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If A=[{:(3,1),(-1,2):}] then prove that ...

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

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SHARAM PUBLICATION-MODEL QUESTION PAPER 12-EXERCISE
  1. Factorise the determinant |[x^3-a^3,x^2,x],[b^2-a^3,b^2,b],[c^3-a^3,c^...

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  2. Factorize the following. [[x+a,b,c],[b,x+c,a],[c,a,x+b]]

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

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  4. Find the value of k if the function f(x) defined by f(x)={(2x-1,whenx<...

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  5. If sin y = x sin (a + y) then show that (dy)/(dx)=(sin^2(a+y))/(sina)

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  6. If y^2cot x = x^2 coty then find (dy)/(dx)

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  7. Find the intervals where function is increasing function y = cos x + s...

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  8. Find the equation of the normal to the curve 5x^2+3y^2=23 at (2,-1)

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  9. Integrate int sec xtanx.sqrt(tan^2x-3).dx

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  10. int(xe^x)/(1+x^2)dx

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  11. Evaluate int0^1[tan^-1x+x/(1+x^2)]dx

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  12. Find the area of region enclosed by y^2 = 4ax and x^2 = 4ay.

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  13. Find the particular solution of the following differential equation : ...

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

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  15. If hati +hatj+hatk and 2hati -alphahatj+3hatk are orthogonal to each o...

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  16. Find the equation of the line through the point (2, 3, 5) and parallel...

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  17. Prove that the lines (x+4)/3=(y+6)/5=(z-1)/(-2) and 3x-2y+z+5=0=2x+3y...

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  18. Solve : tan^(-1)x+tan^(-1)((2x)/(1-x^2))=pi/2

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  19. If y=x^(sinx-cosx)+(x^(2)-1)/(x^(2)+1), then find (dy)/(dx)

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  20. Find the equation of the tangent to the curve y=x^4-6x^3+13x^2-10x+2 a...

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