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Prove that the following. [[a-b-c,2a,2a]...

Prove that the following. `[[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3`

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USHA PUBLICATION-PREVIOUS YEAR QUESTION 2018-PREVIOUS YEAR QUESTION
  1. If A,B,C are matrices of order 2xx2 each and 2A+B+C =[[1,2],[3,0]] A+B...

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  2. Find the inverse of the following matrix [{:(1,1,2),(0,1,2),(1,2,1):}]...

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  3. Prove that the following. [[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=...

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  4. A bag A contains 2 white and 3 red balls and another bag B contains 4 ...

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  5. If P(A) = 0.6, P(B/A) = 0.5, find P(A uu B) when A and B are independe...

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

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  7. Differentiate y=(siny)^(sin2x)

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  8. Test the differentiability and continuity of the following function at...

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  9. Show that the sum of the intercepts on the coordinate axes of any tang...

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

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  11. Evaluate int (dx)/((x+1)sqrt(1-x^2))

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  12. Show that int0^1(Inx)/sqrt(1-x^2)dx=pi/2In1/2

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  13. Find the area enclosed bt the two paraboles y^2=4 ax and x^2=4ay.

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  14. From the differential equation whose general solution is y=asint+be^t.

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  15. Solve the following differential equations (1+y^2)dx+(x-e^(-tan^(-1)...

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  16. Find the area of the triangle ABC with vertices A(1,2,4), B(3,1,-2) an...

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

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  18. If the sum of two unit vectors is a unit vector, show that the magnitu...

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  19. Prove that the measure of the angle between two main diagonals of a cu...

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  20. If the position vectors of two points A and B are 3hati + hatk and 2ha...

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