If A and G are respectively arithmetic and geometric mean between positive no. a and b; then the quadratic equation having a, b as its roots is \( {x}^{2}-2Ax+ {G}^{2}=0\)
The coefficient of \( {x}^{2}{y}^{5}{z}^{3}\) in the expansion of \( {\left(2x+y+3z\right)}^{10}\) is A.\( \frac{10!}{2!3!}{2}^{2}{3}^{2}\) B.\( \frac{10!}{2!5!3!}{2}^{2}{3}^{2}\) C.\( \frac{10!}{2!5!3!}{2}^{2}{3}^{3}\) D.\( \frac{10!}{2!5!3!}\)
A tangent is drawn to the ellipse \( \frac{{x}^{2}}{27}+{y}^{2}=1\) at \( \left(3\sqrt{3} cos \theta ,sin\theta \right)\) where \( \theta \epsilon \left(0, \frac{\pi }{2}\right)\). Then find the value of \( \theta \)such that the sum of intercepts on the axes made by this tangent is minimum.
\( 0\le\;a\le\;3\), \( 0\le\;b\le\;3\) and the equation, \( {x}^{2}+4+3cos(ax+b)=2x\) has atleast one solution then the value of \( a+b\) A) \( \frac{\pi }{2}\) B) \( \frac{\pi }{4}\) C) \( \frac{\pi }{3}\) D) \( \pi \)