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SSC CGL 2022 PYQ — Question 61

SSC CGL - 01 Dec 2022 - Shift 4 • Quantitative Aptitude • Q61

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If a2+b2+c2−1024ab−bc−ca=−2\frac{{{{\mathop{\rm a}\nolimits} ^2} + {{\mathop{\rm b}\nolimits} ^2} + {{\mathop{\rm c}\nolimits} ^2} - 1024}}{{{\mathop{\rm ab}\nolimits} - {\mathop{\rm bc}\nolimits} - {\mathop{\rm ca}\nolimits} }} = - 2 and a + b = 5c, where c > 0, then the value of c is _________.

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. 8

Given:

a + b = 5c

Formula used:

(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)

Calculations:

According to the question;

⇒ a2 + b2 + c2 - 1024 = -2ab + 2bc + 2ca

⇒ a2 + b2 + c2 + 2ab - 2bc - 2ca = 1024

Using the formula given above, we get

⇒ (a + b - c)2 = 322

⇒ a + b - c = 32

⇒ 5c - c = 32

⇒ 4c = 32

⇒ c = 8