Q69.The number of 𝜃∈0, 4𝜋 for which the system of linear equations 3sin3𝜃𝑥- 𝑦+ 𝑧= 2 3cos2𝜃𝑥+ 4𝑦+ 3𝑧= 3 6𝑥+ 7𝑦+ 7𝑧= 9 has no solution is (1) 6 (2) 7 (3) 8 (4) 9
What This Question Tests
This question is multi-conceptual, combining the condition for a system of linear equations to have no solution (determinant of coefficient matrix is zero) with solving trigonometric equations to count valid angles.
Concepts Tested
Formulas Used
Δ = 0 and at least one Δᵢ ≠ 0 for no solution
Determinant of 3x3 matrix
📚 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.
12.5 — A Hydrogen Atom Initially In The Ground Level Absorbs A Photon,
Physics Class 12 · Chapter 12
12.5 A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.
6.11 — Dynamics Of Rotational
Physics Class 11 · Chapter 6
6.11 Dynamics of rotational the motion of extended bodies. motion about a fixed axis A large class of problems with extended bodies can be
📋 Question Details
- Chapter
- Matrices
- Topic
- System of linear equations
- Year
- 2022
- Shift
- 25 Jul Shift 1
- Q Number
- Q69
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 4: Determinants; Class 11 Mathematics Ch 3: Trigonometric Functions
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