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Prove that |(1, a, a^3),(1, b, b^3),(1, ...

Prove that `|(1, a, a^3),(1, b, b^3),(1, c, c^3)|`= (a-b)(b-c)(c-a)(a+b+c).

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SHARAM PUBLICATION-MODEL QUESTION PAPER-5-EXERCISE
  1. Show that 2 tan^-1(1/4) + 2 tan^-1 (2/9) = tan^-1(4/3).

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  2. Prove that |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}|=abc(1+1/a+1/b+1/c)or(ab...

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  3. Prove that |(1, a, a^3),(1, b, b^3),(1, c, c^3)|= (a-b)(b-c)(c-a)(a+b+...

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  4. If A = [(-1, 3, 5),(1, -3, -5),(-1, 3, 5)] then show that A^2 = 9A

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  5. If [(x+y, x-2),(2x-y,0)] = [(2,2),(1,0)] then find the values of x,y?

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  6. Show that (a+1) is a factor of abs([(a+1),2,3],[1,a+1,3],[3,-6,a+1])

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  7. Find the value of a such that the function f defined by f(x)={((sinax...

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  8. Differentiate tan^(-1) frac (sqrt(1+x^2) + sqrt(1-x^2))(sqrt(1+x^2) ...

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  9. If y = (sinx)^x find (dy)/(dx).

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  10. Find the points on the curve y = x^3 - 11x + 5 at which the equation o...

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  11. Evaluate intx/((x^2 + 4)) dx.

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  12. Evaluate int(0)^(pi//4)log(1+tanx)dx.

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  13. Evaluate int(sinx + cosx)/(sqrt(sin2x))dx

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  14. Solve dy + e^-y sin x dx = 0.

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  15. If the sum of two unit vectors is a unit vectors find the magnitude of...

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  16. Find a vector of magnitude 5 units and parallel to the resultant of ve...

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  17. Show that [veca+vecbvecb+veccvecc+veca] = 2[vecavecbvecc]

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  18. Find the equation of the plane through the points (1, 2, -3), (2,3, -4...

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  19. If p is a prime and ab-=0 (mod p) then show that either a=0 (mod p) or...

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  20. If "sin"^(-1)(x/a) + "sin"^(-1) (y/b)=alpha "prove that" x^2/a^2+(2xy)...

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