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question_answer1) If and \[\sum\limits_{k=1}^{n}{{{D}_{k}}}=56\] then find value of n.
question_answer2) If A, B, C are angles of a triangle and the value of is 10 - k then find k.
question_answer3) Matrix \[{{M}_{r}}\] is defined as \[{{M}_{r}}=\left[ \begin{matrix} r & r-1 \\ r-1 & r \\ \end{matrix} \right],\,\,\,r\in N.\] If value of \[\det \left( {{M}_{1}} \right)+\det \,\left( {{M}_{2}} \right)+\det \,\left( {{M}_{3}} \right)+.....\] \[+\det \left( {{M}_{2007}} \right)is\,k\left( 2007 \right)\] then find k.
question_answer4) If then find the value of\[\lambda \].
question_answer5) Using properties of determinants, evaluate:
question_answer6) Find the sun of infinite series
question_answer7) If then find the value of A.
question_answer8) Find the number of values of k, for which the system of equation \[\left( k+1 \right)x+8y=4k,\,kx+\left( k+3 \right)y=3k-1,\] has no solution.
question_answer9) If then find the value of k.
question_answer10) If \[=a{{x}^{5}}+b{{x}^{4}}+c{{x}^{3}}+d{{x}^{2}}+ex+f,\] be an identity in x, where a, b, c, d, e, f are independent of x, then find the value of f.
question_answer11) Given\[2x-y+2z=2,x-2y-z=-4,x+y+\lambda z=4,\]then find the value of \[\lambda \]such that the given system of equation has solution.
question_answer12) If then find the maximum value of\[\Delta \].
question_answer13) If \[2ax-y+2z=0,\,x+ay+5z=0\] and \[2x+az=0\] have a non-trivial solution then find the value of a.
question_answer14) then find the value of \[p+q+r.\]
question_answer15) If \[\omega \] is a complex cube root of unity, then the value of the determinant
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