If alpha is the common positive rootof the equation `x^2-ax+12=0, x^2-bx+15=0 and x^2-(a+b)x+36=0` and `cosx+cos2x+cos3x=alpha`, then `sinx+sin2x+sin3x=` (A) 3 (B) -3 (C) 0 (D) none of these

If the equation x^2+ax+12=0 , x^2 +bx +15 =0 and x^2 +(a+ b) x+ 36 =0 have a common positive root, then b- 2a is equal to

If x=1 is a common root of the equations a x^2+a x+3=0 and x^2+x+b=0 , then a b=

If the equation x ^(2) +ax+12 =9, x ^(2) +bx +15 =0 and x^(2) + (a+b) x +36=0 have a common positive root, then b+2a equal to.

If alpha an integer and P (alpha, alpha^2) is a point in the interior of the quadrilateral x=0, y=0, 4x+y-21=0 and 3x+y-4=0, and (1+ax)^n = 1 + 8x+24x^2 + …, then alpha= (A) a (B) -a (C) a^2 (D) none of these

If (sinx-cosx)= 0 then find (sin^3 x- cos^3x)

If the equation x^2+2x+3=0 and ax^2+bx+c=0 have a common root then a:b:c is

If equations x^2+a x+12=0. x^2+b x+15=0a n dx^2+(a+b)x+36=0, have a common positive root, then find the values of aa n dbdot

Solve cosx+cos3x-2cos2x=0

If sinx+siny=sqrt(3)(cos y-cos x), then sin3x+sin3y= ___________ (a) 2sin3x (b) 0 (c) 1 (d) none of these

If the equation x^(2 )+ 2x + 3 = 0 and ax^(2) +bx+c=0, a, b, c in R , have a common root, then a : b:c is