If Y = \( \left\{x|x\;is\;a positive\;factor\;of\;the\;number {2}^{p-1}\left({2}^{p}-1\right), where {2}^{p}-is\;a prime\;number\right\}.Write\;Y in\;the\;roaster\;form.\)
Let a, b, c and d be non-zero numbers. If the point of intersection of the line \( 4ax+2ay+c=0\) and \( 5bx+2by+d=0\) lies in the fourth quadrant and is equidistant from the two axes then: (1) \( 2bc-3ad=0\)(2) \( 2bc+3ad=0\) (3) \( 3bc-2ad=0\)(4) \( 3bc+2ad=0\)
If the sum of n terms of an A.P. is cn\( \left(n - 1\right)\) where c \( \ne\;0 \), then the sum of the squares of these terms is A.\( {c}^{2}n{\left(n + 1\right)}^{2}\) B.\( \frac{2}{3}{c}^{2}n\left(n - 1\right)\left(2n - 1\right)\) C.\( \frac{{2c}^{2}}{3}n\left(n+ 1\right)\left(2n+ 1\right)\) D.none of these
The equation of the bisector of the acute angle between the lines \( 2x-y+4=0 \)and \( x-2y=1 \)is (a) \( x-y+5=0\) (b)\( x-y+1=0\) (c)\( x-y=5\) (d) none of these
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.\( \frac{10!}{2!5!3!}\)