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- If omega is the complex cube root of unity then |[1,1+i+omega^2,omeg...
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- Consider the determinant "Delta"=|a1+b1x^2a1x^2+b1c1a2+b2x^2a2x^2+b2c2...
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- Evaluate : int dx/(2x^2+x+3)
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- If a x1 2+b y1 2+c z1 2=a x2 2+b y2 2+c z2 2=a x3 2+b y3 2+c z3 2=d ,a...
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- If A , B ,a n dC are the angles of triangle, show that the system o...
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- Let alpha,beta,gamma are the real roots of the equation x^3+a x^2+b x+...
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- If a1, a2, a3,54,a6,a7, a8, a9 are in H.P., and D=|a1a2a3 4 5a6a7a8a9|...
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- Column I, Column II The value of the determinant |x+2x+3x+5x+4x+6x...
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- If a ,b ,and c are the sides of a triangles andA , B and C are the ang...
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- If f(x) is a polynomial of degree <3, prove that |1af(a)//(x-a)1bf(b)/...
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- Prove that =|a c c-a +b c b b-c b+c a-b b-c 0 a-c x y z 1+x+y|=0 impli...
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- Solve for x in R : |((x+a)(x-a),(x+b)(x-b),(x+c)(x-c)),((x-a)^3,(x-b)...
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- Absolute value of sum of roots of the equation |x+22x+3 3x+4 2x+3 3x+4...
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- Let alpha1,alpha2 and beta1, beta2 be the roots of the equation ax^2+b...
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- The product of all values of t , for which the system of equations (a-...
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- Prove that for any A.P. a1, a2, a3, , then determinant |ap+a(p+m)+a(p...
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- Let omega=-1/2+i(sqrt(3))/2, then value of the determinant [[1, 1, 1]...
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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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