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If the inverse eqaution is sin^(-1) x=2 ...

If the inverse eqaution is `sin^(-1) x=2 sin^(-1)` a then prove that `|a| le (1)/sqrt(2)`

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ARIHANT PUBLICATION-SAMPLE PAPER 1-SHORT ANSWER TYPE QUESTIONS
  1. If the inverse eqaution is sin^(-1) x=2 sin^(-1) a then prove that |a|...

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  2. Maximize Z=-x+2y subject to constrainst are x le 3 x +y ge 5 x+2y ge6 ...

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  3. Let f : N rarr N be defined by f(n) = {{:((n+1)/(2), if "n is odd"),...

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  4. If the function'f : R rarrR is given by f(x) = x^(2) +2 and g:R rarr R...

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  5. If (tan^(-1)x)^(2) +(cot^(-1)x)^(2) =(5pi^(2))/(8), then find x.

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  6. If P(A) = 0.4, P(B//A) = 0.3 and P(B^(c)/A^(c)) = 0.2. Find P(B).

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  7. A bag consists of 10 balls each marked with one of the digits 0 to 9 ...

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  8. Using the properties of determinants? show that {:|(y+z,x,y),(z+x,z,...

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  9. Using elementary transformations, find the inverse of [(4,5),(3,4)]

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  10. Find the matrix A such that A[{:(1,2,3),(4,5,6):}]=[{:(-7,-8,-9),(2,4...

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  11. If y=log[x+sqrt(x^(2)+1)], then prove that (x^(2)+1)(d^(2)y)/(dx^(2))+...

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  12. Prove that the function f gives by f(x)=|x-1|x in R is not differentia...

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  13. Using differentials, find approximate value (255)^(1//4)

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  14. The two equal sides of an isosceles triangle with fixed base b are dec...

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  15. If x^y = e^(x-y) then prove that (dy)/(dx)=logx/(1+logx)^2.

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  16. Evaluate int(sqrt(tan x)+sqrt(cot x))dx

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  17. Form the differential equation of the family of circles touching the X...

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  18. Solve each of the following differential equations : x(dy)/(dx)-y= s...

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  19. Using properties of definite integrals, evaluate int(pi//6)^(pi//3)...

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  20. Find the area of the region {(x,y):0 le y le x^(2) +1,0 le y le x +1...

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