NTSE Sample Paper NTSE SAT Practice Test-6

  • question_answer
    The value of             \[{{\left( {{x}^{\frac{b+c}{c+a}}} \right)}^{\frac{1}{a-b}}}\times {{\left( {{x}^{\frac{c+a}{a-b}}} \right)}^{\frac{1}{b-c}}}\times {{\left( {{x}^{\frac{a+b}{b-c}}} \right)}^{\frac{1}{c-a}}}\]is

    A) 1              

    B)        2

    C) 3                     

    D)        ? 1

    Correct Answer: A

    Solution :

    [a] \[x\left\{ \frac{b+c}{(c-a)(a-b)}+\frac{c+a}{(a-b)(b-c)}+\frac{a+b}{(b-c)(c-a)} \right\}\] \[x\left\{ \frac{{{b}^{2}}-{{c}^{2}}}{(a-b)(b-c)(c-a)}+\frac{{{c}^{2}}-{{a}^{2}}}{(a-b)(b-c)(c-a)}+\frac{{{a}^{2}}-{{b}^{2}}}{(a-b)(b-c)(c-a)} \right\}\]\[x\left\{ \frac{{{b}^{2}}-{{c}^{2}}+{{c}^{2}}-{{a}^{2}}+{{a}^{2}}-{{b}^{2}}}{(a-b)(b-c)(c-a)} \right\}=x{}^\circ =1\]    


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