BSc CSIT (TU) Science Mathematics I (BSc CSIT, MTH112) Question Paper 2077
This is the official BSc CSIT (TU) (Science stream) Mathematics I (BSc CSIT, MTH112) question paper for 2077, 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 2077 paper is a great way to practise under real exam conditions.
Section A: Long Answer Questions
Attempt any TWO questions.
Define continuity of a function at a point. Discuss the continuity of (f(x) = \frac{x^2 - 1}{x - 1}) at x = 1 and redefine it to make it continuous.
State and prove the fundamental theorem of integral calculus. Hence evaluate (\int_1^2 (3x^2 + 2x),dx).
Solve the second-order differential equation (\frac{d^2y}{dx^2} - 5\frac{dy}{dx} + 6y = e^{2x}).
Section B: Short Answer Questions
Attempt any EIGHT questions.
Evaluate (\lim_{x \to 0} \frac{\tan x - x}{x^3}).
If (y = \log(\sin x)), find (\frac{dy}{dx}).
State Taylor's theorem and write the Maclaurin series expansion of (e^x).
Find the radius of curvature of the curve (y = x^2) at the point (1,1).
Evaluate (\int e^x \sin x , dx).
Solve ((x^2 + y^2)dx - 2xy,dy = 0).
Find the scalar triple product of (\hat{i}+\hat{j}, \hat{j}+\hat{k}, \hat{k}+\hat{i}).
If (u = \log(x^2 + y^2)), show that (\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0).
Evaluate the double integral (\int_0^1 \int_0^1 (x^2 + y^2),dx,dy).