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

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

A

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

B

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

C

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

D

none of these

Text Solution

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The correct Answer is:
C
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OBJECTIVE RD SHARMA-DETERMINANTS-Exercise
  1. If alpha + beta + gamma = pi, then the value of the determinant |(e^...

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  2. If a != b != c, are value of x which satisfies the equation |(0,x -a...

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  3. The repeated factor of the determinant |(y +z,x,y),(z +x,z,x),(x +y,...

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  4. The value of the determinant Delta = |((1 - a(1)^(3) b(1)^(3))/(1 - ...

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  5. The determinant Delta = |(b,c,b alpha +c),(c,d,c alpha + d),(b alpha...

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  6. Delta = |(1//a,1,bc),(1//b,1,ca),(1//c,1,ab)|=

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  7. If |(1 +ax,1 +bx,1 + bx),(1 +a(1) x,1 +b(1) x,1 + c(1) x),(1 + a(2) x,...

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  8. If a != 0, b!= 0, c!= 0, then |(1 +a,1,1),(1,1 +b,1),(1,1,1 +c)| is ...

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  9. If 1 + (1)/(a) + (1)/(b) + (1)/(c) = 0, then Delta = |(1 +a,1,1),(1,...

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  10. If a, b and c are all different from zero and Delta = |(1 +a,1,1),(1...

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  11. In a Delta ABC, a, b, c are sides and A, B, C are angles opposite to t...

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  12. If |(-12,0,lamda),(0,2,-1),(2,1,15)| = -360, then the value of lamda i...

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  13. If a(i), i=1,2,…..,9 are perfect odd squares, then |{:(a(1),a(2),a(3))...

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  14. If the maximum and minimum values of the determinant |(1 + sin^(2)x...

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  15. If [x] denote the greatest integer less than or equal to x then in ord...

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

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  17. Let f(x) = ax^(2) + bx + c, a, b, c, in R and equation f(x) - x = 0 ha...

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  18. If g(x) = |(f(x + c),f(x + 2c),f(x + 3c)),(f(c),f(2c),f(3c)),(f(c),f'(...

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  19. If a^(2) + b^(2) + c^(2) = -2 and f(x) = |(1 + a^(2)x,(1 + b^(2))x,(1 ...

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  20. Coefficient of x in f(x)=|(x,(1+sinx)^3,cosx),(1,log(1+x),2),(x^2,(1+x...

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