## Friday, January 04, 2019 2014
(November)
MATHEMATICS
(General)
Course: 301
[(Group – A: Coordinate Geometry and
Group – B: Analysis – I (Real Analysis)]
Full Marks: 80
Pass Marks: 32
Time: 3 hours
The figures in the margin indicate full marks for the questions
GROUP – A
(Coordinate Geometry)
SECTION – I
(2-Dimension)
1. (a) Write what should be done to remove term from the equation . 1
(b) Write the transformed equation of the straight line when the origin is transformed to the point .
(c) Find the angle through which the axes must be turned to remove the term from the equation .
2. (a) Straight lines represented by pass through the origin. State true or false.
(b) Show that straight lines represented by are parallel.
(c) Show that the equation 4 represents a pair of straight lines.
(d) Show that the area of the triangle formed by the lines and is     5 Or
Show that the lines and form an equilateral triangle.
3. (a) Let and for the conic . Write the name of the conic. 1
(b)  Find the equation of the tangent at to the conic . 2
(c) Write the definition of a diameter of a conic. 1
(d) Show that the equation 3 represents a hyperbola.
(e) Show that the sum of the squares of two conjugate semi-diameters of a conic is constant. 3
Or
Determine the nature of the conic . Also find the centre of the conic.
SECTION – II
(3-Dimension)
4. (a) Find the intercepts made by the plane on the axes. 1
(b) Express the equation of the plane in normal form. 2
(c) Find the equation to the plane through the point and normal to the straight line joining the points and . 3
Or
Find the coordinates of the point, where the line meets the plane .
(d) Find the distance of the point of intersection of the line and the plane from the point .
5. (a) Define skew lines. 1
(b) Find the shortest distance between the planes and . 2
(c) Find the shortest distance between the lines and . 5
GROUP – B
(Analysis – I)
6. (a) If , then write the value of 1
(b) If then find the length of sub tangent of the curve. 1
(c) Find the radius of curvature at any point on the curve 2
(d) If then find the value of 3
(e) Evaluate: 3 Or
If then find the value of 7. (a) Write when a function is derivable in a closed interval . 1
(b) Write the geometrical interpretation of Lagrange mean value theorem. 2
(c) Prove that if a function is continuous on and , then it assumes every value between and . 4
(d) Discuss the applicability of Rolle’s Theorem to in . 3
Or
Expand by Maclaurin’s theorem with Lagrange form of remainder.
8. (a) If , then find 2
(b) If , then show that 3
Or
If then show that 9. (a) Write the condition when 1
(b) Evaluate: 5
(c) Evaluate: 4
Or
Find the length of the curve from 1 to 2.

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