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If f(x+y) = f(x) f(y) for all x,y and if...

If f(x+y) = f(x) f(y) for all x,y and if f(5) = 2 and f(0) = 3, then what is the value of f '(5)?

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ARIHANT PUBLICATION-SAMPLE PAPER 3 -SHORT ANSWER TYPE QUESTIONS
  1. If A = [{:(0,2),(3,-4):}] and KA = [{:(0, 3a),(2b, 24):}], then find v...

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  2. Show that |{:(1,x, x ^(3)),(1,y,y ^(3)),(1,z,z^(3)):}| = (x-y) (y-z) (...

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  3. Find the inverse of the following matrix [{:(1,3,-2),(-3,0,-1),(2,1,...

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  4. A card from a pack of 52 playing cards is lost. From the remaining car...

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  5. How many times must a man toss a fair coin so that the probability of ...

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  6. If f(x+y) = f(x) f(y) for all x,y and if f(5) = 2 and f(0) = 3, then w...

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  7. Show that the function f(x) given by f(x)={:{(x" sin "(1)/(x)", if ...

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  8. Show that the line (x)/(a) + (y)/(b) = 1, touches the curve y = be^(-x...

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  9. If f(x) = a In x + bx^2 + x has extreme values at x= - 1 and x = 2 the...

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  10. If x = 3 sin t - sin 3t, y = 3 cos t - cos 3t, find (dy)/(dx) at t = (...

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  11. Evaluate int(2x^(3) + 3x^(2) +5x+2) dx

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  12. Solve the following differerntial equation x (dy)/(dx) + y = x cos x +...

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  13. Evaluate int (x ^(2) +1)/( (x +1) ^(2)) dx

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  14. Evaluateint (cosxtan x )/((sec x + tan x )) dx

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  15. Find the area of region included between the parabola 4y = 3x^(2) and ...

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  16. Find the direction consines of the perpendicular from the origin to th...

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  17. If veca and vecb are unit vectors such that vecaxxvecb is a unit vecto...

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  18. Using vectors, find the area of the Delta ABC, whose vertices are A(1,...

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  19. Prove that the lines x = ay + b, z = cy + d and x = a'y + b' , z= c'y ...

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  20. If a xx b = c xx d and a xx c = b xxd , show that (a-d) is parallel to...

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