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1

IIT-JEE 1987

Fill in the Blanks
The set of all $$x$$ in the interval $$\left[ {0,\,\pi } \right]$$ for which $$2\,{\sin ^2}x - 3$$ $$\sin x + 1 \ge 0,$$ is _____.

Answer

$$\,\left[ {0,{\pi \over 6}} \right]U\left\{ {{\pi \over 2}} \right\}U\left[ {{{s\pi } \over 6},\pi } \right]$$
2

IIT-JEE 1987

Fill in the Blanks
The sides of a triangle inscribed in a given circle subtend angles $$\alpha $$, $$\beta $$ and $$\gamma $$ at the centre. The minimum value of the arithmetic mean of $$cos\left[ {\alpha + {\pi \over 2}} \right],\,\cos \left[ {\beta + {\pi \over 2}} \right]$$ and $$cos\left[ {\gamma + {\pi \over 2}} \right]$$ is equal to _______.

Answer

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

IIT-JEE 1987

Fill in the Blanks
The solution set of the system of equations $$X + Y = {{2\pi } \over 3},$$ $$cox\,x + cos\,y = {3 \over 2},$$ where x and y are real, is _____.

Answer

$$\phi $$
4

IIT-JEE 1981

Fill in the Blanks
Suppose $${\sin ^3}\,x\sin 3x = \sum\limits_{m = 0}^n {{C_m}\cos \,mx} $$ is an identity in x, where C0, C1 ,....Cn are constants, and $${C_n} \ne 0$$ , then the value of n is _____.

Answer

6

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