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

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

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

Prove that the following. [[1,1,1],[b+c,c+a,c+a],[b^2+c^2,c^2+a^2,a^2+b^2]] =(b-c)(c-a)(a-b)

Prove the following: [[a,b,c],[b,c,a],[c,a,b]]=3abc-a^3-b^3-c^3

Prove the following: [[-a^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=4a^2b^2c^2

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

Prove that the following. [[b^2+c^2,ab,ac],[ab,c^2+a^2,bc],[ca,cb,a^2+b^2]]=4a^2b^2c^2

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

Prove that the following. [[a,b,c],[a^2,b^2,c^2],[bc,ca,ab]] =(b-c)(c-a)(a-b)(bc+ca+ab)

Prove the following: [[a+b+c,-c,-b],[-c,a+b+c,-a],[-b,-a,a+b+c]] =2(b+c)(c+a)(a+b)

Prove the following: [[1,1,1],[a,b,c],[a^3,b^3,c^3]] =(b-c)(c-a)(a-b)(a+b+c)

USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Show that:4(cot^(-1)(3/2)+cosec^(-1)sqrt(26))=pi.

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  2. Prove that f:RrightarrowR such that f(x)=frac[2x^2][x^2+1] is neither ...

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

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  4. Find B if B^(2)=[{:(17,8),(8,17):}]

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  5. If x,y,z are positive and are the pth, qth and rth terms of a G.P. the...

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  6. Find the adjoint matrix of the matrix [[2,5],[1,4]]

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  7. Solve the following : [[x,1,3],[1,x,1],[3,6,3]]=0

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  8. Find the point on the curve y^2 - x^2 + 2x - 1 =0 where the tangent ...

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  9. Find (dy)/(dx), if y=tan^(-1)((cosx)/(1+sinx)).

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  10. Find the equation of the tangent and normal to the curve y(x-2)(x-3)-x...

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  11. If f(x) = a In x + bx^2 + x has extreme values at x= - 1 and x = 2 the...

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  12. If y=x+frac[1][x+frac[1][x+...infty]] find frac[dy][dx], the rhs bein...

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  13. Solve (x+y+1)frac[dy][dx]=1

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  14. Integrate intfrac[tanx+tanalpha][tanx-tanalpha]dx

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  15. Integrate the following int0^1x^7/sqrt(1-x^2)dx

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  16. Find the area of the circle x^2+y^2=2ax.

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  17. int0^2[x^2]dx

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  18. Show that the line passing through the points (a1,b1,c1) and (a2,b2,c2...

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

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  20. Calculate the area of the triangle ABC (by vector method) where A(1,2,...

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