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Show that the function y=(A+Bx)e^(3x) is...

Show that the function `y=(A+Bx)e^(3x)` is a solution of the equation `(d^(2)y)/(dx^2)-6(dy)/(dx)+9y=0`

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ARIHANT PRAKASHAN-VERY SIMILAR TEST 10-SECTION B (60 MARKS)
  1. If y = ( sin y )^(x), find (dy)/(dx).

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  2. Verify Rolle.s theorem for f(x) = (sin x)/( e^(x)) on 0 le x le pi.

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  3. Show that the function y=(A+Bx)e^(3x) is a solution of the equation (d...

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  4. Solve (x+1) (dy)/(dx) = 2xy.

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  5. Evaluate int e^(x) ((1- sin x)/( 1- cos x) ) dx

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  6. Find the area of the region bounded by the curve y=x^(3) and the lines...

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  7. Show that the points whose position vectors are 5hat(i) + 5 hat(k), 2 ...

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  8. Find the vector equation of the plane passing through the points 3 hat...

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  9. Prove that if a plane has the intercepts a, b, c and is at a distance ...

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  10. Find the equation in vector and Cartesian from of the plane passing th...

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  11. Prove that sin( cos^(-1) ""(3)/(5) + sin^(-1)""(5)/(13) ) = (63)/(65)

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  12. Answer any three questions (b) A house wife wishes to mix together t...

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  13. Answer any three questions (c) Show that f: [-1,1] to R, given by f(...

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  14. Check if the relation R on set of real numbers, defined as R = {(a,b) ...

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  15. Answer any three questions (e) If a gt b gt c gt0, then prove that c...

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  16. A bag contains 6 black and 3 white balls. Another bag contains 5 black...

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  17. If A=[{:(3,1),(-1,2):}] then prove that A^(2)-5A+7I=O

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  18. Answer any three questions (c) If [{:(2,-1),(1,0),(-3,4):}]A = [{:(-...

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  19. If A = [{:(2,5),(2,1):}] and B = [{:(4,-3),(2,5):}], verify that |AB| ...

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  20. The odds against A solving a certain problem are 4 to 3 and the odds i...

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