Related InterviewSolutions

• If A,B,C are the angles of a non right angled triangle ABC. Then find the value of:`|[tanA,1,1],[1,tanB,1],[1,1,tanC]|`
• If p + q + r = a + b + c = 0, then the determinant `|{:(pa,qb,rc),(qc,ra,pb),(rb,pc,qa):}|` equals
• If `|(a,a +d,a +2d),(a^(2),(a + d)^(2),(a + 2d)^(2)),(2a + 3d,2 (a +d),2a +d)| = 0`, thenA. `d = 0`B. `a +d = 0`C. `d = 0 ro a +d = 0`D. none of these
• What is the value of the following determinant?
• Evaluate `|(cosalphacosbeta,cosalphas inbeta,-sinalpha),(-sinbeta,cosbeta,0),(sinalphacosbeta,sinalphasinbeta,cosalpha)|`
• Using the property of determinants and without expanding in questions 1 to 7 prove that , `|{:(a-b,b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c):}|=0`
• Using the property of determinants and without expanding, prove that:`|0a-b-a0-c b c0|=0`
• Value of \(\begin{vmatrix}cos50^o &sin10^o \\[0.3em]sin50^o & cos10^o \\[0.3em]\end{vmatrix}\) is :(a) 0(b) 1(c) 1/2(d) – 1/2
• If `|(x, x^2, x^3 +1), (y, y^2, y^3+1), (z, z^2, z^3+1)|` = 0 and x ,y and z are not equal to any other, prove that, xyz = -1
• Prove that `|[1+a,1,1],[1,1+b,1],[1,1,1+c]|=(abc)(1/a+1/b+1/c+1)=(bc+ca+ab+abc)`