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State whether it is true or false:d/dx(c...

State whether it is true or false:`d/dx(cos^(-1)x)=(-1)/sqrt(1-x^2)`

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JMD PUBLICATION-SOLVED SAMPLE QUESTION PAPERS-EXAMPLE
  1. State whether it is true or false:sin^(-1) (sin x)=x, x in [-π/2,π/2]

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  2. State whether it is true or false:If A=[[3,-4],[1,-1]] then 2A=[[6,-8]...

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  3. State whether it is true or false:d/dx(cos^(-1)x)=(-1)/sqrt(1-x^2)

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  4. State whether it is true or false:int a^x/b^x dx=a^x/(b^x(log a-logb)]...

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  5. State whether it is true or false:y=ax is a solution of xy+y=0

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  6. State whether it is true or false:If abs (vec a.vecb)=abs(veca×vecb) t...

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  7. State whether it is true or false:If a line makes angles alpha, beta, ...

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  8. State whether it is true or false:If A and B are dependent events then...

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  9. Show that the points (a+5,a+4), (a-2,a+3) and (a,a) do not lie on a st...

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  10. If f(x)=[[cos x,-sin x,0],[sin x,cos x,0],[0,0,1]] , show that f(x).f(...

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  11. The slope of the curve 2y^2-ax^2=b at (1,-1) is -1 find a and b.

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  12. integrate int (cos2x-cos2alpha)/(cosx-cosalpha) dx

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  13. solve 'int0^(π/4)sqrt(1+sin2xdx)'

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  14. find the area of the region bounded by 'y^2=4x' and x=2

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  15. Find lambda so that the scalar projection of veca=lambdahati+hatj+4hat...

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  16. Find unit vector in the direction of veca+vecb, where veca=-hati+hatj+...

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  17. Prove that : tan^-1[(sqrt(1+x^2) - sqrt(1-x^2))/(sqrt1+x^2 + sqrt(1-x^...

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  18. If x^y+y^x= (x+y)^(x+y), then prove that dy/dx= ((x+y)^(x+y) [1+log(x+...

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  19. If y= [Log(x+sqrt(x^2+1))]^2 then show that (x^2+1)y2+xy1=0

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  20. Evaluate intdx/(sinx-sin2x)

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