

IIT-JEE 1994

MCQ (Single Correct Answer)
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
$${\tan ^2}\left[ {x + {\pi \over 4}} \right]$$
3

IIT-JEE 1993

MCQ (Single Correct Answer)
Number of solutions of the equation $$\tan x + \sec x = 2\cos x\,$$ lying in the interval $$\left[ {0,2\pi } \right]$$ is:
A
0
B
1
C
2
D
3
4

IIT-JEE 1992

MCQ (Single Correct Answer)
In this questions there are entries in columns 1 and 2. Each entry in column 1 is related to exactly one entry in column 2. Write the correct letter from column 2 against the entry number in column 1 in your answer book.

$${{\sin \,3\alpha } \over {\cos 2\alpha }}$$ is

Column $${\rm I}$$

(A) positive

(B) negative

Column $${\rm I}$$$${\rm I}$$

(p) $$\left( {{{13\pi } \over {48}},{{14\pi } \over {48}}} \right)$$

(q) $$\left( {{{14\pi } \over {48}},\,{{18\pi } \over {48}}} \right)$$

(r) $$\left( {{{18\pi } \over {48}},\,{{23\pi } \over {48}}} \right)$$

(s) $$\left( {0,\,{\pi \over 2}} \right)$$

Options:-

A
$$\left( A \right) - r,\,\left( B \right) - q$$
B
$$\left( A \right) - r,\,\left( B \right) - p$$
C
$$\left( A \right) - s,\,\left( B \right) - r$$
D
$$\left( A \right) - p,\,\left( B \right) - q$$

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