| Detail | Information |
|---|---|
| Examination | Indian Forest Service Exam |
| Year | 2016 |
| Conducting Body | UPSC |
| Paper | Mathematics Paper - I |
| Subject | Mathematics |
| Duration | Three Hours |
| Maximum Marks | 200 |
| Number of Questions | 8 |
| Question Type | Mixed |
This is the Mathematics Paper I from the Indian Forest Service (IFS) Exam conducted in 2016 by UPSC. The paper has a total of 8 questions, of which 5 are to be attempted. Questions 1 and 5 are compulsory, and candidates must select at least one question from each of the two sections (A and B) from the remaining six questions. The exam is designed to test advanced mathematical concepts and problem-solving skills. This paper is crucial for aspirants preparing for the IFS examination, providing insights into the types of questions asked and the difficulty level.
(d) If the point (2, 3) is the mid-point of a chord of the parabola y2 = 4x, then obtain the equation of the chord.
(e) For the matrix A = \beginbmatrix -1 & 2 & 2 \ 2 & -1 & 2 \ 2 & 2 & -1 \endbmatrix, obtain the eigen value and get the value of A4 + 3A3 - 9A2.
(a) After changing the order of integration of ∫0∞ ∫0∞ e^-xy sin nx , dx , dy, show that ∫0∞ (sin nx)/(x) dx = (π)/(2).
(b) A perpendicular is drawn from the centre of ellipse (x2)/(a2) + (y2)/(b2) = 1 to any tangent. Prove that the locus of the foot of the perpendicular is given by (x2 + y2)2 = a2x2 + b2y2.
(c) Using mean value theorem, find a point on the curve y = √(x-2), defined on [2, 3], where the tangent is parallel to the chord joining the end points of the curve.
(d) Let T be a linear map such that T : V3 → V2 defined by T(e1) = 2f1 - f2, T(e2) = f1 + 2f2, T(e3) = 0f1 + 0f2, where e1, e2, e3 and f1, f2 are standard basis in V3 and V2. Find the matrix of T relative to these basis. Further take two other basis B1[(1, 1, 0), (1, 0, 1), (0, 1, 1)] and B2[(1, 1), (1, -1)]. Obtain the matrix T1 relative to B1 and B2.
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The exam is the Indian Forest Service Exam.
This question paper is from the year 2016.
The exam is conducted by UPSC (Union Public Service Commission).
This paper is Mathematics Paper - I.
The maximum marks for this paper are 200.
The time allowed is Three Hours.