The values of 'a' and 'b' if the… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Statistics & Applications

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The values of ' $a$ ' and ' $b$ ' if the equation of straight line trend by least square method is given by $y = a + bx$ such that $\displaystyle \sum x = 0$ , $\displaystyle \sum y = 84$ , $\displaystyle \sum xy = 108$ , $\displaystyle \sum x^2 = 70$ for 6 observation at are:

Official previous-year question

Held on 22 May 2025 · Verified 13 Jul 2026.

Options

A
$a = 0,b = 1.28$
B
$a = 14,b = 1.54$
C
$a = 11.6,b = 0$
D
$a = 14,b = 1.28$

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Solution

The line equation is $\frac{x+3}{3} = \frac{y-1}{-1} = \frac{z-5}{-5}$

When a line cuts the yz-plane, the x-coordinate is 0 at that point. The yz-plane is where $x = 0$ .

Since all three fractions are equal, let this common value be $λ$ .

$\frac{x+3}{3} = λ$

$\frac{y-1}{-1} = λ$

$\frac{z-5}{-5} = λ$

From the first equation:

$\frac{x+3}{3} = λ$

$x + 3 = 3λ$

Since the line cuts the yz-plane, $x = 0$ :

$0 + 3 = 3λ$

$λ = 1$

From the second equation with $λ = 1$ :

$\frac{y-1}{-1} = 1$

$y - 1 = -1$

$y = 0$

From the third equation with $λ = 1$ :

$\frac{z-5}{-5} = 1$

$z - 5 = -5$

$z = 0$

Therefore, the coordinates are $(0, 0, 0)$ .

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