Home
Class 11
MATHS
If f(x)|a-1 0a x a-1a x^2a x a|, using p...

If `f(x)|a-1 0a x a-1a x^2a x a|,` using properties of determinants, find the value of `f(2x)-f(x)dot`

A

`a(2a + 3x)`

B

`ax(2x + 3a)`

C

`ax(2a + 3x)`

D

`x(2a + 3x)`

Text Solution

Verified by Experts

The correct Answer is:
C
Applying `R_(2) rarr R_(2) - xR_(1) and R_(3) rar R_(3) - xR_(3) - xR_(2)`, we get
`f(x) = |(a,-1,0),(0,a +x,-1),(0,0,a +x)| = a (a + x)^(2)`
`:. f(2x) - f(x) = a (a +2x)^(2) -a(a +x)^(2) = ax (2a + 3x)`
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|6 Videos

  • DETERMINANTS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|92 Videos

  • DETERMINANTS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • CARTESIAN CO-ORDINATE SYSTEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|27 Videos

  • DISCRETE PROBABILITY DISTRIBUTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|40 Videos

Similar Questions

Explore conceptually related problems

If f(x)=|[a,-1 ,0],[ax,a,-1],[a x^2,a x, a]|, using properties of determinants, find the value of f(2x)-f(x)dot

If f(x)=|[a,-1, 0],[a x, a,-1],[a x^2,a x, a]|,using properties of determinants find the value of f(2x) − f(x).

If f(x)=|[a-1, 0,a] , [x,a-1,a], [x^2a, x, a]| , using properties of determinants, find the value of f(2x)-f(x) .

If f(x) = |(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(x-1),x(x-1)(x-2),x(x+1)(x-1))| , using properties of determinant, find f(2x) - f(x).

If f(x)=1-1/x then write the value of f(f(1/x))dot

Find the domain of f(x)=sin^(-1)(-x^2)dot

Find the domain of f(x)=sin^(-1)((x^2)/2)dot

If f(x)=x^2+x+1 , then find the value of 'x' for which f(x-1) =f(x)

If f(x)=x^3-x^2+a x+b is divisible by x^2-x , then find the value of f(2)dot

If f(x)=x^3=x^2+a x+b is divisible by x^2-x , then find the value of f(2)dot

OBJECTIVE RD SHARMA ENGLISH-DETERMINANTS-Section I - Solved Mcqs
  1. The value of the determinant |(x+2,x+3,x+5),(x+4,x+6,x+9),(x+8,x+11,x...

    Text Solution

    |

  2. If alpha,beta,gamma are roots of the equation x^(3)+px+q=0 then the va...

    Text Solution

    |

  3. If f(x)|a-1 0a x a-1a x^2a x a|, using properties of determinants, fin...

    Text Solution

    |

  4. If a , b , c are real numbers, prove that |[a,b,c],[b,c,a],[c,a,b]|=-(...

    Text Solution

    |

  5. If omegais an imaginary cube root of unity, then the value of the det...

    Text Solution

    |

  6. If |[x^n, x^(n+2), x^(n+3)], [y^n, y^(n+2), y^(n+3)], [z^n, z^(n+2), z...

    Text Solution

    |

  7. Let "f(x)"=|{:(1,x,x+1),(2x,x(x-1),(x+1)x),(3x(x-1),x(x-1)(x-2),(x+1)x...

    Text Solution

    |

  8. Given a(i)^(2) + b(i)^(2) + c(i)^(2) = 1, i = 1, 2, 3 and a(i) a(j) + ...

    Text Solution

    |

  9. If alpha,beta and gamma are such that alpha+beta+gamma=0, then |(1,cos...

    Text Solution

    |

  10. " If " f(alpha , beta) = |{:(cos alpha ,,-sin alpha,,1),(sin alpha,,c...

    Text Solution

    |

  11. " If " f(alpha , beta) = |{:(cos alpha ,,-sin alpha,,1),(sin alpha,,c...

    Text Solution

    |

  12. Let D(r) = |(a,2^(r),2^(16) -1),(b,3(4^(r)),2(4^(16) -1)),(c,7(8^(r)),...

    Text Solution

    |

  13. If Delta = |(cos (alpha(1) - beta(1)),cos (alpha(1) - beta(2)),cos (al...

    Text Solution

    |

  14. The determinant |{:(y^(2),,-xy,,x^(2)),(a,,b ,,c),(a',,b',,c'):}| is ...

    Text Solution

    |

  15. If |[p,q-y,r-z],[p-x,q,r-z],[p-x,q-y,r]|=0 find the value of p/x+q/y+r...

    Text Solution

    |

  16. The number of distinct real roots of |(sinx, cosx, cosx),(cos x,sin x,...

    Text Solution

    |

  17. The value of a for which system of equations , a^3x+(a+1)^3y+(a+2)^3z=...

    Text Solution

    |

  18. Let A = [(1,sin theta,1),(- sin theta,1,sin theta),(-1,-sin theta,1)],...

    Text Solution

    |

  19. Let |(x,2,x),(x^2,x,6),(x,x,6)|=A x^4+B x^3+C x^2+D x+Edot Then the va...

    Text Solution

    |

  20. If A=|[1, 1, 1],[a, b, c],[ a^2,b^2,c^2]| , B=|[1,bc, a],[1,ca, b],[1,...

    Text Solution

    |