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Solve : cos ^(-1) x + sin ^(-1) "" (x)/...

Solve : ` cos ^(-1) x + sin ^(-1) "" (x)/( 2) = (pi)/(6)`

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ICSE-MODEL TEST PAPER - 7-Section - A
  1. Using L' Hospital' s rule prove that lim(x to (pi)/(2)) (sec x - tan x...

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  2. Show that the function f (x)={ {:(3x^(2) + 12 x - 1,- 1 le x le 2 )...

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  3. Solve : cos ^(-1) x + sin ^(-1) "" (x)/( 2) = (pi)/(6)

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  4. If x^(y) * y^(x) = (x + y) ^(5) , " find " (dy)/( dx)

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  5. Evaluate : int (1) ^(e) ( dx)/( x (1 + log x))

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  6. Evaluate int tan ^(2) x sec^(4) x dx

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  7. Solve : y - x (dy)/( dx) = 2 (1 + x^(2)"" (dy)/( dx))

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  8. Show that the function f : R to defined by f (x) = x^(3) + 3 is inver...

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  9. Find the probability distribution of the number of green balls drawn w...

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  10. Evaluate : int (sqrt(x^(2) + 1) ( log (x^(2) + 1) - 2 log x))/( x^(4))...

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  11. Evaluate : int (-1) ^(1) e^(x) dx .

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  12. If y = tan ^(-1) (sec x + tan x) , " find " (d^(2) y)/( dx^(2)) at x...

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  13. Find the derivative of tan^(-1) "" (sqrt(1 + x^(2)) - 1)/( x) with res...

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  14. Using properties of determinants, prove that |{:(y + z ,z + x ,x + ...

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  15. Show that the homogenous system of equations x - 2y + z = 0, x + y -...

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  16. Show that semi-vertical angle of a cone of maximum volume and given sl...

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  17. Show that the isosceles triangle of maximum area that can be inscribed...

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  18. Evaluate : int (dx)/( (1 - x^(2)) sqrt( 1 + x^(2)))

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  19. You note that your officer is happy with 60% of your calls, so, you as...

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