CUET · MATHS · PYQ PAPER 2025

Data available for profit (₹ Thousands) of a company as
Year 2004 2005 2006 2007 2008 2009 2010
Profit(000) 114 130 126 144 138 156 164
Based on the above data using least square method the trend value for the year ‘2007’ is

A 147.64
B 138.86
C 130.57
D 131.22

Verified Solution

Answer & Solution

Correct Answer

(B) 138.86

Step-by-step Solution

Detailed explanation

Set \(x\) for years (deviation from 2007): \(-3, -2, -1, 0, 1, 2, 3\). \(n = 7\). \(\Sigma y = 114+130+126+144+138+156+164 = 972\). For a linear trend \(y = a + bx\) where \(\Sigma x = 0\), the intercept \(a = \frac{\Sigma y}{n}\). \(a = \frac{972}{7} \approx 138.85714\). For…

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 the Integrating factor of the following Differential equations.

List - I	List - II
(A) \(\frac{d y}{d x}-y=\cos x\)	(I) \(e^x\)
(B) \(\frac{d y}{d x}=\cos x-y\)	(II) \(x^2\)
(C) \(x \frac{d y}{d x}+2 y=x^2\)	(III) \(\frac{1}{x^2}\)
(D) \(\frac{d y}{d x}=x+\frac{2}{x} y\)	(IV) \(e^{-x}\)

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YEAR (X)	2000	2001	2002	2003	2004	2005	2006
PRODUCTION (iN TONNES) (Y)	40	45	46	42	47	50	46

Year	2004	2005	2006	2007	2008	2009	2010
Profit(000)	114	130	126	144	138	156	164

Data available for profit (₹ Thousands) of a company asYear2004200520062007200820092010Profit(000)114130126144138156164Based on the above data using least square method the trend value for the year ‘2007’ is

Step-by-step Solution

Data available for profit (₹ Thousands) of a company as
Year 2004 2005 2006 2007 2008 2009 2010
Profit(000) 114 130 126 144 138 156 164
Based on the above data using least square method the trend value for the year ‘2007’ is