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UPSC NDA I and II 2020 Math Solved Paper

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Question : 11 of 120

Marks: +1, -0

The value of ordinate of the graph of

+ cos x lies in the interval

[0, 1]
[0, 3]
$[-1, 1]$
[1, 3]

Solution:

Concept:

The range of

\cos x

is

[-1, 1]

.

Explanation:

Given

y = 2 + \cos x

.

We know

\cos x

has minimum

-1

and maximum

1

.

Add

2

to both bounds:

2 + (-1) = 1

and

2 + 1 = 3

.

Thus

y

ranges from

1

to

3

, inclusive.

Hence the ordinate (y-coordinate) lies in the interval

[1, 3]

.

Answer:

[1, 3]

(Option D).

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