Home
Class 12
MATHS
If a, b gt 0 and Delta (x)|(x,a,a),(b,x,...

If `a, b gt 0 and Delta (x)|(x,a,a),(b,x,a),(b,b,x)|`, then

A

`Delta(x)` is increasing in `(-sqrt(ab),sqrt(ab))`

B

`Delta(x)` is decreasing in `(sqrt(ab),oo)`

C

`Delta(x)` has a local minimum at `x=sqrt(ab)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) Level -II|19 Videos
  • DETERMINANT

    FIITJEE|Exercise COMPREHENSIONS -I|3 Videos
  • DETERMINANT

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (SUBJECTIVE) Level -II|12 Videos
  • DEFINITE INTEGRAL

    FIITJEE|Exercise NUMERICAL BASED|3 Videos
  • ELLIPSE

    FIITJEE|Exercise NUMERICAL BASED|4 Videos

Similar Questions

Explore conceptually related problems

Let a,b>0 and Delta=|(-x,a,b),(b,-x,a),(a,b,-x)| then (1) a+b-x is a factor of Delta 2) x^2+(a+b)x+a^2+b^2-ab is a factor of Delta (3) Delta=0 has three real roots if a=b 4) all of these

" if " Delta = |{:(-x,,a,,b),(b,,-x,,a),(a,,b,,-x):}|" then a factor of " Delta " is "

if a+b+c=0 then Delta=|{:(a-x,c,b),(c,b-x,a),(b,a,c-x):}|=0 is

" If " Delta_(1) =|{:(x,,b,,b),(a,,x,,b),(a,,a,,x):}|" and " Delta_(2)= |{:(x,,b),(a,,x):}| are the given determinants then

If a + b + c = 0 one root of |(a -x,c,b),(b,b -x,a),(b,a,c -x)|= 0 , is

If Delta=det[[x+a,b,ca,x+b,ca,b,x+c]]=0, then x

FIITJEE-DETERMINANT-ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-I
  1. If Ir^2+mr^2+nr^2=1 where r=1,2,3 and I1I2+m1m2+n1n2=0 …..etc. then ...

    Text Solution

    |

  2. If alpha is a root of x^4 = 1 with negative principal argument then th...

    Text Solution

    |

  3. If a, b gt 0 and Delta (x)|(x,a,a),(b,x,a),(b,b,x)|, then

    Text Solution

    |

  4. If f(x)=|{:(cos(x+alpha),cos(x+beta),cos(x+gamma)),(sin(x+alpha),sin(x...

    Text Solution

    |

  5. The value of f(pi/6) where f(theta)=|{:(cos^2theta,costhetasintheta,-s...

    Text Solution

    |

  6. The system of equation 102x-95y+88z=81,3x+10y+17z=24, 57x+50y+43z=36 h...

    Text Solution

    |

  7. IF ax^3+bx^2+cx+d=|(x^2,(x-1)^2, (x-2)^2),((x-1)^2 (x-2)^2, (x-3)^2), ...

    Text Solution

    |

  8. In a Delta ABC |[1,1,1],[1+sinA,1+sinB,1+sinC][sinA+sin^2A,sinB+sin^2B...

    Text Solution

    |

  9. If a,b,c are sides of a triangle and |(a^(2),b^(2),c^(2)),((a+1)^(2),(...

    Text Solution

    |

  10. The value of |(.^(10)C(4).^(10)C(5).^(11)C(m)),(.^(11)C(6).^(11)C(7).^...

    Text Solution

    |

  11. If D=|{:(2,1,[sin^2theta]),([sin^2theta],costheta,i),(i,1,sintheta):}|...

    Text Solution

    |

  12. If alpha is a root of x^4 = 1 with negative principal argument then th...

    Text Solution

    |

  13. If Delta(x)=|((e^x,sin2x,tanx^2)),((In(1+x),cosx,sinx)),((cosx^2,e^x-1...

    Text Solution

    |

  14. Let x1y1z1,x2y2z2 and x3y3z3 be three 3-digit even numbers and Delta=|...

    Text Solution

    |

  15. If alpha, beta, gamma are the roots of x^(3) + ax^(2) + b = 0, then th...

    Text Solution

    |

  16. The product of all values of t , for which the system of equations (a-...

    Text Solution

    |

  17. Let a,b,c , in R not all are equal and Delta(1)= |{:(a,,b,,c),(b,,c,...

    Text Solution

    |

  18. The value of a for which system of equation , a^3x+(a+1)^3y+(a+2)^3z=0...

    Text Solution

    |

  19. If Delta (x)=|{:(x,1+x^(2),x^(3)),(log(1+x^(2)),e^(x),sinx),(cosx,tanx...

    Text Solution

    |

  20. If ai, bi in N for i 1,2,3, then coefficient of x in the determinant;|...

    Text Solution

    |