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<html> <head> <title>question paper</title> </head> <body leftmargin=100 rightmargin=100 topmargin=100 bottommargin=100> <h2 align= "right">Exam code : 103201</h2> <h2 align= "right">Subject code : 1027</h2> <h2 align= "center">B.A./B.Sc. Semester-I</h2> <h2 align= "center">MATHEMATICS</H2> <H2 ALIGN= "center">Paper-II</H2> <H2 ALIGN= "CENTER">(Calculus & Trignometry)</h2> <h2 align= "left">Time allowed-3 hours &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Maximum Marks-50</h2> <h2 align= "left">Note :- Attempt FIVE questions in all selecting at least TWO questions from each section.</h2> <h2 align= "center">SECTION-A</H2> <h2 align= "left"> I. (a) Give an example to show that the set Q of rationals does not possess the least upper bound property.</h2> <h2 align= "left"> &nbsp;&nbsp;&nbsp;&nbsp;(b) If |x-3|<2,then <U>x<sup>2</sup>+ 2x - 2</U> &epsilon;(1/8,17/4)<br> &emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;x + 3</h2> <h2 align= "left"> II. (a) Prove that lim<sub>x-0</sub>sin1/x does not exist.</h2> <h2 align= "left"> &emsp;&nbsp;(b) show that f(x)=1/x is continuous in(0,1), but it is not uniformly continuous on (0,1)</h2> <h2 align= "left"> III. (a) Diffrentiate <U>x&radic;x<sup>2</sup>-a<sup>2</sup></U> -<U>a<sup>2</sup></U>cosh<sup>-1</sup><U>x</U> w.r.t.x<br> &emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&nbsp;&nbsp;2&emsp;&emsp;&nbsp;2&emsp;&emsp;&nbsp;&nbsp;&nbsp;&nbsp;a

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24.09.2025 15:58

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