CUET UG Mathematics — Algebra previous year questions with solutions.
If A is a square matrix such that $A^2 = A$ and I is the identity matrix of same order as A, then the matrix $(2I+A)^3 - 19A - 3I$ is equal to
If A is a square matrix such that $A^2=A$ and I is the identify matrix of the same order as A then $(I + 2A)^3$-6A is equal to
If A is a square matrix of order $3 \times 3$ and $|A| = 4$. The value of $|(adjA).A|$ is
If A is a square matrix of order 3 such that $A( {adj } A) = \begin{bmatrix} -2 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -2 \end{bmatrix}$, then $|A|$ is equal to
If A is a square matrix of order 3 such that $|A| = 3$, then $|adj(adj A)|$ is equal to:
If A is a square matrix of order 3 and |A| = -5, then |3A| is equal to
If A is a square matrix of order 3 and $|A| = 4$, then the value of $|2A^T|$ is
If A is a square matrix and I is the identity matrix of same order such that $A^2 = I$, then $3(A - I)^3 + 3(A + I)^3 - 15A$ is equal to
If A is a square matrix and I is an identity matrix of same order such that $A^2 = A$, then $(I + A)^3 - 8I$ is equal to
If A is a square matrix and I is the identity matrix of same order such that $A^2 = I$, then $(A - I)^3 + (A + I)^3 - 3A$ is equal to
If A is a skew-symmetric matrix, then which of the following statements is **NOT** true? (A) A is singular if order of A is odd (B) A is non-singular (C) $A^{2025}$ is a skew-symmetric matrix (D) $A^{2025}$ is a symmetric matrix (E) all diagonal elements of A are zeros Choose the correct answer from the options given below:
If A is a singular matrix, then A{adj A} is equal to
If A is a non-singular matrix of order 3 such that $|adj(A)| = 121$, then $|AA^T|$ is equal to:
If A is a matrix of order $m × n$ and $B$ is a matrix such that $AB^T$ and $B^TA$ are both well-defined matrices, then order of matrix B is
If a computer code is correctly programmed, it gives 90% acceptable results. But if it is not correctly programmed, it gives only 40% acceptable results. From previous experience, it is observed that only 80% of codes are correctly programmed. If after a certain programming, the code gives 2 acceptable results, then the approximate probability that the code is correctly programmed is
If A be a square matrix of order 3 such that $|A| = 2$, then $|adj(2A)|$ is equal to
If a, b, c are positive real numbers, then the least value of $(a+b+c)(ab+bc+ca)$ is:
If A and B are two square symmetric matrices of same order, then AB-BA is
If A and B are two square matrices of same order such that $AB = A$ and $BA = B$, then the value of $A^{2024} + B^{2024}$ is equal to
If A and B are two non-singular matrices of order n, then which of the following statement/statements is/are not correct? (A) AB is non-singular. (B) AB is singular. (C) $(AB)^{-1} = A^{-1}B^{-1}$ (D) $(AB)^{-1}$ does not exist. Choose the correct answer from the options given below:
If A and B are two matrices of order 2 × 2 such that A is a symmetric matrix and B is a skew-symmetric matrix, then:
If A and B are two invertible matrices, then which of the following statements are correct? (A) $|A^{-1}| = |A|^{-1}$ (B) $adjA = |A|A^{-1}$ (C) $(AB)^{-1} = A^{-1}B^{-1}$ (D) $(A + B)^{-1} = A^{-1} + B^{-1}$ Choose the **correct** answer from the options given below:
If A and B are two independent events, then which of the following is/are true? (A) $P(A \cap B) = 0$ (B) $P(A \cup B) = 1 - P(A')P(B')$ (C) $P(A \cup B) = P(A)P(B)$ (D) $P(A \cap B) = P(A)P(B)$ Choose the correct answer from the options given below:
If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1 then