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Prove that sin^(-1)(frac[sqrt(1+x)+sqrt(...

Prove that `sin^(-1)(frac[sqrt(1+x)+sqrt(1-x)][2])=frac[pi][4]+frac[1][2]cos^(-1)x,0ltxlt1`

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Prove that f:X rarr Y is surjective iff for all B sube Y, f(f^(-1)(B))...

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  2. Find the maximum value of Z = 2x + 3y subject to conditions x+ yle1 an...

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  3. Prove that sin^(-1)(frac[sqrt(1+x)+sqrt(1-x)][2])=frac[pi][4]+frac[1][...

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  4. Show that the relation ~ on ZZ-{0}timesZZ-{0} defined by (m,n)~(p,q)Le...

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  5. Solve by matrix method. 2x + y = 5 , x-y =1

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  6. If A=[[(1,1)],[(1,1)]] and n inN, then A^n=2^(n-1)A .

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  7. If [[(x,y)],[(x,x/2+x)]]+[[(y,x+t)],[(x/2,x/2)]]=[[(1,4)],[(2,2)]] the...

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  8. Evaluate the determinant abs((4,6,-2),(1,-4,3),(7,-2,1)

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  9. If abs((a,b,a-b),(b,c,b-c),(2,1,0))=0 , then prove that a,b,c are in G...

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  10. evaluate lim(xto1)(x^2-3x+2)/(x-1) .

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  11. If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2 then prove that x^3ydy/dx=1.

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  12. Find the maximum and minimum of f(x)=|x+3|,for all x belongs to R.

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  13. Find the interval on which the function f(x)=x^x decreases.

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  14. Find the solution of the following differential equations: (4x+6y+5)dx...

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  15. Integrate int((1-cosx)/(1+cosx))dx .

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  16. Solve (x+y)^(2)(dy)/(dx)= a^(2).

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  17. If f is periodic with period 3 and f(1) = 1 then what is the value of ...

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  18. Evaluate int(-2)^2abs([x])dx .

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  19. Prove that (vec a × vec b)^(2) = a^(2)b^(2)-(vec a . vec b)^(2).

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  20. Find the perpendicular distance of the point (-1,3,9) from the line (x...

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