CUET PG 2024 — Reasoning PYQ

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Question

CUET PG 2024 — Reasoning PYQ

CUET PG | Reasoning | 2024

One day, Amit left home and cycled 15 km southwards, turned right and cycled 7 km and turned right and cycled 10 km and turned left and cycled 5 km. How many kilometres will he have to cycle to reach his home?

Choose the correct answer:

Explanation

1. Amit ki Movement ka Mathematical Breakdown

Amit ke har move ko coordinates mein convert karte hain:

Starting Point (Home): $A = (0, 0)$
15 km South: Amit niche ki taraf gaya.

$B = (0, -15)$
7 km Right (Turning South se Right matlab West):

$C = (0 - 7, -15) = (-7, -15)$
10 km Right (Turning West se Right matlab North):

$D = (-7, -15 + 10) = (-7, -5)$
5 km Left (Turning North se Left matlab West):

$E = (-7 - 5, -5) = (-12, -5)$

2. Home ( $0,0$ ) tak Pahunchne ke liye Distance ( $d$ )

Amit ab point $E(-12, -5)$ par hai. Usse ghar $(0, 0)$ wapas jana hai.

Distance Formula ka use karte hain:

d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

d = \sqrt{(0 - (-12))^2 + (0 - (-5))^2}

d = \sqrt{12^2 + 5^2}

d = \sqrt{144 + 25}

d = \sqrt{169}

d = 13 \text{ km}

3. Conclusion

Amit ko apne ghar pahunchne ke liye 13 km cycle chalani hogi.

\text{Final Answer: } 13 \text{ km}