LU B.Sc Sem 1 Mathematics Differential Calculus Important Questions 2026 | PYQ Pattern
LU B.Sc 1st Semester Mathematics (Differential Calculus) Important Questions 2026 – Lucknow University (LU) aur affiliated colleges ke B.Sc NEP Semester I (PCM group) students ke liye Mathematics – Differential Calculus (Paper-I) ke sabse important questions, bilkul previous year question paper (PYQ) pattern me. Saare questions neeche page par hi hain – section-wise.
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Paper Details – B.Sc Sem 1 Mathematics (LU NEP 2026)
| University | University of Lucknow (LU) + affiliated colleges |
| Course | B.Sc. I Semester (NEP) – PCM |
| Paper | Mathematics – Differential Calculus (Paper-I) |
| Time / Marks | 2 Hours / 75 Marks |
| Pattern | Kul 4 questions: Section A se 1 (15 marks) + Section B se 3 (20 marks each) |
Section A – Important Questions (15 Marks)
Note: Section A se koi ek question attempt karna hai.
Q1. (a) Prove that f(x) = x sin(1/x) for x ≠ 0 and 0 for x = 0 is continuous at x = 0 but not differentiable there.
(b) Give the statement and proof of Lagrange’s mean value theorem, and verify it for f(x) = (x – 1)(x – 2)(x – 3) on [0, 4]. [15 Marks]
Q2. (a) Show that a function f(x, y) which is differentiable at (a, b) must be continuous there, and that the converse need not hold.
(b) For f(x, y) = xy/√(x² + y²), (x, y) ≠ (0, 0); = 0 at (0, 0), show that f is continuous at (0, 0) but not differentiable there. [15 Marks]
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Section B – Important Questions (20 Marks)
Note: Section B se koi teen questions attempt karne hain.
Q3. (a) Give the statement and proof of Rolle’s theorem and check whether it holds for f(x) = 2 + (x – 1)^(2/3) on [0, 2].
(b) Prove that lim_{(x,y)→(0,0)} xy/(x² + y²) does not exist. [20 Marks]
Q4. (a) Given y = e^(a sin⁻¹x), show that (1 – x²) y_{n+2} – (2n + 1) x y_{n+1} – (n² + a²) y_n = 0, and use it to find (y_n)₀.
(b) Given y = sin⁻¹x, show that (1 – x²) y_{n+2} – (2n + 1) x y_{n+1} – n² y_n = 0. [20 Marks]
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Q5. (a) Using Maclaurin’s theorem, prove that log sec x = x²/2 + x⁴/12 + x⁶/45 + …
(b) Expand sin x in powers of (x – π/2). [20 Marks]
Q6. (a) Give the statement and proof of Euler’s theorem on homogeneous functions.
(b) Given u = sin⁻¹[(x² + y²)/(x + y)], show that x ∂u/∂x + y ∂u/∂y = tan u. [20 Marks]
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Q7. (a) Given x + y + z = u, y + z = uv, z = uvw, prove that ∂(x, y, z)/∂(u, v, w) = u²v.
(b) Obtain the maximum and minimum values of f(x, y) = x³ + y³ – 3x – 12y + 20. [20 Marks]
Q8. (a) Obtain the asymptotes of y³ – 6xy² + 11x²y – 6x³ + x + y = 0.
(b) Obtain the radius of curvature at a general point (r, θ) of the cardioid r = a(1 + cos θ). [20 Marks]
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Q9. (a) Obtain the envelope of the family y = mx + cm³, m being the parameter.
(b) Obtain the envelope of the lines x/a + y/b = 1, where a and b satisfy aⁿ + bⁿ = cⁿ (c constant). [20 Marks]
Q10. (a) Obtain the evolute of the parabola y² = 4ax.
(b) Sketch the curve y²(2a – x) = x³. [20 Marks]
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Exam Tips – Mathematics (Differential Calculus)
- Section A ke long answers ke short notes bana lo – 15 marks pakke karo.
- Section B ke derivations / numericals / diagrams ki practice karo.
- Upar ke questions ko 2 ghante me PYQ ki tarah solve karke dekho.
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FAQs
LU B.Sc 1st Semester Mathematics (Differential Calculus) exam me kitne questions attempt karne hote hain?
Ye 75 marks ka 2 ghante ka paper hai. Kul 4 questions attempt karne hote hain – Section A se 1 question (15 marks) aur Section B se 3 questions (20-20 marks).
Kya ye LU B.Sc Sem 1 Mathematics ka official previous year question paper (PYQ) hai?
Nahi. Ye LUUPDATE team ka banaya 2026 exam ke liye most important questions ka set hai, jo Lucknow University ke previous year papers ke pattern aur NEP syllabus par based hai.
B.Sc Sem 1 Mathematics Differential Calculus ke answers / solutions kahan milenge?
LUUPDATE ke Most Important Questions course (BA, B.Sc, B.Com Sem I, III & V) me har question ka pura solution milta hai – sirf ₹99 me, LUUPDATE App par.
Ye paper kis group ke liye hai – PCM ya ZBC?
Mathematics (Differential Calculus) LU B.Sc NEP Semester I ke PCM group ke students ke liye hai.
Disclaimer: Ye LUUPDATE team dwara taiyar kiye gaye expected important questions hain (previous year pattern par), Lucknow University ka official question paper nahi. Exam pattern aur syllabus ke liye university ka official notice zaroor dekhein.
