BSc CSIT (TU) Science Mathematics I (BSc CSIT, MTH112) Question Paper 2075
This is the official BSc CSIT (TU) (Science stream) Mathematics I (BSc CSIT, MTH112) question paper for 2075, as set in the regular annual examination. It carries 60 full marks and a time allowance of 180 minutes, across 12 questions. On Kekkei you can attempt this Mathematics I (BSc CSIT, MTH112) past paper online with a timer, get instant AI feedback and step-by-step solutions, and track the topics where you lose marks — completely free. Whether you are revising for your BSc CSIT (TU) Mathematics I (BSc CSIT, MTH112) exam or solving previous years' question papers, this 2075 paper is a great way to practise under real exam conditions.
Section A: Long Answer Questions
Attempt any TWO questions.
Define the limit of a function. Evaluate (\lim_{x \to 0} \frac{1 - \cos x}{x^2}) and discuss the continuity of the resulting function.
State Leibnitz's theorem. If (y = \sin^{-1} x), find the nth derivative (y_n) at x = 0.
Find the volume of the solid generated by revolving the region bounded by (y = x^2), x = 0 and x = 2 about the x-axis.
Section B: Short Answer Questions
Attempt any EIGHT questions.
Evaluate (\lim_{x \to \infty} \left(1 + \frac{1}{x}\right)^x).
Differentiate (x^x) with respect to x.
State and verify Lagrange's mean value theorem for (f(x) = x^2) on [2,4].
Find the maximum and minimum values of (f(x) = x^3 - 3x + 2).
Evaluate (\int \frac{x}{(x+1)(x+2)} dx) by partial fractions.
Solve (\frac{dy}{dx} = \frac{x + y}{x - y}).
Find a unit vector perpendicular to both (\vec{a} = 2\hat{i} + \hat{j} + \hat{k}) and (\vec{b} = \hat{i} - \hat{j} + 2\hat{k}).
If (z = x^2 y + xy^2), verify that (\frac{\partial^2 z}{\partial x \partial y} = \frac{\partial^2 z}{\partial y \partial x}).
Evaluate (\int_0^1 \int_0^x xy , dy , dx).