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SSC CGL 2019 PYQ — Question 55

SSC CGL - 10th June 2019 - Shift 1 • Quantitative Aptitude • Q55

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In a ΔABC, right angled at B, AB = 7 cm and (AC – BC) = 1 cm. The value of (sec C + cot A) is?

Show answer & explanation

Correct answer: B

Explanation

Correct Answer is option 2 i.e. 4/3

Concept

Understanding

Application

In triangle ABC:

SecC = AC/BC

CotA = AB/BC

Given

AB = 7 and (AC – BC) = 1

Let BC = x

AC = x + 1

Since ABC is the right-angle triangle at B:

AC2 = AB2 + BC2

⇒ (x + 1)2 = x2 + 72

⇒ x2 + 1 + 2x = x2 + 49

⇒ 2x = 48

⇒ x = 24

Hence, BC = 24 and AC = 25

Now in triangle ABC:

(SecC + CotA)

= 25/24 + 7/24

= 4/3