If `p q r!=0` and the system of equation `(p+a)x+b y+c z=0`, `a x+(q+b)y+c z=0`, `a x+b y+(r+c)z=0` has nontrivial solution, then value of `a/p+b/q+c/r` is a. `-1` b. `0` c.`1` d. 2

If p q r!=0 and the system of equation (p+a)x+b y+c z=0 a x+(q+b)y+c z=0 a c+b y+(r+c)z=0 has nontrivial solution, then value of a/p+b/q+c/r is -1 b. 0 c. 0"" d. not-2

If the system of equations x+a y=0,a z+y=0,a n da x+z=0 has infinite solutions, then the value of equation has no solution is -3 b. 1 c. 0 d. 3

If the system of equations x+a y=0,a z+y=0 and a x+z=0 has infinite solutions, then the value of a is (a) -1 (b) 1 (c) 0 (d) no real values

The system of linear equations x + y + z = 0 (2x)/(a) + (3y)/(b) + (4z)/(c ) = 0 (x)/(a) + (y)/(b) + (z)/(c ) = 0 has non trivia solution then

The product of all values of t , for which the system of equations (a-t)x+b y+c z=0,b x+(c-t)y+a z=0,c x+a y+(b-t)z=0 has non-trivial solution, is (a) |[a, -c, -b], [-c, b, -a], [-b, -a, c]| (b) |[a, b, c], [b, c, a], [c, a, b]| (c) |[a, c, b], [b, a, c], [c, b, a]| (d) |[a, a+b, b+c], [b, b+c, c+a], [c, c+a, a+b]|

The values of k in R for which the system of equations x+k y+3z=0,k x+2y+2z=0,2x+3y+4z=0 admits of nontrivial solution is a. 2 b. 5//2 c. 3 d. 5//4

The values of k in R for which the system of equations x+k y+3z=0,k x+2y+2z=0,2x+3y+4z=0 admits of nontrivial solution is 2 b. 5//2 c. 3 d. 5//4

If the system of equations ax + by + c = 0,bx + cy +a = 0, cx + ay + b = 0 has infinitely many solutions then the system of equations (b + c) x +(c + a)y + (a + b) z = 0 (c + a) x + (a+b) y + (b + c) z = 0 (a + b) x + (b + c) y +(c + a) z = 0 has

Statement I: If a ,\ \ b , c in R\ a n d a!=b!=c\ a n d\ x ,\ y ,\ z are non zero. Then the system of equations a x+b y+c z=0b x+c y+a z=0c x+a y+b z=0 has infinite solutions. because Statement II: If the homogeneous system of equations has no non trivial solution, then it has infinitely many solutions. a. A b. \ B c. \ C d. D

If the system of linear equations x+a y+a z=0,\ x+b y+b z=0,\ x+c y+c z=0 has a non zero solution then (a) System is always non trivial solutions (b) System is consistent only when a=b=c (c) If a!=b!=c then x=0,\ y=t ,\ z=-t\ AAt in R (d) If a=b=c\ t h e n\ y=t_1, z=t_2,\ x=-a(t_1+t_2)AAt_1, t_2 in R