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Prove that int0^(pi/2)lnsinxdx=pi/2ln( 1...

Prove that `int_0^(pi/2)lnsinxdx=pi/2ln( 1 /2)`

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Integrate the following inte^(cos^2x)sin2x dx

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  2. Solve the differential equation (dy)/(dx)= (y-x+1)/(y+x+5).

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  3. Prove that int0^(pi/2)lnsinxdx=pi/2ln( 1 /2)

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  4. If x=(sin^(3)t)/(sqrt(cos2t)) and y=(cos^(3)t)/(sqrt(cos2t)), then fin...

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  5. Let f:XrightarrowY and g:YrightarrowZ. Prove that gof is bijective if ...

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  6. If "cos"^(-1)(x/a) ="cos"^-1(y/b) = theta, "prove that" x^2/a^2 -(2xy)...

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  7. Minimize:Z=20x1+10x2 "Subject to": x1+2x2 le 40 3x1 -x2 ge 30 4x1+3x2 ...

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  8. If y=x sin^-1x+xcos^-1x, then what is dy/dx?

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  9. Give an example of a relation which is symmetric and anti-symmetric.

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  10. What is the value of int0^1sin^2tdt+int0^1cos^2tdt-int0^1dr?

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  11. What is the principal value of sin^(-1)(sin((2pi)/3))?

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  12. What is the value of |[i^(103), 3 ,i^(101)],[i^(56), 5, i^(54)],[i^(23...

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  13. What is the value of hata*hatb+hatb*hatc+hatc*hata if hata+hatb+hatc=v...

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  14. The distance between the parallel planes 2x - 3y + 6z +1 = 0 and 4x - ...

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  15. If is a 3xx3 matrix and absA=7, then which matrix is represented by Ax...

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  16. What is the value of intsin^2xd(sinx)?

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  17. Write the subinterval of (0,pi) in which sin (x+pi/4) is increasing.

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  18. Write whether the equation "tan"^(-1) ("cot"x)=2x has exactly two real...

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  19. Find the feasible solution region of the following: 3x+yge3,x+yge1,xge...

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  20. Prove statement tan ( 2 "tan"^(-1)1/5-pi/4) + 7/17 =0

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