BPSC CCE Mathematics Question Paper 2025 PDF

Bihar Government Jobs Administrative / Civil Services

  • Conducted By BPSC
  • Maximum Marks 300
  • Duration 3 Hours
  • Languages Hindi & English

Exam Details

Detail Information
Examination Combined Competitive Examinations (CCE)
Conducting Body BPSC
Paper Mathematics
Subject Mathematics
Duration 3 Hours
Maximum Marks 300
Question Type Descriptive / Subjective

This is the Mathematics paper for the Combined Competitive Examinations (CCE) conducted by BPSC. The exam allows 3 hours to complete and has a maximum of 300 marks. This paper is crucial for aspirants preparing for administrative and civil services roles under the Bihar government. It features descriptive questions covering advanced mathematical concepts, making it a valuable resource for understanding the exam's difficulty and scope.

Major Topics Covered

  • Vector Calculus
  • Linear Algebra
  • Differential Equations
  • Integral Calculus
  • Geometry
  • Tensor Calculus

Why This Paper is Important

  • Useful for Combined Competitive Examinations (CCE) preparation
  • Helps understand the latest exam pattern
  • Useful for practice and self-assessment
  • Covers frequently asked General Studies topics
  • Helpful for analysing question trends

Related Resources

  • BPSC CCE General Studies Paper 2025
  • BPSC CCE Hindi Paper 2025
  • BPSC CCE Previous Year Papers
  • BPSC CCE Mathematics Answer Key 2025
  • BPSC CCE Mathematics Syllabus
  • BPSC CCE Exam Pattern
  • BPSC 69th CCE
  • BPSC Assistant Engineer Exam

Instructions

  • p_1(x) = x^3 - 2x^2 + 4x + 1 p_2(x) = 2x^3 - 3x^2 + 9x - 1 p_3(x) = x^3 + 6x - 5 p_A(x) = 2x^3 - 5x^2 + 7x + 5 then find the basis of W and dimension of W. यदि W बहुपदों से जनित एक स्थान है p_1(x) = x^3 - 2x^2 + 4x + 1 p_2(x) = 2x^3 - 3x^2 + 9x - 1 p_3(x) = x^3 + 6x - 5 p_4(x) = 2x^3 - 5x^2 + 7x + 5 तब W का आधार और उसकी विमा ज्ञात कीजिए । 1 - 0 - 1 (b) Find the matrix P such that P-1AP is diagonal matrix, where A = \begin{vmatrix} 1 & 2 & 1 \end{vmatrix} 22 3| 1 \t0 \t-1 एक आव्यूह P इस प्रकार ज्ञात कीजिए कि P-1AP विकर्णीय है, जहाँ A = 12 1 1 2 \quad 2 3| (c) Find the volume of a sphere x^2 + y^2 + z^2 = a^2. गोले x^2 + y^2 + z^2 = a^2 का आयतन ज्ञात कीजिए।

Questions (page 2)

Q0.

(a) Solve the differential equation rac{d^2y}{dx2} - rac{4}{x+a} rac{dy}{dx} + rac{6}{(x+a)^2} y = rac{x}{(x+a)^2}; a > 0
अवकल समीकरण को हल कीजिए, a > 0
rac{d^2y}{dx2} - rac{4}{x+a} rac{dy}{dx} + rac{6}{(x+a)^2} y = rac{x}{(x+a)^2}

(b) Prove that a quantity which on inner multiplication by an arbitrary vector always gives a tensor, is itself a tensor.
सिद्ध कीजिए एक राशि जिसे एक स्वेच्छ सदिश से आंतर गुणन करने पर एक टेन्सर प्राप्त होता है, स्वयं एक टेन्सर है।

Q2.

(a) Prove that ∫0π/2 dθ = (\Gamma(m + 1)/(2)) \Gamma(n + 1)/(2)))/(2 \Gamma(m + n + 2)/(2))); m, n > 0 where \Gamma is gamma function.
सिद्ध कीजिए ∫0π/2 , dθ = (\Gamma(m + 1)/(2)) \Gamma(n + 1)/(2)))/(2 \Gamma(m + n + 2)/(2))); m, n > 0 जहाँ \Gamma गामा फलन है ।

(b) Compute the Fernet frame \T, N, B\, curvature k and torsion \tau, of the space curve below : α(θ) = (6 cos 2θ cos3 (2θ)/(3)), 6 sin 2θ cos3 (2θ)/(3)), 1/2 cos 4θ - cos2 2θ) when θ ∈ 0, (π)/(4)).
निम्नलिखित स्पेस वक्र का फर्नेट फ्रेम \T, N, B\, वक्रता k और टारिसन \tau, ज्ञात कीजिए, जहाँ θ ∈ 0, (π)/(4))
α(θ) = (6 cos 2θ cos3 (2θ)/(3)), 6 sin 2θ cos3 (2θ)/(3)), 1/2 cos 4θ - cos2 2θ)

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Frequently asked questions

What is the name of the exam?

The exam is the Combined Competitive Examinations (CCE).

Which conducting body releases this paper?

The Bihar Public Service Commission (BPSC) conducts this examination.

What is the subject of this question paper?

The subject is Mathematics.

What is the duration of the exam?

The time allowed for the exam is 3 Hours.

What is the maximum marks for this paper?

The maximum marks for this paper are 300.

What is the paper code?

The paper code is 02/GO/CC/M-2025-45.

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