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- Consider the following linear equations: a x+b y+c z=0 b x+c y+a z=0 c...
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- Let omega be the complex number cos(2pi/3)+isin(2pi/3) Then the number...
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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^2,a1x^2+b1,c1],[a2+b2x^2,a2x^2...
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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 ^...
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- If A , B ,a n dC are the angles of triangle, show that the system of...
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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=|[a1,a2,a3],[5, 4,a6...
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- If f(x) is a polynomial of degree <3, then, f(x)/((x−a)(x−b)(x−c))is ...
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- Prove that =|[a,c,c-a,a+c],[c,b,b-c,b+c],[a-b,b-c,0,a-c],[x,y,z,1+x+y]...
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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+2,2x+3, 3x+4],[ 2x+...
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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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- "If " a(1) ,a(2), a(3)….." are in A.P, then find the value of the fol...
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- Let omega=-1/2+i(sqrt(3))/2. Then the value of the determinant |(1,1,1...
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- Factorize: a x+b x+a y+b y +a x^2+b y^2+b x^2+a y^2 a^2+b c+a b+...
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- If g(x)=|[a^(-x),e^(x loge a),x^2],[a^(-3x),e^(3x loge a),x^4],[a^(-5x...
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- The sum of values of p for which the equations x+y+z=1, x+2y +4z...
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- The value of |alpha| for which the system of equation alphax+y+z=...
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