CUET PG MCA Matrices Previous Year Questions (PYQs)

CUET PG MCA Matrices Previous Year Questions (PYQs)

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List I List II
A. Kailash Satyarthi I. Chemistry
B. Abhijit Banerjee II. Peace
C. Vinkatraman Ramakrishnan III. Physics
D. Subrahmanyan Chandrasekhar IV. Economics


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If $A=\begin{bmatrix}{\cos B} & {-\sin B} \\ {\sin B} & {\cos B}\end{bmatrix}$ then $A+{A}^T=I$ for B equal to 

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A. If $A$ and $B$ are two invertible matrices, then $(AB)^{-1}=A^{-1}B^{-1}$
B. Every skew symmetric matrix of odd order is invertible
C. If $A$ is non-singular matrix, then $(A^T)^{-1}=(A^{-1})^T$
D. If $A$ is an involutory matrix, then $(I+A)(I-A)=0$
E. A diagonal matrix is both an upper triangular and a lower triangular

Choose the correct answer from the options given below:

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Match List-I with List-II
 List-I List-II        
 (A) If $\begin{vmatrix}\lambda-1&0\\ 0&\lambda-1\end{vmatrix}$ then $\lambda=$ 
(I) 0
(B) If $\Delta=\begin{vmatrix}1&2\\ 2&4\end{vmatrix}$ then $\Delta$ is(II) 1
(C) If $A=\begin{bmatrix}1&0\\ 0&\frac{1}{2}\end{bmatrix}$ then $|A^{-1}|$ is(III) -2
(D) If $\begin{bmatrix}a+1&1\\ 1&2\end{bmatrix}=\begin{bmatrix}-1&1\\ 1&2\end{bmatrix}$ then a is(IV) 2

Choose the correct answer from the options given below:

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Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R 

Assertion A : The system of equations x + y + z = 4, 2x - y + 2z = 5, x - 2y - z = 3 has unique solution. 

Reason R: If A is 3 x 3 matrix and B is a 3 x 1 non-zero column matrix. then the equation AX = B has unique solution if A is non-singular. 

In the light of the above statements, choose the most appropriate answer from the options given below:

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If $S, T$ are symmetric matrices of the same order, then which of the following statements are true? 

(A) $S + T$ is symmetric matrix 
(B) $ST - TS$ is skew symmetric matrix 
(C) $ST + TS$ is symmetric matrix 
(D) $ST - TS$ is symmetric matrix 

(a) A, B, C 
(b) B, C, D
(c) A, B, D 
(d) A, C, D

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Which of the following statements are TRUE?

(A) If each element in a row is a constant multiplier of corresponding element of another row of a determinant, then the value of the determinant is always non-zero.

(B) If each element on one side of the principal diagonal of a determinant is zero, then the value of the determinants the product of the diagonal elements.

(C) The value of determinant of skew symmetric matrix of odd order is always non-zero. 

(D) If A is non-singular matrix of order three, then $adj A=|A|^2$
Choose the correct answer from the options given below:

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Assertion: A(BA) and (AB)A are symmetric matrices.

Reason: AB is symmetric matrix, if matrix multiplication of A with B is commutation.

Options:

(a) Assertion is true, Reason is true, and Reason is the correct explanation of the Assertion.

(b) Assertion is true, Reason is true, but Reason is not the correct explanation of the Assertion.

(c) Assertion is true, but Reason is false.

(d) Assertion is false, but Reason is true.


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A matrix is both symmetric and skew symmetric matrix

(a) A is diagonal matrix

(b) A is zero matrix

(c) A is scalar matrix

(d) A is square matrix


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Which of the following statements are NOT TRUE?
(A) If A and B are symmetric matrices, then AB – BA is a skew symmetric matrix. 
(B) Multiplying a determinant by k means multiply elements of one column by k.
(C) If $A^2-A+I=0$ , then $A^-1$ is equal to A + I.
(D) If A and B are invertible matrices of same order, then $(A+B)^{-1}=B^{-1}+A^{-1}$. 
Choose the correct answer from the options given below:

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