Q64.Let the circle S : 36x2 + 36y2 −108x + 120y + C = 0 be such that it neither intersects nor touches the co- ordinate axes. If the point of intersection of the lines, x −2y = 4 and 2x −y = 5 lies inside the circle S, then: (1) 25 9 < C < 133 (2) 100 < C < 165 (3) 81 < C < 156 (4) 100 < C < 156 = 1, a > b. Let E2 be another ellipse such that it touches the end points of major axis of E1
What This Question Tests
This question involves multiple conditions related to a circle: finding its center and radius, ensuring it doesn't touch/intersect axes, and checking if a point lies inside it, all leading to a range for C.
Concepts Tested
Formulas Used
x^2 + y^2 + 2gx + 2fy + c = 0
r = sqrt(g^2 + f^2 - c)
📚 NCERT Sections This Tests
9.17 — (A) Sin I¢C = 1.44/1.68 Which Gives I¢C = 59°. Total Internal Reflection
Physics Class 12 · Chapter 9
9.17 (a) sin i¢c = 1.44/1.68 which gives i¢c = 59°. Total internal reflection takes place when i > 59° or when r < rmax = 31°. Now, (sin i /sin r max max ) = 1.68 , which gives imax ~ 60°. Thus, all incident rays of angles in the range 0 < i < 60° will suffer total internal reflections in the pipe. (If the length of the pipe is finite, which it is in practice, there will be a lower limit on i determined by the ratio of the diameter to the length of the pipe.) (b) If there is no outer coating, i¢c = sin–1(1/1.68) = 36.5°. Now, i = 90° will have r = 36.5° and i¢ = 53.5° which is greater than i¢c. Thus, all incident rays (in the range 53.5° < i < 90°) will suffer total internal reflections.
9.15 — Apply Mirror Equation And The Condition:
Physics Class 12 · Chapter 9
9.15 Apply mirror equation and the condition: (a) f < 0 (concave mirror); u < 0 (object on left) (b) f > 0; u < 0 (c) f > 0 (convex mirror) and u < 0 (d) f < 0 (concave mirror); f < u < 0 to deduce the desired result.
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
📋 Question Details
- Chapter
- Circles
- Topic
- Equation of a circle, position of a point and circle, non-intersection with axes
- Year
- 2021
- Shift
- 22 Jul Shift 1
- Q Number
- Q64
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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