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Prove that the following. |[(v+w)^2,u^2...

Prove that the following. `|[(v+w)^2,u^2,u^2],[v^2,(w+u)^2,v^2],[w^2,w^2,(u+v)^2]|=2uvw(u+v+w)^3`

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ARIHANT PRAKASHAN-VERY SIMILAR TEST 6 -SECTION B ANSWER ANY THREE QUESTIONS
  1. Solve for x, "tan"^(-1)(x+1)+"tan"^(-1)(x-1)="tan"^(-1)8/(31)[0ltxlt1]...

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  2. If P(A)=0.8 P(B)=0.5 and P(B/A) =0.4 then find the value of P(A cup B)

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  3. Find the inverse of the following matrices using elementary transforma...

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  4. If A=[{:(3,1),(-1,2):}] then prove that A^(2)-5A+7I=O

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  5. Prove that the following. |[(v+w)^2,u^2,u^2],[v^2,(w+u)^2,v^2],[w^2,w...

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  6. Find the mean and the variance of the number obtained on a throw of an...

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  7. Find the equation of the tangent and normal to the curve (x^(2))/(a^(2...

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  8. Find the local maximum and local minimum values of the function f(x) =...

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  9. If logsqrt(x^(2)+y^(2))=tan^(-1)((x)/(y)), then show that (dy)/(dx)=(y...

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  10. If e^(y//x)=(x)/(a+bx) then show that x^(3)(d)/(dx)((dy)/(dx))=(x(dy)/...

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  11. Verify, MVT, if f(x)=x^(2)-4x-3 in the interval [a,b], where a =1 and ...

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  12. Find the solution of the differential equation (dy)/(dx)+y=cosx-sinx.

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  13. Solve (dy)/(dx)+2y tan x=sin x, "if" y(pi/(3))=0.

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  14. Evaluate int(dx)/(e^(4x)-5)

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  15. Evaluate int(1)^(2)(4x^(3)-5x^(2)+6x+9) dx

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  16. Prove that the curves y^(2)=4x and x^(2)=4y divide the area of the squ...

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  17. Find the vector equation of the plane which contains the line of inter...

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  18. Prove that the lines (x-2)/(1) = (y-4)/(4) = (z-6)/(7) and (x+1)/(3) ...

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  19. Prove that (vecaxxhati)^2+(vecaxxhatj)^2+(vecaxxhatk)^2=2veca^2 .

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  20. Prove that the sum of the vectors represented by the sides of a closed...

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