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If |[sin2x,cos^2x,cos4x],[cos^2x,cos2x,s...

If `|[sin2x,cos^2x,cos4x],[cos^2x,cos2x,sin^2x],[cos^4x,sin^2x,sin2x]|=a_0+a_1 (sinx)+a_2(sin^2x)+....+a_n(sin^n x)` then the value of `a_0` is-

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ALLEN-DETERMINANTS-All Questions
  1. If the following equations x+y-3 = 0, (1+lamda)x + (2+lamda) y - 8 = 0...

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  2. If the system of equation x+lambday+1=0,\ lambdax+y+1=0\ &\ x+y+lambda...

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  3. If |[sin2x,cos^2x,cos4x],[cos^2x,cos2x,sin^2x],[cos^4x,sin^2x,sin2x]|=...

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  4. The number of real values of x satisfying |(x,3x+2,2x-1),(2x-1,4x,3x+1...

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  5. If p x^4\ \ q x^3+r x^2+s x+t=|x^2+3xx-1x+3x+1 2-xx-3x-3x+4 3x|t h ...

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  6. For positive numbers x ,\ y\ a n d\ z the numerical value of the deter...

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  7. For a non-/cro real a,b and c |((a^2+b^2)/c,c,c),(a,(b^2+c^2)/a,a),(b,...

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  8. The equation |((1+x)^2,(1-x)^2,-(2+x^2)),(2x+1,3x,1-5x),(x+1,2x,2-3x)...

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  9. Let a determinant is given by A=|[a,b,c],[p,q,r],[x,y,z]| and suppose ...

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  10. If a!=b!=c\ a n d\ |{:(a, b, c), (a^2,b^2,c^2), (b+c, c+a, a+b):}|=0 t...

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  11. If f(x)=|1xx+1 2xx(x-1)(x+1)x3x(x-1)x(x-1)(x-2)(x+1)x(x-1)| then f(500...

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  12. The value of the determinant |{:(a, b,0), (0,a, b),(b,0,a):}| is equal...

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  13. An equilateral triangle has each of its sides of length 6 cm. If (x1, ...

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  14. If the system of equations x + 2y + 3z = 4, x+ py+ 2z = 3, x+ 4y + z =...

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  15. If f^(prime)(x)=|m x m x-p m x+p nn+p n-p m x+2n m x+2n+p m x+2n-p| , ...

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  16. The determinant |a2\ a^2-(b-c)^2b c b^2b^2-(c-a)^2c a c^2c^2-(a-b)^2a ...

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  17. The determinant |a b aalpha+bb c balpha+c aalpha+bbalpha+c0|=0, if a ...

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  18. The parameter on which the value of the determinant |1a a^2"cos"(p-d)x...

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  19. If a^2+b^2+c^2=-2a n df(x)= |a+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c...

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  20. If |a a x m m m b x b|=0,\ then x may be equal to- a.a b. b c.a+b d. ...

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