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If sin (x + y) = y cos (x + y) then prov...

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

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USHA PUBLICATION-PREVIOUS YEAR QUESTION 2020-PREVIOUS YEAR QUESTION
  1. Four cards are drawn successively with replacement from a well shuffle...

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

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

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

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

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

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

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

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  9. The area between x=y^(2) and x=4 is divided into two equal parts by th...

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  10. Solve the following differential equation:- x(dy)/(dx) + y = y^2 lnx

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  11. Solve : In((dy)/(dx)) = 3x+4y given that y=0, when x=0.

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  12. Evaluate the following integrals int(3sinx+28cosx)/(5sinx+6cosx)dx

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  13. If veca = 3hati+hatj-2hatk, vecb = 2hati-3hatj+4hatk then verify that ...

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  14. Passing throughthe point (2,-3,1) and (-1,1-7) and perpendicular to th...

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  15. Find the perpendicular distance of the point (-1,3,9) from the line (x...

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  16. Prove that the measure of the angle between two main diagonals of a cu...

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  17. Prove that the four points with position vectors 2veca+3vecb-vecc, vec...

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  18. If A,B,C are matrices of order 2xx2 each and 2A+B+C =[[1,2],[3,0]] A+B...

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  19. The probability of a shooter hitting a target is (3)/(4) Find the mini...

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  20. Prove the following: [[(b+c)^2,a^2,bc],[(c+a)^2,b^2,ca],[(a+b)^2,c^2...

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