BPSC CCE Mathematics Question Paper 2022 PDF

Bihar Government Jobs Administrative / Civil Services

  • Conducted By BPSC
  • Maximum Marks 300
  • Languages English & Hindi

Exam Details

Detail Information
Examination Combined Competitive Examinations (CCE)
Conducting Body BPSC
Paper Mathematics
Subject Mathematics
Maximum Marks 300
Question Type Objective (MCQ)

This document contains the Mathematics paper for the Combined Competitive Examinations (CCE) conducted by BPSC. The paper is designed for Administrative/Civil Services aspirants and carries a maximum of 300 marks. It features a mix of objective and descriptive questions, testing fundamental mathematical concepts. Solving this paper is crucial for candidates aiming to understand the exam pattern, difficulty level, and important topics for the BPSC CCE.

Major Topics Covered

  • Hermitian Matrices
  • Eigenvalues
  • Eigenvectors
  • Limits
  • Paraboloids
  • Divergence
  • Gradient

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
  • BPSC CCE Hindi Paper
  • Bihar SI Previous Year Papers
  • Bihar PCS General Studies Paper
  • BPSC CCE Mathematics Answer Key 2022
  • BPSC CCE Mathematics Syllabus
  • BPSC Administrative Services Syllabus
  • BPSC CCE Exam Pattern

Instructions

  • पूर्णांक : 300 Instructions : Side . The figures in the margin indicate full marks. • Answer all questions. · Candidates are required to give their answers in their own words as far as practicable. • All questions have been printed both in English and Hindi. In case of any ambiguity in Hindi version, the English version shall be considered authentic. . Parts of the same question must be answered together and must not be interposed between answers to other questions. अनुदेश : • उपांत के अंक पूर्णांक के द्योतक हैं। • सभी प्रश्नों का उत्तर देना अनिवार्य है। • परीक्षार्थी यथासम्भव अपने शब्दों में ही उत्तर दें। • सभी प्रश्न अंग्रेजी और हिन्दी दोनों भाषाओं में छपे हैं।
  • यदि हिन्दी भाषा में कोई संदेह है, तो अंग्रेजी भाषा को ही प्रामाणिक माना जाएगा। • एक ही प्रश्न के विभिन्न भागों के उत्तर अनिवार्य रूप से एक साथ ही लिखे जाएँ तथा उनके बीच में अन्य प्रश्नों के उत्तर न लिखे जाएँ। DK23/134A (Turn Over)

Questions (page 2)

Section I

Q0.

  • (a) Solve the differential equation
    (d2y)/(dx2) + (4)/(x + a) (dy)/(dx) + (6)/((x + a)2) y = (x)/((x + a)2) ; a > 0 अवकल समीकरण को हल कीजिए, a > 0
    (d2y)/(dx2) + (4)/(x + a) (dy)/(dx) + (6)/((x + a)2) y = (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 कि एक राशि जिसे एक स्वेच्छ सदिश से आंतर गुणन करने पर एक टेन्सर प्राप्त होता है, स्वयं एक टेन्सर है।

Section I

Q1.

  • (a) Show that the matrix
    A = \beginbmatrix 2 & 3 + 4i \ 3-4i & 2 \endbmatrix
    is Hermitian. Find its eigenvalues and corresponding eigenvectors. दिखाइए कि आव्यूह
    A = \beginbmatrix 2 & 3 + 4i \ 3-4i & 2 \endbmatrix
    हर्मिटियन है। इसके अभिलाक्षणिक मान और अभिलाक्षणिक सदिश ज्ञात कीजिए।
  • (b) Evaluate :
    limx → a 2 - (x)/(a))^tan(π x)/(2a)) मूल्यांकन कीजिए :
    limx → a 2 - (x)/(a))^tan(π x)/(2a))
  • (c) Find the locus of the points from which three mutually perpendicular tangents can be drawn to the paraboloid (x2)/(a2) - (y2)/(b2) = 2z उन बिन्दुओं का बिंदुपथ ज्ञात कीजिए जिनसे परवलयज (x2)/(a2) - (y2)/(b2) = 2z पर तीन परस्पर लंबवत स्पर्श रेखाएँ खींची जा सकती हैं।
  • (d) Show that div grad rm = m(m+1)r^{m-2}. दिखाइए कि div grad rm = m(m+1)r^{m-2}।

Section I

Q2.

  • (a) Prove that
    ∫0π/2 sinm θ cosn θ 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 कि
    ∫0π/2 sinm θ cosn θ 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,
    α(θ) = (6 cos 2θ cos3 (2θ)/(3), 6 sin 2θ cos3 (2θ)/(3), 1/2 cos 4θ - cos2 2θ) जहाँ θ ∈ (0, (π)/(4))

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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 organizes this exam?

The exam is conducted by BPSC.

What is the subject of this question paper?

The subject is Mathematics.

What is the maximum marks for this paper?

The maximum marks for this paper are 300.

What is the question paper code?

The question paper code is DK23/134A.

What is the question type for this paper?

The question type is objective, with some descriptive questions also present.

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