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If f(theta)=|sinthetacosthetasinthetacos...

If `f(theta)=|sinthetacosthetasinthetacosthetasinthetacosthetacosthetasinthetasintheta|` , then 1. `f(theta)=0` has exactly 2 real solutions in `[0,pi]` 2. `f(theta)=0` has exactly 3 real solutions in `[0,pi]` 3. range of function `(f(theta))/(1-sin2theta)i s[-sqrt(2),sqrt(2)]` 4. range of function `(f(theta))/(sin2theta-1)i s[-3,3]`

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CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. If P = {1,2}, form set set P xx P xx P

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  2. Statement 1: If b c+q r=c a+r p=a b+p q=-1, then |{:(ap ,a, p) ,(bq,...

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

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  4. If f(theta)=|[sin^2A,cot A,1],[sin^2B,cotB,1],[sin^2C,cotC,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. The determinant |(a^(2)+10,ab, ac),(ab, b^(2)+10, bc),(ac, bc, c^(2)...

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

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  10. 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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  11. Let f(n)=|n n+1 n+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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  12. 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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  13. 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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  14. Find the number of real root of the equation |[0,x-a, x-b],[ x+a,0,x-...

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

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

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

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

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  19. Let f(x)=a(5)x^(5)+a(4)x^(4)+a(3)x^(3)+a(2)x^(2)+a(1)x, "where" a(i),s...

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  20. Evaluate |(cosalphacosbeta,cosalpha sinbeta , - sin alpha),(-sin beta,...

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