Q77.If A is a 3 × 3 matrix such that |5 adjA| = 5, then |A| is equal to (1) ± 251 (2) ±5 (3) ± 51 (4) ±1
What This Question Tests
This question tests the application of fundamental properties of determinants, specifically for scalar multiplication and adjoint matrices. The calculation for the given expression leads to |A|=±1/5, which is not among the options, suggesting a possible typo in the problem statement (where RHS should likely be 125 to yield |A|=±1).
Concepts Tested
Formulas Used
|kA| = k^n|A|
|adjA| = |A|^(n-1)
📚 NCERT Sections This Tests
5.18 — What Is Crystal Field Splitting Energy? How Does The Magnitude Of Do Decide
Chemistry Class 11 · Chapter 5
5.18 What is crystal field splitting energy? How does the magnitude of Do decide the actual configuration of d orbitals in a coordination entity?
5.11 — Draw All The Isomers (Geometrical And Optical) Of:
Chemistry Class 11 · Chapter 5
5.11 Draw all the isomers (geometrical and optical) of: (i) [CoCl2(en)2] + (ii) [Co(NH3)Cl(en)2] 2+ (iii) [Co(NH3)2Cl2(en)]+
2.2 — A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its
Physics Class 11 · Chapter 2
2.2 A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.
📋 Question Details
- Chapter
- Matrices & Determinants
- Topic
- Properties of Determinants of Adjoint Matrix
- Year
- 2015
- Shift
- 11 Apr Online
- Q Number
- Q77
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 4: Determinants
More from this Chapter
Q75.The number of values of k for which the linear equations 4x + ky + 2z = 0; kx + 4y + z = 0; 2x + 2y + z = 0 possess a non-zero solution is (1) 2 (2) 1 (3) zero (4) 3
Q77.Statement 1: If the system of equations x + ky+ 3z = 0, 3x + ky −2z = 0, 2x + 3y −4z = 0 has a nontrivial solution, then the value of k is 31 . Statement 2: A system of three homogeneous equations in three variables 2 has a non trivial solution if the determinant of the coefficient matrix is zero. JEE Main 2012 (26 May Online) JEE Main Previous Year Paper (1) Statement 1 is false, Statement 2 is true. (2) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1. (3) Statement 1 is true, Statement 2 is true,, (4) Statement 1 is true, Statement 2 is false. Statement 2 is not a correct explanation for Statement 1.
Q80.The number of values of k, for which the system of equations : (k + 1)x + 8y = 4k JEE Main 2013 (07 Apr) JEE Main Previous Year Paper kx + (k + 3)y = 3k −1 has no solution, is : (1) 2 (2) 3 (3) Infinite (4) 1
Q81.If y = sec(tan−1 x), then dxdy at x = 1 is equal to (1) 1 (2) √2 (3) 1 (4) 1 √2 2 x