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If f(theta)=|sinthetacosthetasinthetacos...

If `f(theta)=|sinthetacosthetasinthetacosthetasinthetacosthetacosthetasinthetasintheta|` , then `f(theta)=0` has exactly 2 real solutions in `[0,pi]` `f(theta)=0` has exactly 3 real solutions in `[0,pi]` range of function `(f(theta))/(1-sin2theta)i s[-sqrt(2),sqrt(2)]` range of function `(f(theta))/(sin2theta-1)i s[-3,3]`

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CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. Prove that |cosalpha-cosbeta| le |alpha-beta|

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  2. Statement 1: If b c+q r=c a+r p=a b+p q=-1, t h e n|a p a p b q b q c...

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  3. If f(theta)=|sinthetacosthetasinthetacosthetasinthetacosthetacosthetas...

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  4. If f(theta)=|[sin^2A,cot A,1],[sin^2B,cosB,1],[sin^2C,cosC,1]| , then...

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  5. The roots of the equation |^x Cr^(n-1)Cr^(n-1)C(r-1)^(x+1)Cr^n Cr^n C(...

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  6. Let Delta(x)=|[3,3x,3x^2+2a^2] , [3x, 3x^2+2a^2, 3x^3+6a^2x] , [3x^2+2...

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  7. Consider a system of linear equation in three variables x,y,z a1x+b...

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  8. If f(x)=|[a,-1, 0],[a x, a,-1],[a x^2,a x, a]|,using properties of det...

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  9. If g(x)=(f(x))/((x-a)(x-b)(x-c)),w h e r ef(x) is a polynomial of degr...

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  10. If (x)=|[x^2+4x-3 2x+4 13] [2x^2+5x-9 4x+5 26] [ 8x^2-6x+1 16 x-6 104]...

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  11. If |y z-x^2z x-y^2x y-z^2x z-y^2x y-z^2y z-x^2x y-z^2y z-x^2z x-y^2|=|...

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  12. Let f(n)=|nn+1n+2^n Pn^(n+1)P(n+1)^n Pn^n Cn^(n+1)C(n+1)^(n+2)C(n+2)| ...

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  13. If |[ x^n ,x^(n+2) ,x^(2n)],[1 ,x^a , a ],[x^(n+5),x^(a+6),x^(2n+5)]...

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  14. Let x<1, then value of |[x^2+2, 2x+1 ,1],[ 2x+1,x+2, 1],[ 3, 3 ,1]| is...

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  15. Find the number of real root of the equation |[0,x-a, x-b],[ x+a,0,x-...

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  16. Value of |[x+y, z,z ],[x, y+z, x],[y, y, z+x]|, where x ,y ,z are nonz...

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  17. If e^(itheta)=costheta+isintheta, find the value of |[1,e^(ipi//3),e...

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  18. Which of the following is not the root of the equation |[x,-6,-1],[ 2,...

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  19. If A,B,C are the angles of a non right angled triangle ABC. Then find ...

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  20. Let f(x)=a5x^5+a4x^4+a3x^3+a2x^2+a1x , where ai ' s are real and f(x)=...

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