BSc CSIT (TU) Science Mathematics I (BSc CSIT, MTH112) Question Paper 2080
This is the official BSc CSIT (TU) (Science stream) Mathematics I (BSc CSIT, MTH112) question paper for 2080, 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 2080 paper is a great way to practise under real exam conditions.
Section A: Long Answer Questions
Attempt any TWO questions.
Define the derivative of a function from first principles. Find the derivative of (\sin x) using the first-principle method.
Obtain the reduction formula for (\int \sin^n x , dx) and hence evaluate (\int_0^{\pi/2} \sin^5 x , dx).
Solve the differential equation (\frac{dy}{dx} = \frac{y}{x} + \tan\frac{y}{x}) (homogeneous).
Section B: Short Answer Questions
Attempt any EIGHT questions.
Evaluate (\lim_{x \to 0}\frac{\log(1 + x)}{x}).
If (y = x^n \log x), find (y_n).
State and verify Cauchy's mean value theorem for (f(x) = x^2, g(x) = x) on [1,2].
Find the maximum and minimum values of (f(x) = \sin x + \cos x).
Evaluate (\int \frac{x^2}{(x^2 + 1)(x^2 + 4)},dx).
Solve (\frac{dy}{dx} + y\cot x = \cos x).
Find the work done by a force (\vec{F} = 2\hat{i} + 3\hat{j} + \hat{k}) in moving a particle along (\vec{d} = \hat{i} + \hat{j} + \hat{k}).
If (u = \tan^{-1}(y/x)), find (\frac{\partial u}{\partial x}) and (\frac{\partial u}{\partial y}).
Evaluate (\int_0^1 \int_0^{\sqrt{1 - x^2}} dy , dx).