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If the lines ax+y+1=0, x+by+1=0, x+y+c=0...

If the lines ax+y+1=0, x+by+1=0, x+y+c=0, (a, b, c are distinct and not equal to 1), are concurrent, then find the value of `1/(1-a)+1/(1-b)+1/(1-c)`

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CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. The lines 2x-y-1=0, ax+3y-3=0 and 3x+2y-2=0 are concurrent for

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  2. if f(alpha,beta)=|[cos alpha,-sin alpha,1],[sin alpha,cos alpha,1],[co...

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  3. If the lines ax+y+1=0, x+by+1=0, x+y+c=0, (a, b, c are distinct and no...

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  4. If (1+x+x^(2))^(25)=a(0)+a(1)x+a(2)x^(2)+...+a(50).x^(50), then a(0)+a...

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  5. Find the value of lambda for which the homogeneous system of equations...

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  6. If f,g,a n d \ h are differentiable functions of x and d(x)=|[f,g,h]...

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  7. Let a ,b ,c be positive and not all equal. Show that the value of the ...

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  8. if f(x)=|{:(x^(n),,n!,,2),(cos x,,cos.(npi)/(2),,4),(sin x,,sin .(npi)...

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  9. Without expanding a determinant at any stage, show that abs((x^2+x ,x+...

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  10. The value of determinant |[b c-a^2,a c-b^2,a b-c^2],[a c-b^2,a b-c^2,b...

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  11. Show that the system of equations 3x-y + 4z = 3, x + 2y-3z =-2 and 6x ...

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  12. The determinant |(a^(2)+10,ab, ac),(ab, b^(2)+10, bc),(ac, bc, c^(2)...

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  13. If y=|[sinx,cosx,sinx],[cosx,-sinx,cosx],[x,1, 1]| find (dy)/(dx)dot

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  14. Consider the system of equation x+y+z=6,x+2y+3z=10 ,a n dx+2y+lambdaz=...

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  15. Consider the system linear equations in x ,y ,a n dz given by (sin3the...

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  16. If alpha,beta "and" gamma are real number without expanding at any sta...

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  17. If 3 digit numbers A28, 3B9 and 62C are divisible by a fixed constant ...

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  18. If a=costheta+isintheta,b=cos2theta-isin2theta,c=cos3theta+i sin3theta...

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  19. Prove that |[a1alpha1+b1beta1, a1alpha2+b1beta2, a1alpha3+b1beta3], [a...

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  20. If alpha,beta,gamma are the roots of p x^3+q x^2+r=0, then the value o...

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