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If Delta(x)=|[sin2x, e^x sinx+x cosx, si...

If `Delta(x)=|[sin2x, e^x sinx+x cosx, sinx+x^2 cosx] , [cosx+sinx, e^x+x, 1+x^2] , [e^x cosx, e^2x, e^x]|` then

A

`Delta'(0)=0`

B

`Delta'(pi/2)=0`

C

`Delta'(pi/4)=0`

D

all the above

Text Solution

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The correct Answer is:
D
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FIITJEE-DETERMINANT-ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-I
  1. If Sr=|{:(2r,x,n(n+1)),(6r^2-1,y,n^2(2n+3)),(4r^3-2nr,z,n^3(n+1)):}|, ...

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  2. Let omega = - (1)/(2) + i (sqrt3)/(2), then the value of the determina...

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  3. If Delta(x)=|[sin2x, e^x sinx+x cosx, sinx+x^2 cosx] , [cosx+sinx, e^x...

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  4. Let g(x)=|(f(x+alpha), f(x+2a), f(x+3alpha)), f(alpha), f(2alpha), f(3...

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  5. If Delta(x)=|{:(4x-4,(x-2)^2,x^3),(8x-4sqrt2,(x-2sqrt2)^2,(x+1)^3),(12...

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  6. Statement I If A=[(a^2+x^2,ab-cx,ac+bx),(ab+cx,b^2+x^2,bc-ax),(ac-bx...

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  7. If a,b,c are even natural numbers, then |{:(a-1,a,a+1),(b-1,b,b+1),(c-...

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  8. If f(x) =|{:(cosx,1,0),(1,2 cosx,1),(0,1,2 cosx):}|, "then" |overset(p...

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  9. If f(x)=|{:(x,cosx,e^(x^2)),(1,2 cosx,1),(0,1,2 cosx):}| then the valu...

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  10. If the expression |{:(x^2+x+3,1,4),(2x^4+x^3+2x+1,2,3),(x^2+x,1,1):}| ...

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  11. The determinant Delta=|{:(a,b,aalpha+c),(b,c,balpha+c),(aalpha+b,balph...

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  12. If alpha,beta & gamma are the roots the equations x^(3)+px+q=0 then th...

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  13. The number of values of k for which the system of the equations (k+1)x...

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  14. The determinant Delta =|(a^2(1+x),ab,ac),(ab,b^2(1+x),bc), (ac,bc,c^2(...

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  15. If alpha , beta and gamma the roots of the equation x^2(px + q) = r(x...

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  16. If the system of equations x+a y=0,a z+y=0 and a x+z=0 has infinite so...

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  17. If A+B+C =pi , then the value of determinant |{:(sin^2A,cotA,1),(sin^2...

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  18. For A=a^2+b^2+c^2,B=ab+bc+ca,(a^3,b^3c^3-3abc)^2 is equal to

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  19. If A, B, C are angle of a triangle ABC, then the value of the determi...

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  20. If the expression |{:(x^2+x+3,1,4),(2x^4+x^3+2x+1,2,3),(x^2+x,1,1):}| ...

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