નિશ્ચાયક $\left| \begin{array}{ccc} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 6 \end{array} \right|$ એ નીચેનામાંથી કોના બરાબર નથી?
- A$\left| \begin{array}{ccc} 2 & 1 & 1 \\ 2 & 2 & 3 \\ 2 & 3 & 6 \end{array} \right|$
- B$\left| \begin{array}{ccc} 2 & 1 & 1 \\ 3 & 2 & 3 \\ 4 & 3 & 6 \end{array} \right|$
- C$\left| \begin{array}{ccc} 1 & 2 & 1 \\ 1 & 5 & 3 \\ 1 & 9 & 6 \end{array} \right|$
- D$\left| \begin{array}{ccc} 3 & 1 & 1 \\ 6 & 2 & 3 \\ 10 & 3 & 6 \end{array} \right|$
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Similar Questions
નિશ્ચાયકના ગુણધર્મોનો ઉપયોગ કરીને સાબિત કરો કે:
$\left|\begin{array}{ccc} 1 & 1 & 1 \\ a & b & c \\ a^{3} & b^{3} & c^{3} \end{array}\right|=(a-b)(b-c)(c-a)(a+b+c)$
$\left|\begin{array}{ccc} 1 & 1 & 1 \\ a & b & c \\ a^{3} & b^{3} & c^{3} \end{array}\right|=(a-b)(b-c)(c-a)(a+b+c)$
Difficult
View Solution$\left| {\begin{array}{ccc} 1 & 1+ac & 1+bc \\ 1 & 1+ad & 1+bd \\ 1 & 1+ae & 1+be \end{array}} \right| = $
Medium
View Solutionનિશ્ચાયક $\left| {\begin{array}{*{20}{c}}{{b_1} + {c_1}}&{{c_1} + {a_1}}&{{a_1} + {b_1}}\\{{b_2} + {c_2}}&{{c_2} + {a_2}}&{{a_2} + {b_2}}\\{{b_3} + {c_3}}&{{c_3} + {a_3}}&{{a_3} + {b_3}}\end{array}} \right|$ બરાબર શું થાય?
Medium
View Solutionજો $\left|\begin{array}{ccc}x & x^2 & 1+x^3 \\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3\end{array}\right|=0$ અને $x \neq y \neq z$ હોય, તો $1+x y z$ ની કિંમત શોધો.
DifficultTS EAMCET 2010
View Solutionધારો કે $a, b, c, d$ એ સામાન્ય તફાવત $\lambda$ સાથે સમાંતર શ્રેણીમાં છે. જો
$\left|\begin{array}{lll} x+a-c & x+b & x+a \\ x-1 & x+c & x+b \\ x-b+d & x+d & x+c \end{array}\right|=2$
હોય,તો $\lambda^{2}$ ની કિંમત $.....$ છે.
$\left|\begin{array}{lll} x+a-c & x+b & x+a \\ x-1 & x+c & x+b \\ x-b+d & x+d & x+c \end{array}\right|=2$
હોય,તો $\lambda^{2}$ ની કિંમત $.....$ છે.
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