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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2001

  • question_answer
    \[\underset{x\to 0}{\mathop{\lim }}\,\frac{(1-\cos 2x)\sin 5x}{{{x}^{2}}\sin 3x}\]is equal to?

    A)  10/3                                     

    B)  3/10

    C)  6/5                                       

    D)  5/6

    Correct Answer: A

    Solution :

    \[\underset{x\to 0}{\mathop{\lim }}\,\frac{1-(1-2{{\sin }^{2}}x)\sin 5x}{{{x}^{2}}\sin 3x}\] \[\Rightarrow \]\[\underset{x\to 0}{\mathop{\lim }}\,\frac{2{{\sin }^{2}}x\sin 5x.3x.5x}{{{x}^{2}}\sin 3x.3x.5x}\] \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin x}{x}=1=\frac{10}{3}\]


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