CUET · MATHS · PYQ PAPER 2025

For the given five values, 13, 17, 21, 22, 32; the 3-year moving averages are :

A 17, 20, 21
B 17, 21, 25
C 16, 20, 24
D 17, 20, 25

Verified Solution

Answer & Solution

Correct Answer

(D) 17, 20, 25

Step-by-step Solution

Detailed explanation

Calculation for first moving average: \((13 + 17 + 21) / 3 = 51 / 3 = 17\) Calculation for second moving average: \((17 + 21 + 22) / 3 = 60 / 3 = 20\) Calculation for third moving average: \((21 + 22 + 32) / 3 = 75 / 3 = 25\) The 3-year moving averages are: 17, 20, 25

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

Match List I with List II

List - I	List - II
(A) \(\|\vec{a} \times \hat{i}\|^2+\|\vec{a} \times \hat{j}\|^2+\|\vec{a} \times \hat{k}\|^2\)=	(I) \(\|\vec{a}\|^2\)
(B) \(\frac{(\vec{a} \cdot \vec{b})^2+\|\vec{a} \times \vec{b}\|^2}{\|\vec{b}\|^2}=\)	(II) \(\sqrt{3}\|\vec{a}\|\)
(C) \(\vec{a}, \vec{b}\) and \(\vec{c}\) are three mutually perpendicular vectors of equal magnitude then \(\|\vec{a}+\vec{b}+\vec{c}\|=\)	(III) \(\frac{1}{2}\|\vec{a} \times \vec{b}\|\)
(D) Area of parallelogram with diagonals \(\vec{a}\) and \(\vec{b}\)	(IV) \(2\|\vec{a}\|^2\)

Choose the correct answer from the options given below:

CUET 2023 Hard

The set of points where the function given by \(f(x) = |x - 2|\) is differentiable is:

CUET 2023 Easy

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List - I	List - II
(A) \(\|\vec{a} \times \hat{i}\|^2+\|\vec{a} \times \hat{j}\|^2+\|\vec{a} \times \hat{k}\|^2\)=	(I) \(\|\vec{a}\|^2\)
(B) \(\frac{(\vec{a} \cdot \vec{b})^2+\|\vec{a} \times \vec{b}\|^2}{\|\vec{b}\|^2}=\)	(II) \(\sqrt{3}\|\vec{a}\|\)
(C) \(\vec{a}, \vec{b}\) and \(\vec{c}\) are three mutually perpendicular vectors of equal magnitude then \(\|\vec{a}+\vec{b}+\vec{c}\|=\)	(III) \(\frac{1}{2}\|\vec{a} \times \vec{b}\|\)
(D) Area of parallelogram with diagonals \(\vec{a}\) and \(\vec{b}\)	(IV) \(2\|\vec{a}\|^2\)

LIST I	LIST II
A. Trichoderma polysporum	I. Statins
B. Monascus purpureus	II. Butyric acid
C. Aspergillus niger	III. Cyclosporin A
D. Clostridium butylicum	IV. Citric acid