JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2015

  • question_answer
    The equation of the curve whose tangent at any  point  \[f(0)=0\]   makes   an   angle\[f(1)=0\]with X-axis and which passes through (1, 2), is

    A) \[^{47}{{C}_{4}}+\sum\limits_{r=1}^{5}{^{52-r}}{{C}_{3}}\]

    B) \[^{47}{{C}_{6}}\]

    C) \[^{52}{{C}_{4}}\]

    D) \[^{52}{{C}_{5}}\]

    Correct Answer: A

    Solution :

    It is given that \[\frac{\pi }{2}\] Now, \[\frac{\pi }{4}\] \[\frac{\pi }{3}\]                               \[\text{5a}+\text{2b}\] Above equation is a linear .differential equation in y. Its integrating factor is given by \[\text{a}-\text{3b}\] Now, solution of above differential equation is given as \[|a|=2\sqrt{2},|b|=3\]                 \[\frac{\pi }{4}\]               \[\sqrt{369}\] \[\sqrt{593}\]    \[\sqrt{113}\] \[2x+y-7=0\]      \[\left( \frac{9}{5},\frac{17}{5} \right)\] Since, equation of curve passes through (1, 2) \[2x+y=1\]          \[3{{x}^{2}}+4yx-4x+1=0\] \[\frac{\pi }{2}\]               \[\frac{\pi }{3}\] \[\frac{\pi }{4}\]               \[\frac{\pi }{6}\] Hence, the equation of the curve is \[6x+9y+2=26{{e}^{3(x-1)}}\]


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