Q75.If y = y(x) is the solution of the differential equation, dxdy + 2y tan x = sin x, y( π3 ) = 0, then the maximum value of the function y(x) over R is equal to : (1) 8 (2) 21 (3) −154 (4) 18
What This Question Tests
This question combines solving a first-order linear differential equation with initial conditions and then finding the maximum value of the solution function using differentiation.
Concepts Tested
Formulas Used
dy/dx + P(x)y = Q(x)
Integrating Factor (I.F.) = e^(∫P(x)dx)
y * I.F. = ∫(Q(x) * I.F.)dx
Finding extrema using first derivative test
📚 NCERT Sections This Tests
9.18 — For Fixed Distance S Between Object And Screen, The Lens Equation
Physics Class 12 · Chapter 9
9.18 For fixed distance s between object and screen, the lens equation does not give a real solution for u or v if f is greater than s/4. Therefore, fmax = 0.75 m.
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.
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.
📋 Question Details
- Chapter
- Differential Equations
- Topic
- Linear differential equations
- Year
- 2021
- Shift
- 16 Mar Shift 1
- Q Number
- Q75
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 9: Differential Equations
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