Find the values of 'a' for which `-3<(x^2+ax-2)/(x^2+x+1)<2` is valid for all real `x.`

Find the values of lambda for which 3-lambda,-1,1-1,5-lambda,-11,-1,3-lambda]|=0

Find the values of x for which 3costheta=x^2-8x+19 holds good.

Find the values of x for which 3costheta=x^2-8x+19 holds good.

Find the real value of a for which 3i^(3)-2ai^(2)+(1-a)i+5 is real

Find the real value of a for which 3i^3-2a i^2+(1-a)i+5 is real.

Find the value of lamda for which 3hat(i) + 4hat(j) - hat(k) and -2 hat(i) + lamda hat(j) + 10 hat(k) are perpendicular?

Find the value of 'k' for which the plane : 3x - 6y - 2z = 7 and 2x + y - kz = 3 are perpendicular to each other.

Find the value of x for which |[3,x],[x,1]|=|[3,2],[4,1]|