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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. Show that |{:((b+c)^2,a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2):}...

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  2. Prove the following by vector method. Altitudes of a triangle are conc...

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

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  4. Let f : R to R be defined by f(x)=3x+5. Show that f is bijective. Find...

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  5. Prove that tan (pi/4+1/2cos^(-1)""a/b)+tan(pi/4-1/2cos^(-1)""a /b)=(2b...

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  6. Find the extreme values of the function f(x)=x^2e^(-x^2) and show that...

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  7. Find the extreme points of the following functions. Specify if the ext...

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  8. Show that f(x)=[3x+ 11] is discontinuous at x=-11/3

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  9. Find the solution of the following differential equations: (4x+6y+5)dx...

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  10. int0^pi(xdx)/(1+sinx)

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  11. Show that int0^pixInsinx=pi^2/2In1/2

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  12. If A is a 4xx5 matrix and B is a matrix such that A^(T)B and BA^(T) bo...

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  13. What is F’(x) if F(x)=int0^xe^(3t)cos4t dt ?

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  14. Find r if -501 in[r]5.

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  15. To which coordinate axis is the plane 2y – 5z=0 parallel ?

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  16. What does the solution set of the inequation 2x+ygt5 represents?

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  17. What is the value of int(d)/(dx)f(x)dx-(d)/(dx)intf(x)dx?

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  18. IF [{:(3,5,3),(2,4,2),(lamda,7,6):}] is a singular matrix, then write ...

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  19. What is the angle between hati+ hatj and hati-hatj ?

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  20. Write a logarithmic functions which is differentiable atevery point in...

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