[OBJECTIVE]

Subject: Mathematics A -II, [Plane Curves & Analytic Geometry]

Time Allowed: 15 Minutes

Max Marks: 10

NOTE: Attempt this Paper on this Question Sheet only. Please encircle the correct option. Division of marks is given in front of each question. This Paper will be collected back after expiry of time limit mentioned above.

 

Part-I  Answer the following Questions, cutting and overwriting are not allowed. (10)

A pair of straight lines is given by the equation 622 + zy — y* — 2lz — 8y +9=0. The angle between these lines is

(a) π/2                                                                                                  (b) 0

(c) π/3                                                                                   (d) π/4

The equation r? = a? sin 26 can be expressed in rectangular co-ordinates as

(a) 4xy(x²-y²)                                                                     (b) (x² + y²) ² – 2a²xy = 0

(c) (a² + y²) = 2a²x²y²                                                       (d) y² = 4ax

3. The equation r = 4/1+cosθ represents

(a) ellipse                                                                            (b) parabola

(c) hyperbola                                                                     (d) circle

The curve x² + y² = 14 is symmetric about

(a) line x-axis                                                                     (b) line x = y

(c) line y-axis                                                                      (d) both x and y axes

The locus of centers of curvatures for a given curve is called its .

(a) involute                                                                         (b) envelope

(c) diameter                                                                       (d) evolute

The parametric equations of the curve r = e⁰ are

(a) x² =e^θ, y² =e^θ                                                               (b) x² +y² = e ^θ, x² -y² = 0

(c) x = e^θcosθ, y= e^θsinθ                                                                (d) None of these

The curve 2x³ — 15x² + 36x + 10 has relative minimum at x =

(a) -1                                                                                     (b) 3

(c) 2                                                                                       (d) 0

8. A point through which there pass two branches of a curve is called

(a) simple point                                                                (b) ordinary point

(c) double point                                                                (d) corner point

 

[SUBJECTIVE]

Subject: Mathematics A -II, [Plane Curves & Analytic Geometry]

Time Allowed: 2 Hours 45 Minutes

Max Marks: 50

NOTE: ATTEMPT THIS (SUBJECTIVE) ON A SEPARATE ANSWER SHEET PROVIDED

 

Part-II  Give Short Answers, Each question carries equal marks. (20)

 

Part-III  Give Long Answers, Each question carries equal marks. (30)