The value of `|alpha|` for which the system of equation
`alphax+y+z=alpha-1`
`x+alphay+z=alpha-1`
`x+y+alphaz=alpha-1`
has no solution , is `"____"`

The system of equations x +2y+3z=1, x-y+4z=0, 2x+y+7z=1 has

If a , b , c are non-zero, then the system of equations (alpha+a)x+alphay+alphaz=0,alphax+ , (alpha+b)y+alphaz=0,alphax+alphay+(alpha+c)z=0 has a non-trivial solution if alpha^(-1)= (A) -(a^(-1)+b^(-1)+c^(-1)) (B) a+b+c (C) alpha+a+b+c=1 (D) none of these

An ordered pair (alpha, beta) for which the system of linear equations (1+alpha)x+betay+z=2 , alphax+(1+beta)y+z=3 and alphax+betay+2z=2 has unique solution is: (a) (2,4) (b) (-3,1) (c) (-4,2) (d) (1,-3)

alpha beta x ^(alpha-1) e^(-beta x ^(alpha))

Let lambda and alpha be real. Then the numbers of intergral values lambda for which the system of linear equations lambdax +(sin alpha) y+ (cos alpha) z=0 x + (cos alpha) y+ (sin alpha) z=0 -x+(sin alpha) y -(cos alpha) z=0 has non-trivial solutions is

If the system fo equations x+y+z = 5 x + 2y + 3z = 9 x + 3y + alphaz = beta has infinitely many solution, then beta - alpha equals

Let alpha ,beta and gamma be the roots of the equations x^(3) +ax^(2)+bx+ c=0,(a ne 0) . If the system of equations alphax + betay+gammaz=0 beta x +gamma y+ alphaz =0 and gamma x =alpha y + betaz =0 has non-trivial solution then

If x sin ^3 alpha + y cos^3 alpha = sin alpha cos alpha and x sin alpha - y cos alpha =0 , then x^2 +y^2 is

If sin^(-1)x=2sin^(-1)alpha has a solution, then

The minimum integral value of alpha for which the quadratic equation (cot^(-1)alpha)x^(2)-(tan^(-1)alpha)^(3//2)x+2(cot^(-1)alpha)^(2)=0 has both positive roots