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11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-2

  • question_answer
    If\[\mathbf{3}{{.}^{\mathbf{x}+1}}{{\mathbf{C}}_{\mathbf{2}}}{{+}^{\mathbf{2}}}{{\mathbf{P}}_{\mathbf{2}}}.\mathbf{x}=\mathbf{4}{{.}^{\mathbf{X}}}{{\mathbf{P}}_{\mathbf{2}}},\mathbf{x}\in \mathbf{N}\]. Then the value of x is:

    A) 5                     

    B) 4              

    C) 3                                 

    D) 6

    Correct Answer: C

    Solution :

    [c] \[{{3.}^{x+1}}{{C}_{2}}{{+}^{2}}{{P}_{2}}.x={{4.}^{x}}{{P}_{2}}\] \[\Rightarrow 3.\frac{x+1}{2x-1}+2.x=4.\frac{x}{x-2}\Rightarrow 3.\frac{\left( x+1 \right)x}{2}+2\text{x}=4{{x}^{2}}-4x(x-1)\] \[\Rightarrow 3{{x}^{2}}+3x+4x=8{{x}^{2}}-8x\] \[5{{x}^{2}}-15x=0\Rightarrow 5x\left( x-3 \right)=0\] x=3 Hence, the option [c] is correct.


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