SarkariPYQ

SSC CHSL 2021 PYQ — Question 74

SSC CHSL - 12 April 2021 - Shift 3 • Quantitative Aptitude • Q74

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Comprehension:
In the following passage, some words have been deleted. Select the most appropriate option
to fill in each blank.
In the 19th century, there was an industrial revolution in Europe. As a result, millions of people
left the (1) ______ and went to work in big factories in cities. Today, it is the reverse. In several
major cities, people have started moving out. Why? They want a cleaner, (2) ______
environment. There are fewer jobs in ‘heavy’ industries like steel and power generation. (3)
______, there are more jobs in service industries like banking, tourism and food delivery.
Besides, modern transport and communications have made it easier for people to (4) ______
to work or even work from home. The result of this revolution in the 21st century will be
‘spread cities’ – cities are growing fast, but (5) ______, away from city centres and people are
choosing to live 40, 50 or 60 kilometres away.

2 cosθ + secθ - 2√2 = 0, where θ is an acute angle. Find the value of θ.

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Correct answer: A

Explanation

The correct answer in option 1 i.e. 45º

2 cos θ + sec θ - 2√2 = 0

⇒ 2 cos θ + 1/ cos θ - 2√2 = 0

⇒ 2 cos2 θ + 1 - 2√2 cos θ = 0

⇒ 2 cos2 θ - 2√2 cos θ + 1 = 0

⇒ 2 cos2 θ - √2 cos θ - √2 cos θ + 1 = 0

⇒ √2 cos θ (√2 cos θ - 1) - 1(√2 cos θ - 1) = 0

⇒ (√2 cos θ - 1)2 = 0

⇒ √2 cos θ - 1 = 0

⇒ √2 cos θ = 1 

⇒ cos θ = 1/√2 

∴ cos 45° = 1/√2 

⇒ θ = 45°