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If the letters of the word GARDEN are pe...

If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then find the ranks of the words
Q GARDEN

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FULL MARKS-SAMPLE PAPER 12-PART
  1. For any two vectors veca and vecb prove that |vecaxxvecb|^(2)+(veca*ve...

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  2. Find the derivative of x^(cosx) with respect to x.

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  3. Evaluate int(1)/(4-x^(2))dx.

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  4. The length of the perpendicular drawn from the origin to a line is 6 a...

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  5. Prove that sin 105^(@) + cos 105^(@) = cos 45^(@)

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  6. How many triangles can be formed by joining 15 points on the plane, in...

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  7. Find the equation of the locus of a point such that the sum of the squ...

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  8. If A^(T)=[(4,5),(-1,0),(2,3)]and B=[(2,-1,1),(7,5,-2)], verify the ...

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  9. Show that the points whose position vectors are 2veci+3vecj-5veck,3vec...

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  10. Test the existance of the limit lim(xto1)(4|x-1|+x-1)/(|x-1|),xne1

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  11. If y=tan^(-1)((1+x)/(1-x)) find y'.

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  12. Evalute int(5x^(2)-4+(7)/(x)+(2)/(sqrt(x)))dx

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  13. If x^(2) + x + 1 is a factor of the polynomial 3x^(3) + 8x^(2) + 8x ...

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  14. (a) If f(x)=(x-1)/(x+1) then show that. (i) f((1)/(x))=-f(x) (ii) ...

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  15. Determine the region in the plane determined by the inequalities. x l...

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  16. If the letters of the word GARDEN are permuted in all possible ways an...

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  17. If y=x+x^(2)/2+x^(3)/3+x^(4)/4+... then show that x=y-y^(2)/(2!)+y^(3)...

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  18. If A(i),B(i),C(i) are the cofactors of a(i),b(i),c(i) respectively,i=1...

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  19. lim(alphato0)(sin(alpha^(n)))/((sinalpha)^(m))

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  20. (a) Find (dy)/(dx) where y=(x^(2)+1)root(3)(x^(2)+2) (b) Evaluate ...

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