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If `f(x), g(x), h(x)` are polynomials of three degree, then `phi(x)=|(f'(x),g'(x),h'(x)), (f''(x),g''(x),h''(x)), (f'''(x),g'''(x),h'''(x))|` is a polynomial of degree (where `f^n (x)` represents nth derivative of f(x))

A

3

B

4

C

5

D

None of these

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The correct Answer is:
D
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MCGROW HILL PUBLICATION-DETERMINANTS-SOLVED EXAMPLES (LEVEL 2 SINGLE CORRECT ANSWER TYPE QUESTIONS)
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  2. Let Delta(x)=|(3+2sin^(4)x,2cos^(4)x,sin^(2)2x),(2sin^(4)x,3+2cos^(4)x...

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  3. If f(x), g(x), h(x) are polynomials of three degree, then phi(x)=|(f'(...

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  4. The value of Delta = |(a,a +b,a +2b),(a +2b,a,a +b),(a +b,a +2b,a)| is...

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  5. Let Delta(x)=|(sinx, cosx, sin2x+cos2x),(0,1,1),(1,0,-1)| then Delta...

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  6. Let Delta(x)=|(cos^(2)x,cosxsinx,-sinx),(cosxsinx,sin^(2)x,cosx),(sinx...

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  7. The value of the determinant Delta=|(sqrt(13)+sqrt3,2sqrt5,sqrt5),(sqr...

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  10. If a+b+c!=0, the system of equations (b+c)(y+z)-ax=b-c, (c+a)(z+x)-by=...

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  11. Let a ,b , c be the real numbers. The following system of equations in...

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  12. If the system of equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero ...

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  13. If the system of equations lamdax(1)+x(2)+x(3)+lamdax(2)+x(3)=1,x(1)+x...

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  14. If p != a, q!=b,r!=cand the system of equations px + ay + az = 0 and b...

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  15. Let lambda and alpha be real. Then the numbers of intergral values ...

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  16. If f(r)(x), g(r)(x), h(r) (x), r=1, 2, 3 are polynomials in x such th...

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  17. The number of real values of a for which the system of equations x+a...

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  18. Find the solution set of the system x+2y+z=1 2x-3y-w=2 xgeq0,ygeq0,zge...

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

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  20. Suppose a,b,c epsilon R and let f(x)=|(0,a-x,b-x),(-a-x,0,c-x),(-b-x...

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