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12th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-3

  • question_answer
    The slope of the tangent to the curve \[\mathbf{x}={{\mathbf{t}}^{\mathbf{2}}}-\mathbf{3t}+\mathbf{5}\]and \[\mathbf{y}=\mathbf{2}{{\mathbf{t}}^{\mathbf{2}}}-\mathbf{2t}+\mathbf{6}\text{ }\mathbf{at}\,\mathbf{t}=\mathbf{2}\]is:

    A) 6                     

    B) 5              

    C) 4                                 

    D) 1

    Correct Answer: A

    Solution :

    [a] \[\because x={{t}^{2}}-3t+5\] \[y=2{{t}^{2}}-2t+6\] Now, slope of the tangent \[\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}=\frac{2.2.t-2}{2.t-3}=\frac{4t-2}{2.t-3}\]             \[\therefore {{\left( \frac{dy}{dx} \right)}_{at\,t=2}}=\frac{8-2}{4-3}=6\] Hence, option [a] is correct.


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