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- If =|-x a bb-x a a b-x| , then a factor is a+b+x x^2-(a-b)+x+a^2+b...
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- If g(x)=|a^(-x)e^(x loge a)x^2a^(-3x)e^(3x loge a)x^4a^(-5x)e^(5x loge...
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- the sum of values of p for which the equations x+y+z=1x+2y +4z=p...
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- The value of |alpha| for which the system of equation alphax+y+z=...
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- Let D1=|a b a+b c d c+d a b a-b|a n dD2=|a c a+c b d b+d a c a+b+c| th...
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- If |xx+y x+y+z2x3x+2y4x+3y+2z3x6x+3y 10 x+6y+3z|=64 , then the real va...
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- If =|1 3costheta1s intheta1 3costheta1s intheta1| , then the value of ...
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- If |x^n x^(n+2)x^(n+4)y^n y^(n+2)y^(n+4)z^n z^(n+2)z^(n+4)|=(1/(y^2)-1...
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- The value of |2x1y1x1y2+x2y1x1y3+x3y1x1y2+x2y1 2x2y2x2y3+x3y2x1y3+x3y1...
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- Given A=|a b2c d e2fl m2n|,B=|f2d e2n4l2m c2a b| , then the value of B...
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- Number of real roots of the equation[[1, x, x], [ x, 1, x],[ x, ...
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- If |[sqrt(3) x-x^2, x-1 , x-sqrt3], [sqrt3 x , x , sqrt3-1] ,[x-1, ...
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- If f(x)=|cos (x+alpha) , cos (x+beta) , cos (x+gamma)],[ sin (x+alpha...
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- Let f(x)=|[1+sin ^2 x, cos ^2 x , 4 sin 2 x],[ sin ^2 x ,1+cos ^2 x...
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- Given 2 x-y+2 z=1 , x-2 y+z=-4 , and x+y+lambda z =4. Then the. value ...
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- If M and m are maximum and minimum value, respectively of |[1 , cos th...
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- The value of |[log (3) 512 , log (4) 3 ],[ log (3) 8 , log (4) 9]||[...
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- If |[1 , x, x^2],[ x , x^2 , 1],[ x^2 , 1 , x]|=3, then the value ...
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- If a, b, c are the sides of a scalene triangle such that |[a , a^2 , a...
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- Let a+b+c=s and |[s+c, a, b],[ c ,s+a, b],[ c, a , s+b]|is cqua...
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