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question_answer1) The value of \[{{a}^{2}}\] for which the system of linear equations \[x+y+z=2\] \[2x+3y+2z=5\] \[2x+3y+({{a}^{2}}-1)z=a+1\] is inconsistent, is
question_answer2) Let \[A=\left| \begin{matrix} 5 & 5\alpha & \alpha \\ 0 & \alpha & 5\alpha \\ 0 & 0 & 5 \\ \end{matrix} \right|\]. If \[\left| {{A}^{2}} \right|=25,\] then \[\left| \alpha \right|\] equals
question_answer3) The number of values of \[\theta \in (0,\pi )\] for which the system of linear equations \[x+3y+7z=0\] \[-x+4y+7z=0\] \[(\sin 3\theta )x+(\cos 2\theta )y+2z=0\] has a non-trivial solution, is
question_answer4) If \[1,\omega ,{{\omega }^{2}}\] are the cube roots of unity, then is equal to
question_answer5) If \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=-2\] and then degree of polynomial \[f(x)\] is
question_answer6) Let where \[b>0\]. If the minimum value of \[\frac{\det (A)}{b}\] is \[q\sqrt{r},\] then \[\frac{r}{q}=\]
question_answer7) The greatest value of \[c\in R\] for which the system of linear equations \[x-cy-cz=0\] \[cx-y+cz=0\] \[cx+cy-z=0\] has a non-trivial solution, is
question_answer8) If \[{{a}_{1}},{{a}_{2}},{{a}_{3}},.........,{{a}_{n}},......\] are in G P., then the determinant is equal to
question_answer9) If then the value of A is
question_answer10) The sum of the real roots of the equation is equal to
question_answer11) If then the value of t is
question_answer12)
question_answer13) If is the inverse of a \[3\times 3\] matrix A, then the sum of all values of \[\alpha \] for which det \[(A)+1=0,\] is
question_answer14) \[l,m,n\] are the \[{{p}^{th}},{{q}^{th}}\] and \[{{r}^{th}}\] term of a G. P. all positive, then equals
question_answer15) If then c is equal to
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