Q72.If the following system of linear equations 2x + y + z = 5 x −y + z = 3 x + y + a z = b has no solution, then : (1) a = −13 , b ≠73 (2) a ≠13 , b = 73 (3) a ≠−13 , b = 73 (4) a = 13 , b ≠73
What This Question Tests
This question assesses the conditions for a system of linear equations to have no solution, involving the calculation of determinants and checking consistency conditions.
Concepts Tested
Formulas Used
For no solution: Δ = 0 and at least one Δ_x, Δ_y, Δ_z ≠ 0 (Cramer's Rule) or Rank(A) ≠ Rank([A|B])
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13.5 The Q value of a nuclear reaction A + b ® C + d is defined by Q = [ mA + mb – mC – md]c2 where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic. (i) 11 H+13 H →12 H+12 H (ii) 126 C+126 C →1020 Ne+ 24 He Atomic masses are given to be m ( 12 H ) = 2.014102 u m ( 13 H) = 3.016049 u m ( 126 C ) = 12.000000 u m ( 1020 Ne ) = 19.992439 u
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📋 Question Details
- Chapter
- Matrices & Determinants
- Topic
- System of linear equations
- Year
- 2021
- Shift
- 31 Aug Shift 1
- Q Number
- Q72
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 4: Determinants
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