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For x∈(0,π) , the equation sinx+2sin2...

For `x∈(0,π)` , the equation `sinx+2sin2x−sin3x=3` , has

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ALLEN-TEST PAPER-MATHS
  1. If both roots are less than 3 then 'a' belongs to

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  2. If ytan(θ− π/6)=xtan(θ+ 2π/3) , then (y+x)/(y-x) =

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  3. For x∈(0,π) , the equation sinx+2sin2x−sin3x=3 , has

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  4. If 32tan ^8 θ=2cos^2 α−3cosα and 3cos2θ=1 then the general value...

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  5. If logx, logsqrt(6-2x),log(x-1) re in A.P .then value of (x)/(3) is

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  6. The general solution of sinx−3sin2x+sin3x=cosx−3cos2x+cos3x is

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  7. The sum of 'n' terms of an A.P is 715.If first term is incrased by 1, ...

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  8. The value of k for which equations x^(2)+(2k-6)x+7-3k=0 and x^(2)+(2k-...

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  9. If the function f(x)=x^3+e^(x/2) and g(x)=f ^(−1)(x), then the val...

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  10. The least integral value of lambda for which the expression (lambdax^(...

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  11. Prove that : sin^(-1)(5/13) +cos ^(−1)(3/5)=tan (−1)(63/16) ​

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  12. If f(x)=x+tanx and f is inverse of g, then g ′(x) is equal ...

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  13. 1/(i-1) + 1/(i+1) is a. purely imaginary b. purely rational number....

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  14. |{:(,"List-I(Atom/Ions)",,"List-II(Electron Affinity in eV/atom and co...

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  15. |{:(,"List-I(Orbitals)",,"List-II"),(,"(Approach axis is z-axis)",,"(T...

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  16. Which of the following values of a and b will make a(sin^(6)theta+cos^...

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  17. Which of the following expression gives rational values ?

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  18. Find the root of the equation |x-1|^(x^(2)+x-2)=1

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  19. A circumcircle is a circle which passes through all vertices of a tria...

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  20. A circumcircle is a circle which passes through all vertices of a tria...

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