Related InterviewSolutions

• The solution of the differential equation, \(\frac{{{\rm{d}}y}}{{{\rm{d}}x}} = {(x - y)^2}\)when y(1) = 1, is:1. \({\rm{lo}}{{\rm{g}}_{\rm{e}}}\left| {\frac{{2 - x}}{{2 - y}}} \right| = x - y\)2. \(- {\rm{lo}}{{\rm{g}}_{\rm{e}}}\left| {\frac{{1 - x + y}}{{1 + x - y}}} \right| = 2\left( {x - 1} \right)\)3. \(- {\rm{lo}}{{\rm{g}}_{\rm{e}}}\left| {\frac{{1 + x - y}}{{1 - x + y}}} \right| = x + y - 2\)4. \({\rm{lo}}{{\rm{g}}_{\rm{e}}}\left| {\frac{{2 - y}}{{2 - x}}} \right| = 2\left( {y - 1} \right)\)
• Rolle's Theorem is applicable in the interval [-5, 5] for the function1. \(\rm f (x) = x^4\)2. \(\rm f (x) = 5x^4\)3. \(\rm f (x) = 2x^3 + 3\)4. \(\rm f(x) = \pi |x|\)
• Consider the differential equation, \({{\rm{y}}^2}{\rm{dx}} + \left( {{\rm{x}} - \frac{1}{{\rm{y}}}} \right){\rm{dy}} = 0\). If value of y is 1 when x = 1, then the value of x for which y = 2, is:1. \(\frac{5}{2} + \frac{1}{{\sqrt {\rm{e}} }}\)2. \(\frac{3}{2} - \frac{1}{{\sqrt {\rm{e}} }}\)3. \(\frac{1}{2} + \frac{1}{{\sqrt {\rm{e}} }}\)4. \(\frac{3}{2} - \sqrt {\rm{e}}\)
• In which of the following interval is f (x) = -\(\rm x^2\)satisfy Rolle's Theorem?1. (0, 2)2. (3, 4)3. (-3, -1)4. None of these
• Which of the following is not true about Rolle's Theorem?1. f (x) is continuous on the open interval [a, b]2. f (x) is differentiable on the open interval (a, b)3. f (a) = f (b)4. None of these
• Let f : R → R be a continuously differentiable function such that f(2) = 6 and \({\rm{f'}}\left( 2 \right) = \frac{1}{{48}}\). If \(\mathop \smallint \nolimits_6^{{\rm{f}}\left( {\rm{x}} \right)} \left( {4{{\rm{t}}^3}} \right){\rm{dt}} = \left( {{\rm{x}} - 2} \right){\rm{g}}\left( {\rm{x}} \right),{\rm{\;then\;}}\mathop {{\rm{lim}}}\limits_{{\rm{x}} \to 2} {\rm{\;g}}\left( {\rm{x}} \right)\)is equal to:1. 182. 243. 124. 36
• What is the rate of change of \(\rm \sqrt {{x^2} + 48} \)relative to x2 at x = 4?1. 1/42. 1/83. 1/164. 1/24