Question

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Answer 1

$\orange{\mathfrak{Question\:(1)}} \\ \\ \tt 1 + {tan}^{2}\theta = ? \\ \\ \tt \implies 1 + {tan}^{2}\theta = {sec}^{2}\theta \\ \\ \tt \therefore \boxed{\bold{\underline{\red{\tt Option\:C)\:{sec}^{2}\theta}}}} \\ \\ \orange{\mathfrak{Question\:(2)}} \\ \\ \tt The\:point\: lying\:on\:right\:side\:of\:X-axis \\ \tt have\:a\:positive\:ordinate\:and\:0\:as\:abscissa \\ \\ \tt \therefore \boxed{\bold{\underline{\red{\tt Option\:D)\:(2,0) }}}} \\ \\ \orange{\mathfrak{Question\:(3)}} \\ \\ \tt Distance\:of\:point\:(x,y)\:from\:origin\:is\:given\:by \\ \\ \tt \boxed{\bold{\underline{\green{\tt D = \sqrt{{x}^{2}+{y}^{2}} }}}} \\ \\ \tt So\:the\:distance\:of\:(-3,4)\:from\:origin\:is \\ \\ \tt \implies D = \sqrt{{-3}^{2}+{4}^{2}} \\ \\ \tt \implies D = \sqrt{9 + 16} \\ \\ \tt \implies D = \sqrt{25} \\ \\ \tt \implies D = 5\:units \\ \\ \tt \therefore \boxed{\bold{\underline{\red{\tt Option\:C)\:5}}}} \\ \\ \orange{\mathfrak{Question\:(4)}} \\ \\ \tt It\:is\:a\: statement \\ \\ \tt The\:number\:of\:tangents\:drawn\:to\:a \\tt point\:on\:a\:circle\: is \:one \\ \\ \tt The\:number\:of\:tangents\:drawn\:to\:a \\ \tt point\:outside\:a\:circle\:is\:two \\ \\ \tt \therefore \boxed{\bold{\underline{\red{\tt Option\:C)\:1}}}} \\ \\ \orange{\mathfrak{Question\:(5)}} \\ \\ \tt Two\:circles\:with\:radii\:{r}_{1}\:and\:{r}_{2} \\ \tt touch\:each\: other\:then\:distance\:between\:their\:centres \\ \\ \tt \boxed{\bold{\underline{\green{\tt D = {r}_{1}+{r}_{2} ...If\:they\: touches\: externally}}}} \\ \tt \boxed{\bold{\underline{\green{\tt D = {r}_{1}-{r}_{2} ...If\:they\:touches\: internally }}}} \\ \\ \tt \implies D = 5.5 + 3.3 \:\:or\:\: D = 5.5-3.3 \\ \\ \tt \implies D = 8.8 \:\:or\:\: D = 2.2 \\ \\ \tt \therefore \boxed{\bold{\underline{\red{\tt Option\:D)8.8\:or\:2.2}}}} \\ \\ \orange{\mathfrak{Question\:(6)}} \\ \\ \tt If\:two\:circles\: touching\: externally\:only\:one\:common \\ \tt tangent\:can\:be\:drawn \\ \\ \tt \therefore \boxed{\bold{\underline{\red{\tt Option\:A)\:one}}}}$