CUET Mathematics 2025 2 June Shift 1 PYQs

If matrix $A_n = \begin{bmatrix} p(p+1) \\ p(p-1) \end{bmatrix}_{p \in N} \$(where N is the set of natural numbers), then the value of $|A_1| + |A_2| + |A_3| + ... + |A_{2025}|$ is:

$\Delta=\left|\begin{array}{ccc}1 & \cos x & 1 \\ -\cos x & 1 & \cos x \\ -1 & -\cos x & 1\end{array}\right|$

(A) $\Delta=2\left(1-\cos ^{2} x\right)$

(B) $\Delta=2\left(2-\sin ^{2} x\right)$

(C) Minimum value of $\Delta$ is $2$

(D) Maximum value of $\Delta$ is $4$

Choose the correct answer from the options given below :

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: