BSc CSIT (TU) Science Mathematics I (BSc CSIT, MTH112) Question Paper 2078
This is the official BSc CSIT (TU) (Science stream) Mathematics I (BSc CSIT, MTH112) question paper for 2078, 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 2078 paper is a great way to practise under real exam conditions.
Section A: Long Answer Questions
Attempt any TWO questions.
Define limit and continuity. Evaluate (\lim_{x \to 0}\frac{e^x - 1}{x}) and (\lim_{x \to 0}\frac{a^x - 1}{x}).
If (y = (\sin^{-1} x)^2), prove that ((1 - x^2)y_{n+2} - (2n+1)xy_{n+1} - n^2 y_n = 0).
Find the area enclosed between the curves (y = x^2) and (y = x).
Section B: Short Answer Questions
Attempt any EIGHT questions.
Evaluate (\lim_{x \to 0}\frac{\sin 3x}{\sin 5x}).
Differentiate (\tan^{-1}\left(\frac{2x}{1 - x^2}\right)) with respect to x.
State and verify Rolle's theorem for (f(x) = \sin x) on ([0, \pi]).
Find the points of inflection of (y = x^3 - 6x^2 + 9x).
Evaluate (\int_0^{\pi/2} \cos^6 x , dx).
Solve (\frac{dy}{dx} + 2xy = x).
Find the projection of (\vec{a} = \hat{i} + 2\hat{j} - \hat{k}) on (\vec{b} = 2\hat{i} - \hat{j} + 3\hat{k}).
If (z = f(x/y)), show that (x\frac{\partial z}{\partial x} + y\frac{\partial z}{\partial y} = 0).
Evaluate (\int_0^a \int_0^b xy , dx , dy).