MCQ
$\sin 12^\circ \sin 48^\circ \sin 54^\circ = $
- A$1/16$
- B$1/32$
- ✓$1/8$
- D$1/4$
$ = \frac{1}{2}\,\left[ {\frac{{\sqrt 5 + 1}}{4} - \frac{1}{2}} \right]\,\left[ {\frac{{\sqrt 5 + 1}}{4}} \right] $
$= \frac{1}{2}\,\left[ {\frac{{\sqrt 5 - 1}}{4}} \right]\,\left[ {\frac{{\sqrt 5 + 1}}{4}} \right]$
$ = \frac{{5 - 1}}{{32}} = \frac{4}{{32}} = \frac{1}{8}$.
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$2.$ Equation of a common tangent with positive slope to the circle as well as to the hyperbola is
$(A)$ $2 x-\sqrt{5} y-20=0$ $(B)$ $2 x-\sqrt{5} y+4=0$
$(C)$ $3 x-4 y+8=0$ $(D)$ $4 x-3 y+4=0$
$2.$ Equation of the circle with $\mathrm{AB}$ as its diameter is
$(A)$ $x^2+y^2-12 x+24=0$ $(B)$ $x^2+y^2+12 x+24=0$
$(C)$ $\mathrm{x}^2+\mathrm{y}^2+24 \mathrm{x}-12=0$ $(D)$ $x^2+y^2-24 x-12=0$
Give hte answer question $1, 2$