BSc CSIT 1st Semester Mathematics: Past Year & Important Questions

Mathematics is a crucial subject in the BSc CSIT 1st semester, covering topics like functions, limits, differentiation, integration, and numerical methods. Preparing past questions helps understand exam patterns and frequently asked concepts.

Below is a comprehensive list of past and important questions, categorized by topics.

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1. Functions and Graphs

1. Define a function. How is it different from a relation?

2. If f(x) = (2x² - 3x + 5) / (x - 1), find domain and range.

3. Sketch the graph of y = |x - 2| - 3.

4. Determine if f(x) = x³ + 5x - 7 is an even, odd, or neither function.

5. Find the inverse of f(x) = (3x + 2) / (x - 4).

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2. Limits and Continuity

1. Find lim (x → 0) (sin x) / x.

2. Show that lim (x → 2) (x² - 4) / (x - 2) exists.

3. Evaluate lim (x → ∞) (3x² - 5) / (2x² + x + 1).

4. Find whether the function f(x) = (x² - x - 2) / (x - 2) is continuous at x = 2.

5. Prove that lim (x → 0) |x| / x does not exist.

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3. Differentiation

1. Differentiate f(x) = x³ + 2x² - 5x + 6.

2. Find dy/dx if y = e^(x²) + sin(3x) + ln(x).

3. Find the second derivative of y = x⁴ - 3x² + 7.

4. Find the tangent line equation at (1, 3) for y = 2x² + 1.

5. Use Rolle’s theorem for f(x) = x² - 4 on [-2,2].

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4. Integration

1. Evaluate ∫ (3x² + 2x - 4) dx.

2. Compute ∫ e^x sin x dx using integration by parts.

3. Find the area under the curve of y = x² from x = 1 to x = 3.

4. Evaluate the improper integral ∫ (from 0 to 3) dx / (x - 1).

5. Solve ∫ (x / (x² + 4)) dx.

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5. Numerical Methods

1. Use Newton’s method to find √3, taking x₀ = 1.5.

2. Use the Trapezoidal rule to approximate ∫ (1 to 3) (x² + 1) dx with n = 4.

3. Use the Simpson’s 1/3 rule to estimate ∫ (0 to 2) e^x dx with n = 6.

4. Apply Euler’s method for dy/dx = x + y, given y(0) = 1, with h = 0.1.

5. Solve f(x) = x³ - x - 1 = 0 using Newton-Raphson method, taking x₀ = 1.

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6. Matrices and Determinants

1. Find the determinant of

   $$A = \begin{bmatrix} 3 & 2 \\ -1 & 4 \end{bmatrix}$$

2. Compute the inverse of

   $$B = \begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix}$$

3. Find eigenvalues of

   $$C = \begin{bmatrix} 1 & 2 \\ 2 & 1 \end{bmatrix}$$

4. Solve the system Ax = B where

   $$A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}, x = \begin{bmatrix} x \\ y \end{bmatrix}, B = \begin{bmatrix} 5 \\ 11 \end{bmatrix}$$

5. Prove that AB ≠ BA in general for two matrices A and B.

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7. Vector Algebra

1. Find |a| if a = (3, -4, 1).

2. Find the dot product of a = (1, 2, 3) and b = (-2, 0, 5).

3. Find the cross product of a = (1, 2, 3) and b = (3, 4, 5).

4. Find the angle between vectors a = (2, 2, -1) and b = (1, 3, 2).

5. If a = (i + 2j - 3k) and b = (2i - j + 4k), find a × b.

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8. Partial Differentiation

1. Find ∂z/∂x for z = x²y + sin(xy) + e^(xy).

2. Find the second partial derivatives of f(x, y) = x² + xy + y².

3. Use Euler’s theorem to prove x(∂z/∂x) + y(∂z/∂y) = 2z for z = x² + y².

4. Find the Jacobian determinant for u = x² - y², v = xy.

5. Show that f(x, y) = x³ + 3xy² - y³ has a saddle point at (0,0).

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9. Double and Triple Integrals

1. Evaluate ∬ (x²y dx dy), where 0 ≤ x ≤ 2, 0 ≤ y ≤ 1.

2. Change the order of integration for ∫ (0 to 2) ∫ (x to 2) f(x, y) dy dx.

3. Compute ∭ (x² + y²) dx dy dz, where 0 ≤ x, y, z ≤ 1.

4. Convert ∬ xy dA into polar coordinates, where x² + y² ≤ 1.

5. Solve ∬ (1 + x²) dA, where region R is bounded by x = 0, x = 1, y = x².

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Conclusion

Practicing past exam questions is the best strategy to excel in BSc CSIT 1st Semester Mathematics. These questions cover fundamental topics, ensuring a strong conceptual foundation.

🚀 Pro Tips for Success: ✔️ Solve at least five questions from each topic daily.
✔️ Focus on numerical accuracy in integration and differentiation.
✔️ Use past papers to analyze repeated questions.
✔️ Learn shortcuts for matrix operations and vector calculations.

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