BCA 2nd Semester
Math II 2024 Board Question Paper (2023 Batch)

Define Indeterminate forms.

Evaluate: \(\lim_{x \to 0} \frac{\tan x - \sin x}{x^3}\)

Find \(\frac{dy}{dx}\) if a) \(x = t^2 - 1, y = t^4 - 1\)     b) \({x^2 + y^2}={\sin xy}\).

Using the trapezoidal rule, compute \(\int_0^2 (2x^2 - 1)dx\) with 4 intervals. Find the absolute error of approximation from its actual value.

Evaluate the following integrals:
a) \(\int \frac{2x+3}{x^2 + 3x} dx\)      b) \(\int e^x \cos x \, dx\)

Solve the differential equation: \(x \frac{dy}{dx} + 2y = x^2 \log x\)

Using the simplex method, find the optimal solution of the following linear programming problem.
Maximize, \(z = 15x + 12y\)
Subject to, \(2x + 3y \leq 21\)
        \(3x + 2y \leq 24\)
         \(x, y \geq 0\)

a) Using Simpson's \(\frac{1}{3}\) Rule, evaluate \(\int_0^1 \sqrt{1 + 2x^2} \, dx\); \(h = 0.25\).
b) Find the maximum and minimum values of the function \(f(x) = 4x^3 - 15x^2 + 12x - 1\). Also, find the point of inflection.

a) Find the area of the region between the curve \(y = 4 - x^2\), \(0 \leq x \leq 3\) and the x-axis.
b) Solve: \(\frac{dy}{dx} = \frac{x^2 + y^2}{2x^2}\)