Mathematics-I 1st Semester BCA-101 Previous Year Question Paper
Ccs BCA Mathematics Bca-101 Previous Year Question Paper
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📘 Exam Details
Course: BCA I Semester
Subject: Mathematics-I
Paper Code: BCA-101
University: CCS University
Exam Year: December 2024
Time: 3 Hours
Maximum Marks: 75
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📄 Section-A (V. Short Answer Questions)
Note: Attempt all questions. Each question carries 3 marks.
1. If \(A = \begin{bmatrix}3 & 5 \ 4 & 2\end{bmatrix}\), find \(A^2 - 2A\).
2. Evaluate \(\lim_{x \to 0} \frac{\tan x}{x}\).
3. Differentiate \(x \log x\).
4. Find \(\int e^{x^2} dx\).
5. If \(\vec{a} = 2i + 3j + 6k\) and \(\vec{b} = 3i - 6j + 2k\), show that \(\vec{a}\) and \(\vec{b}\) are perpendicular vectors.
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📄 Section-B (Short Answer Type Questions)
Note: Attempt any two questions out of the following three questions. Each question carries 7½ marks.
6. Verify Rolle’s theorem for the function
\(f(x) = x^2, ; x \in [-1, 1]\).
7. Solve using Cramer’s Rule:
\(2y - 3z = 0\),
\(x + 3y = -4\),
\(3x + 4y = 3\).
8. Find
\(\int \frac{x + 1}{x^2 + 4} dx\).
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📄 Section-C (Long Answer Type Questions)
Note: Attempt any three questions out of the following five questions. Each question carries 15 marks.
9. Find the characteristic equation of the matrix
\(A = \begin{bmatrix}1 & 1 & 3 \ 5 & 2 & 6 \ -2 & -1 & -3\end{bmatrix}\)
and verify Cayley-Hamilton theorem.
10. (a) Show that
\(f(x) = \begin{cases} 1 + x & \text{if } x \le 2 \ 5 - x & \text{if } x > 2 \end{cases}\)
is continuous at \(x = 2\).
(b) Show that \(f(x) = |x|\) is continuous at \(x = 0\).
11. (a) Amongst all pairs of positive numbers with sum 24, find those whose product is maximum.
(b) Expand \(\cos x\) in ascending powers of \(x\) up to three terms.
12. Find the following integrals:
(a) \(\int \frac{dx}{x(x^4 + 1)}\)
(b) \(\int \frac{dx}{(x - 1)(x - 2)}\)
(c) \(\int x \log x , dx\)
13. Find the area of a parallelogram whose adjacent sides are determined by the vectors
\(\vec{a} = i + 2j + 3k\) and
\(\vec{b} = -3i - 2j + k\).
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🗞️ About Question Paper
Agar aap CCS University BCA 1st Semester ke student hain, to yahan aapko Mathematics-I (BCA-101) December 2024 Previous Year Question Paper mil jayega.
Yeh question paper exam preparation, important topics revision aur previous year pattern samajhne ke liye bahut helpful hai.
Is paper ko solve karke students apni preparation ko aur strong kar sakte hain.
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📢 Note:
Yeh question paper students ki academic help aur exam preparation ke purpose se provide kiya gaya hai.
💡 Exam Tip:
Previous year papers ko solve karte waqt time management aur step-wise solution practice zaroor karein — especially Mathematics jaise subject me.
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