Q33 / 83 · NTA Abhyas (JEE Main) 2020 · Mathematics · Trigonometric Equations

The number of ordered pairs $(x, y)$ satisfying the equations $y = 2 \sin x a n d y = 5 x^{2} + 2 x + 3$ is/are

Correct answer
A
$0$
B
$1$
C
$2$
D
Infinite

Solution

2 \sin x = 5 x^{2} + 2 x + 3

\Rightarrow 2 \sin x = 4 x^{2} + {(x + 1)}^{2} + 2

But,

2 \sin x \leq 2

and

4 x^{2} + {(x + 1)}^{2} + 2 > 2

, so it has no solution

Hence, the correct answer is option: 'A'.

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