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If int(-1/2)^(1/2) cosx In(1+x)/(1-x) dx...

If `int_(-1/2)^(1/2) cosx In(1+x)/(1-x) dx = kIn^2` then write the value of k.

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USHA PUBLICATION-PREVIOUS YEAR QUESTION 2020-PREVIOUS YEAR QUESTION
  1. Find the derivative of tan^(-1)((cosx+sinx)/(cosx-sinx)) w.r.t. x.

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  2. If f(x) = sin x + 2 in the interval [-pi/2,pi/2], what can you say abo...

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  3. If int(-1/2)^(1/2) cosx In(1+x)/(1-x) dx = kIn^2 then write the value ...

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  4. Write the differential equation of all non-horizontal lines in a plane...

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  5. Prove that for any f:X rarr Y , f o idx = f =idY of.

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  6. Solve equation 3"tan"^(-1)1/((2+sqrt3)) - "tan"^(-1) 1/x ="tan"^(-1) 1...

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  7. Prove that tan{(pi)/(4)+(1)/(2) "cos"^(-1)(a)/(b)}+tan{(pi)/(4)-(1)/(2...

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  8. A man plans to start a poultry farm by investing at most ₹ 3000. He ca...

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  9. Test whether the relation : R = {(m, n):2|(m+n)} on ZZ is reflexive, ...

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  10. There are two families A and B. There are 4 men, 6 women and 2 childre...

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  11. Eliminate x,y,z from a=x/y-z, b=y/z-x, c=z/x-y

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  12. There are 25 girls and 15 boys in class XI and 30 boys and 20 girls in...

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  13. Four cards are drawn successively with replacement from a well shuffle...

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  14. Find the inverse of the matrix [{:(4,-2),(3,1):}]

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  15. If sin (x + y) = y cos (x + y) then prove that dy/dx =-(1 + y^2)/y^2

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  16. What is the derivative of sec^(-1)(1/(2x^2-1)),with respect to(sqrt(1...

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  17. Find the approximate value of sqrt(0.24).

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  18. Show that the tangent to the curve x = a (t - sin t), y = at (1 + cos ...

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  19. Examine the contiunity of the following functions at the indicated poi...

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  20. Evaluate the following integrals : int(0)^(pi//2)log|(4+3sinx)/(4+3c...

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