Let A=\left[a_{i j}\right]_{3 \times 3} be a matrix, defined by a_{i j}=\left\{\begin{array}{ll}2 i+3 j & , i j\end{array}\right.. The number of elements in A. which are greater than 6, is

CUET · MATHS · PYQ PAPER 2025

Let \(A=\left[a_{i j}\right]_{3 \times 3}\) be a matrix, defined by \(a_{i j}=\left\{\begin{array}{ll}2 i+3 j & , i < j \\ 6 & , i=j \\ 3 i-2 j & , i > j\end{array}\right.\). The number of elements in A. which are greater than 6, is

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Answer & Solution

Correct Answer

(C) 4

Step-by-step Solution

Detailed explanation

\(a_{12} = 2(1)+3(2) = 8 > 6\) \(a_{13} = 2(1)+3(3) = 11 > 6\) \(a_{23} = 2(2)+3(3) = 13 > 6\) \(a_{21} = 3(2)-2(1) = 4 \not> 6\) \(a_{31} = 3(3)-2(1) = 7 > 6\) \(a_{32} = 3(3)-2(2) = 5 \not> 6\) \(a_{11}=a_{22}=a_{33}=6 \not> 6\) Number of elements greater than 6 is 4.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

If \(A=\left[\begin{array}{ll}1 & 2 \\ 4 & 5\end{array}\right]\) then
Match List-I with List-II

List-I	List-II
(A) \(\operatorname{det}(A)\)	(I) \(-\frac{1}{3}\)
(B) \(\operatorname{det}\left(A^{-1}\right)\)	(II) \(- 12\)
(C) \(\operatorname{det}(2 A)\)	(III) \(- 3\)
(D) \(\operatorname{det}\left( 3 A ^T\right)\)	(IV) \(- 27\)

Choose the Correct answer from the options given below :

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List-I	List-II
(A) The value of \(\int_0^4\|x\| d x\) is	(I) 3
(B) The value of \(\int_{-2}^2\|x\| d x\) is	(II) -1
(C) The value of \(\int_0^3[x] d x\) is	(III) 8
(D) The value of \(\int_{-1}^1[x] d x\) is	(IV) 4