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1

### IIT-JEE 1995

Subjective
Find the smallest positive number $$p$$ for which the equation $$\cos \left( {p\,\sin x} \right) = \sin \left( {p\cos x} \right)$$ has a solution $$x\, \in \,\left[ {0,2\pi } \right]$$.

$${{\pi \sqrt 2 } \over 4}$$
2

### IIT-JEE 1993

Subjective
Determine the smallest positive value of number $$x$$ (in degrees) for which $$\tan \left( {x + {{100}^ \circ }} \right) = \tan \left( {x + {{50}^ \circ }} \right)\,\tan \left( x \right)\tan \left( {x - {{50}^ \circ }} \right).$$\$

$${30^ \circ }$$
3

### IIT-JEE 1992

Subjective
Show that the value of $${{\tan x} \over {\tan 3x}},$$ wherever defined never lies between $${1 \over 3}$$ and 3.

Solve it.
4

### IIT-JEE 1991

Subjective
If $$\exp \,\,\,\left\{ {\left( {\left( {{{\sin }^2}x + {{\sin }^4}x + {{\sin }^6}x + \,\,\,..............\infty } \right)\,In\,\,2} \right)} \right\}$$ satiesfies the equation $${x^2} - 9x + 8 = 0,$$ find the value of $${{\cos x} \over {\cos x + \sin x}},\,0 < x < {\pi \over 2}.$$

$${{\sqrt 3 - 1} \over 2}$$

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NEET

Class 12