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Verify Rolle.s theorem for f(x) = (sin x...

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

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ARIHANT PRAKASHAN-VERY SIMILAR TEST 10-SECTION B (60 MARKS)
  1. Check if the relation R on set of real numbers, defined as R = {(a,b) ...

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

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

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

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

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

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

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  8. Find the equations of all the lines of slope 2 and that are tangent to...

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  9. Prove that the function f(x) = tan x -4x is strictly decreasing on (- ...

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  10. If y=sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^(2))] then find (dy)/(dx)

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  11. If (cosx)^(y)=(cosy)^(x), then find (dy)/(dx).

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

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

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

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

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

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

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  18. Answer any three questions (b) Find the vector equation of the plane...

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

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

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