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IMPORTANT
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The value of the determinant cos(θ+α)-sin(θ+α)cos2αsinθcosθsinα-cosθsinθλcosα is

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Important Questions on Determinant

MEDIUM
JEE Main
IMPORTANT

If the system of linear equations 

x+2ay+az=0

x+3by+bz=0

x+4cy+cz=0 has a non-zero solution, then a,b,c are in

HARD
JEE Main
IMPORTANT

The equations (λ-1)x+(3λ+1)y+2λz=0(λ-1)x+(4λ-2)y+(λ+3)z=0 and 2x+(3λ+1)y +3(λ-1)z=0 gives non-trivial solution for some values of λ. Then the ratio x:y:z when λ has the smallest of these values, is

MEDIUM
JEE Main
IMPORTANT

The system of homogeneous equations:

tx+t+1y+t-1z=0,

t+1x+ty+t+2z=0,

t-1x+t+2y+tz=0 has a non-trivial solution for

MEDIUM
JEE Main
IMPORTANT

If a, b, c are nonzero, then the system of equations, (α+a)x+αy+αz=0αx+(α+b)y+αz=0 and αx+αy+(α+c)z=0 has a non-trivial solution, if

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JEE Main
IMPORTANT

The values of θλ for which the following equations,

 sinθx-cosθy+(λ+1)z=0;

cosθx+sinθy-λz=0;

λx+(λ+1)y+cosθz=0, have non trivial solution, is

MEDIUM
JEE Main
IMPORTANT
If the system of equations, x-2y+z=a, 2x+y-2z=b and x+3y-3z=c have at least one solution, then
MEDIUM
JEE Main
IMPORTANT

If A,B,C are the angles of a triangle, the system of equations,

(sinA)x+y+z=cosA,

x+(sinB)y+z=cosB,

x+y+(sinC)z=1-cosC

has

MEDIUM
JEE Main
IMPORTANT

A solution set of the equations,

  x+2y+z=1,

x+3y+4z=k,

x+5y+10z=k2is