Q69.The parabolas : ax2 + 2bx + cy = 0 and d2 + 2ex + fy = 0 intersect on the line y = 1. If a, b, c, d, e, f are positive real numbers and a, b, c are in G. P., then (1) d, e, f are in A.P. (2) ad , eb , fc are in G.P. (3) a d , eb , fc are in A.P. (4) d, e, f are in G.P.
What This Question Tests
This question tests the properties of parabolas and their intersection, along with the definition of a geometric progression, requiring substitution and algebraic manipulation.
Concepts Tested
Formulas Used
y = ax^2 + bx + c (general quadratic)
b^2 = ac (for GP)
📚 NCERT Sections This Tests
9.8 — A Beam Of Light Converges At A Point P. Now A Lens Is Placed In The
Physics Class 12 · Chapter 9
9.8 A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12cm from P. At what point does the beam converge if the lens is (a) a convex lens of focal length 20cm, and (b) a concave lens of focal length 16cm?
10.2 — What Is The Shape Of The Wavefront In Each Of The Following Cases:
Physics Class 12 · Chapter 10
10.2 What is the shape of the wavefront in each of the following cases: (a) Light diverging from a point source. (b) Light emerging out of a convex lens when a point source is placed at its focus. (c) The portion of the wavefront of light from a distant star intercepted by the Earth.
12.1 — (A) No Different From
Physics Class 12 · Chapter 12
12.1 (a) No different from (b) Thomson’s model; Rutherford’s model (c) Rutherford’s model (d) Thomson’s model; Rutherford’s model (e) Both the models
📋 Question Details
- Chapter
- Coordinate Geometry
- Topic
- Parabola and Geometric Progression
- Year
- 2023
- Shift
- 30 Jan Shift 2
- Q Number
- Q69
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections (Parabola)
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