MHT CET 2026 15th April Evening Shift | Matrices and Determinants Question 23 | Mathematics

The element in the third row and the second column in the inverse matrix of a matrix $\begin{bmatrix} 1 & 3 & 3 \\ 3 & 1 & 3 \\ 3 & 3 & 4 \end{bmatrix}$ is

$\dfrac{3}{2}$

$\dfrac{2}{3}$

$\dfrac{-3}{2}$

$\dfrac{-2}{3}$

MHT CET 2026 15th April Morning Shift

MCQ (Single Correct Answer)

-0

Let $A = \begin{bmatrix} 2k-1 & 1 & 1 \\ 0 & 2k-1 & 1 \\ 0 & 0 & 2k-1 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & 2k-1 & 1 \\ 1-2k & 0 & k \\ -1 & -k & 0 \end{bmatrix}$ where k is a real number. If $\det(\text{adj} A) + \det(\text{adj} B) = 11^6$, then the value of $k - 5$ is equal to...

$1$

$2$

$4$

$6$

MHT CET 2026 15th April Morning Shift

MCQ (Single Correct Answer)

-0

If $A = \begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}$, then the matrix $A^{-3}$ when $\theta = \dfrac{\pi}{6}$ is equal to...

$\begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix}$

$\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$

$\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$

$\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$

MHT CET 2025 5th May Evening Shift

MCQ (Single Correct Answer)

-0

If $A=\left[\begin{array}{rrr}1 & -2 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4\end{array}\right]$ then $A(I+\operatorname{adj} A)=$

$\left[\begin{array}{ccc}9 & -2 & 2 \\ 0 & 10 & -3 \\ 3 & -2 & 11\end{array}\right]$

$\left[\begin{array}{ccc}8 & -2 & 2 \\ 0 & 9 & -3 \\ 3 & -2 & 10\end{array}\right]$

$\left[\begin{array}{rrr}9 & -2 & 2 \\ 0 & 10 & -3 \\ 3 & -2 & 12\end{array}\right]$

$\left[\begin{array}{ccc}3 & 2 & -2 \\ 0 & 10 & 3 \\ -3 & 2 & 12\end{array}\right]$

PREVIOUS NEXT

MHT CET Subjects

Browse all chapters by subject

Chemistry

Physical Chemistry

Some Basic Concepts of Chemistry Atomic Structure States of Matter Thermodynamics Chemical Equilibrium Ionic Equilibrium Liquid Solution Redox Reactions Surface Chemistry Solid State Electrochemistry Chemical Kinetics Nuclear Chemistry

Inorganic Chemistry

Periodic Table and Periodicity Chemical Bonding and Molecular Structure Metallurgy Hydrogen and It's Compounds s-Block Elements p-Block Elements d and f Block Elements Coordination Compounds Environmental Chemistry

Organic Chemistry

IUPAC Nomenclatures General Organic Chemistry Isomerism Hydrocarbons Haloalkanes and Haloarenes Alcohol, Phenols and Ethers Aldehyde and Ketone Carboxylic Acids and Its Derivatives Compounds Containing Nitrogen Polymers Biomolecules Chemistry in Everyday Life Practical Organic Chemistry