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_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_answer9) If 
then find the value of k.
question_answer12) If 
then find the maximum value of\[\Delta \].
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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\[=a{{x}^{5}}+b{{x}^{4}}+c{{x}^{3}}+d{{x}^{2}}+ex+f,\] be an identity in x, where a, b, c, d, e, f are independent of x, then find the value of f. 