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Prove that the measure of the angle betw...

Prove that the measure of the angle between two main diagonals of a cube is `cos^(-1)frac[1][3]`.

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Prove that f:X rarr Y is injective iff f^(-1) (f(A)) = "A for all" A s...

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  2. Prove that cos^(-1)(frac[b+acosx][a+bcosx])=2tan^(-1)(sqrt(frac[a-b][a...

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

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  4. Show that the shortest distance between the lines x+a=2y=-12z and x=y+...

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

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  11. Let f:RrightarrowR be defined as f(x)=3x. Then f is one-one and onto

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  12. Let f:RrightarrowR be defined as f(x)=3x. Then f is one-one and onto

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  13. Let f:RrightarrowR be defined as f(x)=3x. Then f is one-one and onto

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  14. Let f:RrightarrowR be defined as f(x)=3x. Then f is one-one and onto

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  15. Find the number of binary operations on the set {a,b}.

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  16. If A, B are symmetric matrices of same order, then find AB-BA.

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  17. Let A be square matrix of order 3times3, then find abs(KA) where, k is...

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  18. If A is an invertible matrix of order 2, then find det(A^(-1)).

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  19. Find intx^2e^(x^3)dx

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