| Detail | Information |
|---|---|
| Examination | ASSISTANT CONSERVATOR OF FOREST,MAIN EXAM. |
| Conducting Body | JPSC |
| Paper | Mathematics Paper-I |
| Subject | Mathematics |
| Duration | 3 Hours |
| Maximum Marks | 200 |
| Question Type | Descriptive / Subjective |
This document contains the Mathematics Paper-I for the JPSC Assistant Conservator of Forest (ACF) Main Examination. The exam is conducted by the Jharkhand Public Service Commission (JPSC) and is designed to assess candidates for the ACF role. This paper, with a maximum of 200 marks and a duration of 3 hours, is divided into two sections: Section A and Section B. Section A includes compulsory subjective questions, while Section B offers optional subjective questions. Aspirants can use this question paper for focused preparation, understanding the exam pattern, and practicing subjective question answering techniques.
Section A
(a)
हरमिशियन तथा स्क्यु–हर्मिटियन आव्यूह की परिभाषा दीजिए। सिद्ध कीजिए कि प्रत्येक वर्ग आव्यूह A को अद्वितीय रूप से एक हर्मिटियन तथा एक स्क्यु-हर्मिटियन आव्यूह के योग के रूप में व्यक्त किया जा सकता है। [10]
Define Hermitian and skew-Hermitian matrices. Prove that any square matrix A can be uniquely expressed as the sum of a Hermitian matrix and a skew Hermitian matrix.
Section A
(a)
तीन सदिशों के स्केलर त्रिगुणन की परिभाषा दीजिए तथा इसका ज्यामितीय अर्थ स्पष्ट कीजिए। निम्नलिखित सदिशों का स्केलर त्रिगुणन ज्ञात कीजिए। [10]
ec{a} = hat{i} + 2hat{j} + 3hat{k}, ec{b} = 2hat{i} - hat{j} + hat{k}, ec{c} = 3hat{i} + hat{j} - 2hat{k}
तथा उनसे बने समांतर चतुर्भुजाय का आयतन ज्ञात कीजिए।
Define the scalar triple product of three vector and state its geometrical interpretation. Evaluate the scalar triple product of the vectors
ec{a} = hat{i} + 2hat{j} + 3hat{k}, ec{b} = 2hat{i} - hat{j} + hat{k}, ec{c} = 3hat{i} + hat{j} - 2hat{k}
and hence determine the volume of the parallelepiped formed by them.
Section A
(a)
किसी अंतरिक्ष वक्र की वक्रता तथा मरोड़ की परिभाषा दीजिए। सेरेट–फ्रेनेट सूत्र लिखिए। कार्य–ऊर्जा प्रमेय का कथन लिखिए। किसी कण की गतिज ऊर्जा का व्यंजक प्राप्त कीजिए तथा उसका भौतिक महत्व स्पष्ट कीजिए। [10]
Define curvature and torsion of a space curve. Write the Serret-Frenet formulae. State the work-energy theorem. Obtain the expression for the kinetic energy of a particle and explain its physical significance.
Section A
(a)
चर पृथक्करण विधि द्वारा अवकल समीकरण को हल करने की विधि समझाइए। इस विधि की सीमायें भी लिखिए। निम्नलिखित अवकल समीकरण को हल कीजिए। [10] (dy)/(dx) = (x2 - y2)/(2xy) जहाँ x = 1 पर y = 1 है।
Explain the method of solving differential equation by the method of separation of variables. Also write the limitations of this method. Solve the following differential equation.
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This paper is for the ASSISTANT CONSERVATOR OF FOREST, MAIN EXAM. conducted by JPSC.
The subject is Mathematics, specifically Paper-I.
The maximum marks for this paper is 200.
The time allowed for this paper is 3 Hours.
The Jharkhand Public Service Commission (JPSC) is the conducting body.
The question paper is divided into two sections: Section A and Section B.