BCA 1st Semester
Math I Board Question Paper 2021

In an examination, 58% failed in Account, 39% in English, and 25% in Statistics; 32% in Accounts and English, 19% in Account and Statistics, 17% in English and Statistics, and 13% in all three subjects. Find:
i) What percent passed in all three subjects?
ii) What percent failed in exactly two subjects?

If \( \sqrt{x + ty} = a + ib \), then find \( \sqrt{x - ty} \) and \( x^2 + y^2 \).

A class consists of boys whose ages are in A.P. (common difference = 4 months). The youngest boy is 8 years old, and the total age of the class is 168 years. Find the number of boys.

If \( A = \begin{pmatrix} 4 & 0 \\ 0 & 5 \end{pmatrix} \), find a matrix \( X \) such that \( AX = \begin{pmatrix} 1 & 2 \\ 2 & 4 \end{pmatrix} \).

Find the equation of the ellipse whose latus rectum is 3 and eccentricity is \( \frac{1}{\sqrt{2}} \).

Prove by vector method: \( \cos(A - B) = \cos A \cos B + \sin A \sin B \).

Define a function, its domain, and range. Find the domain and range of \( f(x) = \sqrt{2 - x - x^2} \).

a) Three numbers in A.P. sum to 15. If 1, 3, 9 are added to them respectively, they form a G.P. Find the original numbers.
b) Find the sum to \( n \) terms of the series \( \frac{1}{2} + \frac{2}{4} + \frac{3}{8} + \cdots \).

a) Find the angle between vectors \( \mathbf{u} = 4\mathbf{i} - 2\mathbf{j} + \mathbf{k} \) and \( \mathbf{v} = \mathbf{i} + \mathbf{j} - \mathbf{k} \).
b) Find the Maclaurin series of \( f(x) = \cos x \).