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What will be the substitution for which ...

What will be the substitution for which the equation `frac[dy][dx]+p(x)cdoty=q(x)cdoty^n,ngt2` can be reduced to linear form.

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USHA PUBLICATION-PRACTICE PAPER-PRACTICE PAPER
  1. Write the least value of f(x)=ax+frac[b][x], where agt0,bgt0 andxgt0.

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  2. Write the value of intfrac[(x^2+1)dx][1+x^4].

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  3. What will be the substitution for which the equation frac[dy][dx]+p(x)...

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  4. If veca=2vecb and vecc=-3vecb, then what is the angle between veca and...

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  5. What is the number of independent constants that occur in the general ...

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  6. Show that the relation R on Z – {0} defined by R={(m,n)|frac[m][n] is ...

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  7. Show that the function f:RRrightarrowRR defined by f(x)={(x^2-frac[1][...

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  8. Solve for x, cos^(-1)x +sin^(-1)((x)/(2)) =(pi)/(6).

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  9. Prove that cos^(-1)(frac[b+acosx][a+bcosx])=2tan^(-1)(sqrt(frac[a-b][a...

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  10. A diet for a sick person must contain at least 4000 units of vitamins,...

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  11. Prove that abs[[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=2abs[[a,b,c]...

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  12. Find inverse of the following matrices by elementary row/column operat...

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  13. If A =[[1,-2,2],[3,1,-1]] B[[2,4],[1,2],[3,-1]] "verify" "that" (AB)^...

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  14. Without expanding prove that |[1,a,a^(2),-bc],[1,b,b^(2),-ca],[1,c,c^(...

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  15. Verify that A=[[a,b],[c,d]] satisfies the equation A^2-(a+d)A+(ad-bc...

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  16. Test differentiability and continuity of the following functions. |1...

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  17. If x =sin t,y = sin 2t then prove that (1-x^2)(d^2y)/(dx^2)- x dy/dx +...

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  18. Find dy/dx if y = x cot^(-1) (x/y)

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  19. Find the point (S) on the curve x=(3at)/(1+t^2), y=(3at^2)/(1+t^2) whe...

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  20. Show that 2sinx+3tanxgt3x for all xin(0,frac[pi][2])

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