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Find the values of a and b, if the funct...

Find the values of a and b, if the function f defined as f(x) `{(x^2+3x+a, if xle1),(bx+2,if x>1):}` is diffentiable at `x = 1`

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MODERN PUBLICATION-TEST PAPER 3-PROBLEM
  1. Solve the following : [[x+1,omega,omega^2],[omega,x+omega^2,1],[omega^...

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  2. If the matrix A is such that [[1,-1],[2,3]]A=[[-4,1],[7,7]], find A.

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  3. Find the values of a and b, if the function f defined as f(x) {(x^2+3x...

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  4. Differentiate with respect to x: y=3^(x^2)+tan^-1((cosx+sinx)/(cosx-si...

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  5. Find the dy/dx when cos x = sqrt ((1)/(1+t^2)), sin y = (2t)/(1+t^2)

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  6. Show that the line y = mx + c touches the parabola y^(2) = 4ax if c = ...

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  7. Show that 2sinx+tanxge3x for all x epsilon(0,(pi)/(2)).

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  8. Evaluate : int (xe^x)/(x+1)^(2) dx

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  9. Evaluate the following integrals int(x^2)dx/((x^2+3)(x^2+2))

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  10. Solve : dy/dx + 1 = e^(x+y)

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  11. Solve : (x + 2y^3)dy/dx = y.

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  12. Find the equation of the plane passing through the points (2,1,3), (3,...

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  13. Find the image of the point (3,-2,1) in the plane x-y+3z=2.

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  14. Determine k such that a vector vec(r) is at right angles to each of th...

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  15. Find the foot of the perpendicular drawn from the point (5,7,3) to the...

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

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  17. Find the product of matrices A and B, where A = [[-5,1,3],[7,1,-5],[1,...

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  18. Show that |{:((b+c)^2,a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2):}...

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  19. Find the inverse of the following matrices using elementary transforma...

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  20. If x=acos theta+bsin theta and y=a sin theta-bcos theta, then show tha...

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