BSc CSIT (TU) Science Mathematics I (BSc CSIT, MTH112) Question Paper 2074
This is the official BSc CSIT (TU) (Science stream) Mathematics I (BSc CSIT, MTH112) question paper for 2074, 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 2074 paper is a great way to practise under real exam conditions.
Section A: Long Answer Questions
Attempt any TWO questions.
State and prove that a differentiable function is continuous. Examine the continuity and differentiability of f(x) = |x| at x = 0.
Evaluate the integral (\int \frac{dx}{a^2 + x^2}) and (\int \frac{dx}{\sqrt{a^2 - x^2}}). Hence find (\int \frac{dx}{x^2 + 4x + 8}).
Find the area bounded by the parabola (y^2 = 4ax) and its latus rectum.
Section B: Short Answer Questions
Attempt any EIGHT questions.
Evaluate (\lim_{x \to 0} \frac{\sin x}{x}) using the definition of limit.
If (y = e^{ax}\sin bx), find (\frac{dy}{dx}).
State and verify Rolle's theorem for (f(x) = x^2 - 4x + 3) on [1,3].
Find the asymptotes of the curve (y = \frac{x^2 + 1}{x - 1}).
Evaluate (\int_0^{\pi/2} \sin^4 x , dx) using the reduction formula.
Solve the differential equation (\frac{dy}{dx} + y\tan x = \sec x).
Find the angle between the vectors (\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}) and (\vec{b} = 3\hat{i} - 2\hat{j} + \hat{k}).
If (u = x^2 + y^2), find (\frac{\partial u}{\partial x}) and (\frac{\partial u}{\partial y}).
Evaluate the double integral (\int_0^1 \int_0^2 (x + y), dy, dx).