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Prove that |[1,logxy,logxz],[logyx,1,log...

Prove that `|[1,log_xy,log_xz],[log_yx,1,log_yz],[log_zx,log_zy,1]|=0`

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UNITED BOOK HOUSE-QUESTION PAPER 2017-EXERCISE
  1. Evaluate : sec^2(tan^(-1)2)+cosec^2(cot^(-1)3).

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  2. Show that , A =1/3[[-1,2,-2],[-2,1,2],[2,2,1]] is proper orthogonal ma...

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  3. Prove that |[1,logxy,logxz],[logyx,1,logyz],[logzx,logzy,1]|=0

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  4. If x = sqrt(a^(sin^(-1)t)) and y= sqrt(a^(cos^(-1)t) show that (dy)/(...

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  5. Verify Rolle' theorem for the function f(x)= x^2-4x+3 in 1lexle3.

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  6. Evaluate: int(cos x-cos 2x)/(1-cosx)dx.

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  7. A particle starts with the velocity u and moves in a straight line, i...

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  8. Find the interval where f(x) = 1/(1+x^2) decrease.

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  9. If f(x)= f(a+x) then prove that the value of overset(a+t)underset(a)in...

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  10. If vec a= 3hati+hatj+9 hat k and vecb = hati +lambda hat j+3 hat k the...

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  11. Find the vector equation of a plane through the point hati+ hat j+hat ...

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  12. If P(A)=2/3,P(B)=1/2 and P(AnnB)=1/6 then find the value of P(AnnB^C).

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  13. Solve: tan^(-1)(x+1)+tan^(-1)(x-1)=tan^(-1)(8/31).

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  14. If A=([2,-1],[1,3]) then show that A^2-5A+7I2=0 hence find A^(-1)

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  15. Solve by Cramer's rule: x+3y= 4,y+3z = 7, 4x+z= 6.

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  16. Prove that |[2ab,a^2,b^2],[a^2,b^2,2ab],[b^2,2ab,a^2]|=-(a^3+b^3)^2.

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  17. If f(x)= ((a+x)/(b+x))^(a+b+2x) then prove that f'(0)= [2log(a/b)+(b...

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  18. Evaluate: int (xdx)/(x^4-x^2+1)

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  19. Solve: ydx-(x+2y^2)dy=0.

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  20. In a certain culture the rate of increment of bacterial at any instant...

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