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If f(x)=|(x^n, sinx, cosx),(n!, sin((npi...

If `f(x)=|(x^n, sinx, cosx),(n!, sin((npi)/2), cos((npi)/2)),(a, a^2,a^3))|, then show that `d^n/dx^n [f(x)] at x=0` is 0

A

0

B

p

C

`p^3`

D

independent of p

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The correct Answer is:
A, D
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ML KHANNA-DETERMINANTS -Problem Set (3) (MULTIPLE CHOICE QUESTIONS)
  1. If l1^2+m1^2+n1^2=1 etc. and l1l2+m1m2+n1n2=0 etc. then Delta=|(l1,m...

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  2. If Delta1=|(2bc-a^2,c^2,b^2),(c^2,2ca-b^2,a^2),(b^2,a^2,2ab-c^2)| and ...

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  3. If Delta^2=|(b^2+c^2,ab,ac),(ab,c^2+a^2,bc),(ac,bc,a^2+b^2)| , then De...

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  4. If sr=alpha^r+beta^r+gamma^r, then Delta=|(s0,s1,s2),(s1,s2,s3),(s2,s3...

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  5. If Delta=|(py+qz,rz-px,qx+ry),(bp+cq,-ap+cr,aq+br),(mp+nq,nr-lp,lq+mr)...

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  6. If z is a complex number and all ai 's and bi 's are real numbers, the...

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

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  8. If y=sin mx the value of the determinant |{:(y,y(1),y(2)),(y(3),y(4),y...

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  9. If F(X) , G(X) and H(X) are three polynomials of degree 2, then phi(...

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

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  11. Let f(x) =|(x^3, sinx,cosx),(6,-1,0),(p,p^2,p^3)| , where p is a cons...

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  12. If f(x)=|(x^n, sinx, cosx),(n!, sin((npi)/2), cos((npi)/2)),(a, a^2,a^...

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  13. Let f(x)=|cos(x+x^2)sin(x+x^2)-cos(x+x^2)sin(x-x^2)cos(x-x^2)sin(x-x^2...

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  14. If a,b,c be real , then determine the interval of monotonicity of the ...

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  15. If Delta=|(x^2-5x+3,2x-5,3),(3x^2+x+4,6x+1,9),(7x^2-6x+9,14x-6,21)| = ...

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  16. If Delta=|(x,x^2,x^3),(1,2x,3x^2),(0,2,6x)| then d/(dx)(Delta)=

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  17. If f(x)=|(x+a^2,x^4+1,3),(x+b^2,2x^4+2,3),(x+c^2,3x^4+7,3)| where x n...

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  18. If Delta=|(x+1,x^2+2,x(x+1)),(x^2+1,x+1,x^2+2),(x^2+2,x(x+1),x+1)| = ...

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  19. If Delta(x)=|(e^(x^2),log(1+x)),(tanx,sinx)|, then {:(Lt),(xrarr0):}(D...

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  20. The system of equations alphax+y+z=alpha-1, x+alphay+z=alpha-1 ...

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