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If a, b, c, are in A.P, then the determi...

If a, b, c, are in A.P, then the determinant `|(x+2,x+3,x+2a),( x+3,x+4,x+2b ),(x+4,x+5,x+2c)|` is
(A) `0` (B) `1` (C) `x` (D) `2x`

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To solve the problem, we need to evaluate the determinant given that \( a, b, c \) are in Arithmetic Progression (A.P). The determinant is given as: \[ D = \begin{vmatrix} x + 2 & x + 3 & x + 2a \\ x + 3 & x + 4 & x + 2b \\ ...
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NCERT ENGLISH-DETERMINANTS-All Questions
  1. Let A=[[1,sintheta,1],[-sintheta,1,sintheta],[-1,-sintheta,1]], where ...

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  2. If x, y, z are non-zero real numbers, then the inverse of matrix A=[(...

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  3. If a, b, c, are in A.P, then the determinant |(x+2,x+3,x+2a),( x+3,x+4...

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  4. Solve the system of equations2/x+3/y+(10)/z=4,4/x-6/y+5/z=1,6/x+9/y-(2...

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  5. Using properties of determinants. Prove that |(sinalpha,cosalpha,cos(a...

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  6. Using properties of determinants. Prove that|[1 ,1+p,1+p+q],[2, 3+2p,4...

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  7. Using properties of determinants. Prove that|[3a,-a+b,-a+c],[-b+a,3b,-...

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  8. Using properties of determinants, prove the following: |xx^2 1+p x...

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  9. Using properties of determinants. Prove that|(alpha,alpha^2,beta+gamma...

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  10. Evaluate |[1,x, y],[1,x+y, y],[1,x,x+y]|

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  11. Write Minors and Cofactors of the elements of following determinants:...

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  12. Using Cofactors of elements of second row, evaluate Delta=|(5, 3, 8),(...

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  13. Write Minors and Cofactors of the elements of following determinants:...

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  14. If Delta=|[a(11),a(12),a(13)],[a(21),a(22),a(23)],[a(31),a(32),a(33)]|...

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  15. Using Cofactors of elements of third column, evaluate Delta=|(1,x, y ...

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  16. Without expanding, prove that Delta=|(x+y,y+z,z+x),(z,x,y),(1,1,1)|=0

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  17. EvaluateDelta=|1a b c1b c a1c a b|

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  18. Show that |a b c a+2x b+2y c+2z x y z|=0

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  19. Prove that |a a+b a+b+c2a3a+2B4a+3b+2c3a6a+3b 10 a+6b+3c|=a^3

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  20. Show that|[1+a,1,1],[1,1+b,1],[1,1,1+c]|=abc(1+1/a+1/b+1/c)=abc+bc+ca+...

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