Home
Class 12
MATHS
If a,b,c are in A.P., then the determina...

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

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    V PUBLICATION|Exercise QUESTION BANK|168 Videos

  • DIFFERENTIAL EQUATIONS

    V PUBLICATION|Exercise QUESTION BANK|149 Videos

Similar Questions

Explore conceptually related problems

If a, b , c are in A.P show that |[x+1, x+2, x+a],[ x+2, x+3, x+b],[ x+3, x+4, x+c]|=0

If x,y,z are in A.P., then the value of the determinant |(a+2,a+3,a+2x),(a+3,a+4,a+2y),(a+4,a+5,a+2z)| is a)1 b)0 c)2a d)a

The value of the determinant |(x+2,x+3,x+5),(x+4,x+6,x+9),(x+8,x+11,x+15)| is A)2 B)-2 C)3 D)-1

The coefficient of x^(2) in the expansion of the determinant |(x^(2) , x^(3) +1, x^(5)+2),(x^(3)+3, x^(2)+x, x^(3)+x^(4)),(x+4,x^(3)+x^(4),2^(3))| is a) -10 b) -8 c) -2 d) -6

By using properties of determinants, prove that |[x+4,2x,2x],[2x,x+4,2x],[2x,2x,x+4]|=(5x+4)(4-x)^2

The maximum degree of x by which determinant |(x+y,x,x),(5x+4y,4x,2x),(10x+8y,8x,3x)| divisible is a)0 b)1 c)2 d)3

If |(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))| = (a - b) (b - c) (c - a) (a + b + c) , where a,b,c are all different, then the determinant |(1,1,1),((x-a)^(2),(x-b)^(2),(x-c)^(2)),((x-b)(x-c),(x-c)(x-a),(x-a)(x-b))| vanishes when a)a + b + c = 0 b) x = (1)/(3) (a + b + c) c) x = (1)/(2) (a + b + c) d) x = a + b + c

If A(x_1, y_1), B(x_2, y_2) and C(x_3, y_3) are vertices of an equilateral triangle whose each side is equal to 'a', then prove that, |[x_1, y_1, 2 ],[ x_2, y_2, 2],[ x_3, y_3, 2]|^2=3 a^4

Find the domain of the function f(x)=(x^2+3x+5)/(x^2-5x+4)

S.T abs[[x+a,b,c],[a,x+b,c],[a,b,x+c]]=x^2(x+a+b+c)

V PUBLICATION-DETERMINANT-QUESTION BANK
  1. Using properties of determinants, prove that |[sinalpha,cosalpha,cos...

    Text Solution

    |

  2. Consider a system of linear equations which is given below, 2/x+3/...

    Text Solution

    |

  3. If a,b,c are in A.P., then the determinant |[x+2, x+3, x+2a],[x+3,x+...

    Text Solution

    |

  4. If x, y, z are non zero real numbers, then find the inverse of matrix ...

    Text Solution

    |

  5. Let A = [[1,Sintheta,1],[-Sintheta,1,Sintheta],[-1,-Sintheta,1]], wher...

    Text Solution

    |

  6. If A(x1, y1), B(x2, y2) and C(x3, y3) are vertices of an equilateral t...

    Text Solution

    |

  7. Solve the following system of equations using matrix method. 2 x+5 y=1...

    Text Solution

    |

  8. If [[2,5],[-3,7]]xxA=[[17,-1],[47,-13]] then Find the 2x2 matrix A.

    Text Solution

    |

  9. Let A=[[1 , 4, 0],[ -1, 2, 2],[ 0, 0, 2]] i) is A singular? i...

    Text Solution

    |

  10. Solve the following system of equations using matrix method. 2 x+5 y=1...

    Text Solution

    |

  11. Find the minors and cofactors of a(11), a(1 2) and a(13) of the matrix...

    Text Solution

    |

  12. Let |A|=|[x1, x2, x3],[ y1, y2, y3],[ z1 , z2, z3]|.Expand |A| ...

    Text Solution

    |

  13. Evaluate the determinant of A=[[3, -1, 2],[ 1, 2, -1],[ 4, 0, ...

    Text Solution

    |

  14. Evaluate the determinant |[27, 2, 3],[ 45, 5, 5],[ 36, 9, 4]|

    Text Solution

    |

  15. Find the value of the determinant |[1, a, b+c],[ 1, b, c+a],[ 1,...

    Text Solution

    |

  16. Find the area of a triangle whose vertices are (-4,1),(5,-3) and (2,3)...

    Text Solution

    |

  17. Evaluate the determinant of 'A=[[1, 2],[ 3, 4]]'

    Text Solution

    |

  18. Evaluate the determinant of A=[[1 , 3 , 2],[ 2, 0, 1 ],[ 3 , 4, 3]...

    Text Solution

    |

  19. Find the minors and co-factors of the elements 1,-3 and 4 in Delta=|[2...

    Text Solution

    |

  20. Without expanding, evaluate |[2, 1, 5],[ -3, -1, 4],[ 6, 2, -8...

    Text Solution

    |