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Consider the function f(x) = |{:(a^(2)+x...

Consider the function f(x) = `|{:(a^(2)+x,,ab,,ac),(ab,,b^(2)+x,,bc),(ac,,bc,,c^(2)+x):}|`
In which of the following interval f(x) is strictly increasing

A

`x^(2)`

B

`(a^(2) + x) (b^(2) + x) (c^(2) + x)`

C

`(1)/(x)`

D

none of these

Text Solution

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The correct Answer is:
A
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OBJECTIVE RD SHARMA ENGLISH-DETERMINANTS-Exercise
  1. if |{:(1,,1,,1),(a,,b,,c),(a^(3),,b^(3),,c^(3)):}|= (a-b)(b-c)(c-a)(a+...

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  2. Show that a x+b y+r=0,b y+c z+p=0a n dc z+a x+q=0 are perpendicular to...

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  3. Consider the function f(x) = |{:(a^(2)+x,,ab,,ac),(ab,,b^(2)+x,,bc),(a...

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  4. The equation |(x-a,x-b,x-c),(x-b,x-a,x-c),(x-c,x-b,x-a)|=0 (a,b,c are ...

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

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  6. If a,b,c are non-zero real number such that |(bc,ca,ab),(ca,ab,bc),(ab...

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  7. The value of the determinant |{:(ka,,k^(2)+a^(2),,1),(kb,,k^(2)+b^(2)...

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  8. The system of simulataneous equations kx + 2y -z = 1 (k -1) y -2z ...

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  9. The value of the determinant |(1,omega^(3),omega^(5)),(omega^(3),1,ome...

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  10. If a,b,c are non-zero real number such that |(bc,ca,ab),(ca,ab,bc),(ab...

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  11. If the system of equations x + ay + az = 0 bx + y + bz = 0 cx + ...

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  12. The determinant D=|{:(cos(alpha+beta),-sin(alpha+beta),cos2beta),(sina...

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  13. If omega is a cube root of unity, then Root of polynomial is |(x + 1...

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  14. " If " Delta(1) =|{:(x,,b,,b),(a,,x,,b),(a,,a,,x):}|" and " Delta(2)...

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  15. If y= sin px and y(n) is the nth derivative of y, then |{:(y,y(1),y(...

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  16. If |p b c a q c a b r|=0 , find the value of p/(p-a)+q/(q-b)+r/(r-c),\...

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  17. Using properties of determinants, show that |{:(x, p, q), ( p, x, q)...

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  18. The factors of |(x,a,b),(a,x,b),(a,b,x)|, are

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  19. Let omega=-1/2+i(sqrt(3))/2dot Then the value of the determinant |1 1 ...

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  20. If a+b+c=0, one root of |a-x c b c b-x a b a c-x|=0 is x=1 b. x=2 c. ...

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