Questions asked by Rajit R.

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• Find the orthogonal canonical reduction of the quadratic form #x²+y²+z²-2xy-2xz-2yz#. Also find its principal axes?
  
• Let (x1,x2,x3) and (y1,y2,y3) represent the coordinates with respect to the bases B1={(1,0,0),(0,1,0),(0,0,1)},B2={(1,0,0),(0,1,2),(0,2,1)}.If Q(x)=x1²+2x1x2+2x2x3+x2²+x3²,find the representation if Q in terms of (y1,y2,y3).?
  
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• A farmer has 200 m of fencing with which he wishes to enclose a rectangular field.One side of the field can make use of a fence that already exists. What is the maximum area he can enclose?
  
• From 7 men and 4 women a committee of 6 is to be formed. In how many ways can this be done (i)when the committee contains exactly 2 women, (ii)at least 2 women?
  
• Find the equation of the plane passing through (2,3,-1) and perpendicular to the line joining the points (3,4,-1) and (2,-1,5) ?
  
• A particle is acted on by constant forces =-3i+2j+5k and 2i+j+-3k and is displaced from point (2,-1,-3) to the point (4,-3,7).Find the total work done by the forces?
  
• This statement is true or false?Please give reasons for your answer. 2x+3y+4z=0 represents a line in 3-dimensional space.
  
• Find the values of x for which the function f(x)=x²-2x+1 is increasing or decreasing.Sketch the graph of y=f(x) ?
  
• Which of the following statements are true or false?Please give reasons for your answers. (i)The derivative of quotient of two functions is equal to the quotient of derivatives of two functions.